Visualizing Nodal Heavy Fermion Superconductivity

(From Left to Right) Brian Zhou, Shashank Misra, and Ali Yazdani

Authors: Brian Zhou, Shashank Misra, and Ali Yazdani

Affiliation: Joseph Henry Laboratories and Department of Physics, Princeton University, USA

Link to Yazdani Lab >>

Superconductors, broadly speaking, can be divided into two classes by how its electrons bind together to form the “Cooper pairs” that sustain dissipation-less current flow. The first class of “conventional” superconductors contains all of the metallic superconductors, such as mercury, lead, or niobium. Here the attractive potential, or pairing symmetry (represented by a circle in Fig. 1a), of the Cooper pair is equally strong for all electrons, and transition temperature T_c at which superconductivity emerges is limited to at most 30 K, only one tenth of room temperature. The second class of “unconventional”, or extraordinary, superconductors behave much differently – and strikingly can possess transition temperatures in excess of 150 K, half of room temperature. The pairing potential (represented by a four-leaf clover in Fig. 1b) now depends sensitively on the direction of the electron’s momentum, with certain directions (called nodes) having zero pairing strength.

Fig.1 a) Representation of the pairing symmetry of a conventional superconductor by a circle. The paring amplitude is isotropic in direction. b) Representation of the pairing symmetry for an unconventional (d_x²-y²) superconductor by a clover shape. The pairing amplitude is zero for certain directions called the nodes, depicted by the dashed lines.

Heavy fermion materials, whose electrons behave as if they have greatly enhanced mass due to strong interactions between them, belong to this unconventional class of superconductors that also includes the widely known high-T_c copper-oxide “cuprate” superconductors. Intense research effort has determined the pairing symmetry of the cuprate superconductors to be of d_x²-y² form (clover leaves separated by nodes occurring diagonal to the axis); however, an understanding of its mechanism and the precise cause of their high transition temperatures remain elusive [1]. Heavy fermions, such as CeCoIn₅, have been suggested to share the same paring symmetry, and thus possibly the same underlying mechanism, as the cuprate superconductors [2]. Nevertheless, the superconducting phase of heavy fermions has largely dodged the same intense experimental spotlight, as their low transition temperatures preclude access by conventional experimental tools such as photoemission (ARPES) and, until recently, scanning tunneling microscopy (STM) [3, 4].

To probe superconductivity in the prototypical heavy fermion CeCoIn₅, synthesized by our collaborators at Los Alamos National Laboratory, we developed a new state-of-the-art STM operating at dilution-fridge temperature and high magnetic field. Like the high-T_c cuprates, superconductivity in CeCoIn₅ emerges in close proximity to an anti-ferromagnetic critical point and out of a normal state showing strong non-Fermi liquid behavior [5]. Accordingly, angle-resolved thermal transport and neutron scattering experiments [6, 7] have shown data consistent with a d_x²-y² gap symmetry; however, until our experiment, no phase sensitive identification has been performed. Unlike the high-T_c cuprates and more favorable to experiment, unconventional superconductivity occurs in the undoped, and thus ultra-clean, sample of CeCoIn₅ and can be extinguished here by an experimentally-accessible magnetic field (5 T perpendicular to the c-axis).

STM can probe the pairing symmetry of an unconventional superconductor through two ways: 1) studying the surface electron waves caused by the interference of quasiparticles scattering off impurities, or 2) studying the bound state formed by a pair-breaking impurity. Our research is the first to perform this comprehensive set of experiments on superconducting CeCoIn₅, reaching a temperature of 245 mK, well below CeCoIn₅’s Tc of 2.3 K. To isolate the salient effects of superconductivity, we in fact conducted each experiment first at zero magnetic field, where superconductivity is strongest, and then repeated each experiment again at 5.7 T, where superconductivity is extinguished. The quasi-particle interference (QPI) patterns reveal heavy bands (m* ~ 25 m₀) in the normal state that rapidly close within ~10 mV above the Fermi level (see Fig. 2). These heavy bands develop significant changes with the onset of superconductivity; however, the particular fashion in which these changes occur in our data cannot be explained by the simplest (electron-hole symmetric) model of QPI that has previously been applied to the cuprate superconductors. This is unsurprising because the Fermi surface of CeCoIn₅ possesses multiple bands with complicated shapes, in contrast to the typical single circular hole barrel of the cuprate Fermi surface. Consequently, conclusions drawn from the superconducting QPI would require a large number of assumptions that cannot be independently justified.

Fig. 2 a) Electron waves formed by the interference of heavy electrons on the surface of CeCoIn₅. b) The discrete Fourier transform of the real space conductance map in a) gives information on the wavelength and direction of the waves seen in the image. By performing these measurements as a function of energy, we determine the relation between energy and momentum of the heavy electrons that pair together to produce superconductivity, showing them to behave with effective masses up to 30 times the bare electron mass.

While the QPI in CeCoIn₅ could not provide an unambiguous result, the spatial distribution of an impurity bound state fortuitously revealed a direct nanoscale fingerprint of the superconducting gap symmetry. Excitations in a superconductor are so called Boguliubov quasiparticles, which are mixtures of electrons and holes in the Fermi sea. The spectrum in Fig 3a, with enhancement at positive bias, shows an impurity attractive to the electron part of the Boguliubov quasiparticle. This electron-like component leaks out away from the impurity along the minima of pairing potential, thereby pinpointing the nodes to occur at diagonal to the crystal axis in d_x²-y² form [8,9]. We can further confirm the identity of this signal by imaging the hole component of the same impurity state, showing it to be spatially complementary to the electron component as is expected for superconducting pairing. As a final check of its superconducting origin, this bound state disappears when superconductivity is extinguished.

Fig. 3 An impurity in an unconventional superconductor locally disturbs the Cooper pairs of the electron sea. In a), we determine that this particular impurity attracts the electron component of the Cooper pair as its spectrum shows an enhancement at positive energies relative to the spectrum far away from it. The characteristic energy-dependent spatial patterns of how this impurity locally perturbs superconductivity (shown for negative and positive energy in b) and c), respectively) directly reveal the symmetry of unconventional Cooper pairing in this compound.

Our research on CeCoIn₅ firmly establish its pairing symmetry to parallel that of the high-T_c cuprate superconductors and extend for the first time the power of the STM to another class of extraordinary superconductors, the heavy fermions. In fact, the parallel to the high-T_c goes even further: our spectroscopy reveals superconductivity to develop within a depression of the density of states near the Fermi level that persists above T_c and above the critical magnetic field. Could this gap have a similar origin as the peculiar normal state “pseudogap” in the cuprates? Most importantly, the ability to study CeCoIn₅ broadens the experimental tool-kit for tackling the questions of unconventional superconductivity – what role of magnetism, other competing phases, and electron-electron interaction in the normal state play in making these special superconductors the most robust of the bunch.

References:
[1] C.C Tsuei, J.R. Kirtley, "Pairing symmetry in cuprate superconductors". Review of Modern Physics, 72, 969-1016 (2000). Abstract.
[2] Joe D. Thompson and Zachary Fisk. "Progress in Heavy-Fermion Superconductivity: Ce115 and Related Materials". Journal of the Physical Society of Japan, 81, 011002 (2012). Abstract.
[3] Brian B. Zhou, Shashank Misra, Eduardo H. da Silva Neto, Pegor Aynajian, Ryan E. Baumbach, J. D. Thompson, Eric D. Bauer, Ali Yazdani. "Visualizing nodal heavy fermion superconductivity in CeCoIn₅". Nature Physics, 9, 474-479 (2013). Abstract.
[4] M. P. Allan, F. Massee, D. K. Morr, J. Van Dyke, A. W. Rost, A. P. Mackenzie, C. Petrovic, J. C. Davis. "Imaging Cooper pairing of heavy fermions in CeCoIn₅". Nature Physics, 9, 468-473 (2013). Abstract.
[5] Pegor Aynajian, Eduardo H. da Silva Neto, András Gyenis, Ryan E. Baumbach, J. D. Thompson, Zachary Fisk, Eric D. Bauer & Ali Yazdani. "Visualizing heavy fermions emerging in a quantum critical Kondo lattice". Nature, 486, 201-206 (2012). Abstract,
[6] K. Izawa, H. Yamaguchi, Yuji Matsuda, H. Shishido, R. Settai, and Y. Onuki. "Angular position of nodes in the superconducting gap of quasi-2D heavy-fermion superconductor CeCoIn₅". Physical Review Letters, 87, 057002 (2001). Abstract.
[7] C. Stock, C. Broholm, J. Hudis, H. J. Kang, and C. Petrovic. "Spin Resonance in the d-Wave Superconductor CeCoIn₅". Physical Review Letters, 100, 087001 (2008). Abstract.
[8] Stephan Haas, Kazumi Maki. "Quasiparticle bound states around impurities in d_x²-y²-wave superconductors". Physical Review Letters, 85, 2172-2175 (2000). Abstract.
[9] A.V. Balatsky, I. Vekhter, J.X. Zhu. "Impurity-induced states in conventional and unconventional superconductors". Review of Modern Physics, 78, 373-433 (2006). Abstract.

Macroscopic, Sub-Kelvin Refrigeration from Electron Tunneling

From left to right: Jason Underwood, Peter Lowell, Galen O’Neil, Joel Ullom

Authors: Peter Lowell, Galen O’Neil, Jason Underwood, Joel Ullom

Affiliation: 
National Institute of Standards and Technology, Boulder, Colorado, USA

Modern science often requires sub-Kelvin temperatures in order to observe quantum mechanical effects. Examples include quantum information studies, quantum computing and quantum sensors that can be used for measurements of radiation from microwave to gamma-ray wavelengths with unprecedented sensitivity. Cryogenic temperatures of 4K are easily reached using commercial mechanical refrigerators. The simplest method of reaching lower temperatures is by vacuum pumping on cryogenic liquids such as liquid ³He, which can reach as low as about 300mK. Achieving yet lower temperature is challenging and requires large, complex and expensive refrigerators. Our goal is to improve the availability of sub-300mK temperatures by creating simpler refrigeration techniques.

Normal metal–insulator–superconductor (NIS) tunnel junctions can be utilized for a new type of refrigeration for cooling below 300mK using quantum mechanical effects. When a voltage bias is applied to a NIS junction, it cools the electrons in a normal metal because only the hottest electrons from the normal metal can tunnel into the superconductor, which causes the electron gas remaining in the normal metal to cool down. The selective tunneling is made possible by the energy gap in the superconductor. The effect is analogous to blowing on a cup of coffee; the stream of air removes the hottest particles, which causes the coffee to cool down. The cooling power of a NIS junction is controlled by the voltage bias, so any temperature between the launch and base temperature is accessible by changing the voltage bias. Also, since individual NIS devices provide the cooling power, simply adding more junctions can increase the cooling power.

As a result of electron-phonon decoupling at sub-Kelvin temperatures, NIS refrigerators ordinarily cool the electrons, while the atomic lattice remains at roughly the same temperature. To cool the atomic lattice, we extended the normal metal containing the cold electrons onto a thin, thermally isolating membrane. Such a structure allows the NIS refrigerator to cool down the atomic lattice along with the electrons. The NIS junctions will then cool anything connected to the membrane. The downside to this technique is that the membrane is small and fragile, which makes it difficult to connect to other objects.

The ability of NIS junctions to behave as refrigerator is well known [1] but they have never been able to be used as a general refrigerator since scientists could not attach arbitrary payloads. The novel process, as described in Applied Physics Letters [2], was to make NIS refrigerators behave more like a general-purpose refrigerator, where the user can cool any arbitrary object, much like one can cool an arbitrary object inside a kitchen refrigerator. This was difficult because of the fragility of the membranes and the low cooling power of a single NIS device. To build a general-purpose refrigerator, we suspended a copper block with thin Kevlar cords to minimize stray power loads. This copper block was connected to the cooled membrane of the NIS refrigerator by tiny gold wires, which required extremely delicate microassembly to avoid breaking the fragile membrane.

Figure 1: Photograph of NIST's prototype solid-state refrigerator uses quantum physics in the square chip mounted on the green circuit board to cool the much larger copper platform (in the middle of the photo) below standard cryogenic temperatures. Other objects can also be attached to the platform for cooling.

Measurements of our refrigerator (see Figure 1) showed that over the course of about 18 hours, the copper block was cooled from 290mK to 256mK with about 700pW of cooling power at 290mK. This is the same fractional temperature reduction that is achieved by a kitchen refrigerator. One of the current refrigeration technologies used to reach sub-300mK temperatures, the dilution refrigerator, resembles a kitchen refrigerator in that it relies on compressors and pumps, which makes it complicated to use and prone to mechanical failure. In comparison, our NIS refrigerator is powered by quantum mechanics and has no moving parts. It only requires a small voltage bias to operate and can be powered off of a small battery. The simplicity of operation and relatively small size, several inches on a side, provide advantages over dilution and adiabatic demagnetization refrigerators.

Although we have demonstrated cooling a block of copper about one million times larger than the refrigerators themselves, these refrigerators aren’t quite ready for commercialization. We will improve the NIS refrigerators so they can cool from 300mK to 100mK by using more devices, and making more aggressive design choices. We can further expand the temperature range of our refrigerator using similar devices made of different materials. For example, electron coolers have demonstrated cooling from 1K to 400mK [3] and below 100mK [4] based on the same quantum mechanical principles. We can apply the same techniques to build general-purpose refrigerators based on these electron coolers. Eventually, our goal is to develop a composite, multi-stage cooler that can cool from 1K to below 100mK.

This work is supported by NASA.

References:
[1] Juha T Muhonen, Matthias Meschke and Jukka P Pekola, "Micrometre-scale refrigerators". Reports on Progress in Physics, 75, 046501 (2012). Abstract.
[2] Peter J. Lowell, Galen C. O'Neil, Jason M. Underwood, and Joel N. Ullom, "Macroscale refrigeration by nanoscale electron transport". Applied Physics Letters, 102, 082601 (2013). Abstract.
[3] O. Quaranta, P. Spathis, F. Beltram, and F. Giazotto, "Cooling electrons from 1 to 0.4 K with V-based nanorefrigerators", Applied Physics Letters, 98, 032501 (2011). Abstract.
[4] Galen C. O'Neil, Peter J. Lowell, Jason M. Underwood, and Joel N. Ullom, "Measurement and modeling of a large-area normal-metal/insulator/superconductor refrigerator with improved cooling", Physical Review B, 85, 134504 (2012). Abstract.

Nanostructuring Improves Vortex Pinning in Superconductors at Elevated Temperatures and Magnetic Fields

Photos of all authors -- ordered as the author list below, from top left to bottom right.

Authors:
R. Córdoba^1,2, T. I. Baturina^3,4, J. Sesé^1,2, A. Yu. Mironov³, J. M. De Teresa^2,5, M. R. Ibarra^1,2,5, D. A. Nasimov³, A. K. Gutakovskii³, A.V. Latyshev³, I. Guillamón^6,7, H. Suderow⁶, S.Vieira⁶, M. R. Baklanov⁸, J. J. Palacios⁹ & V.M.Vinokur⁴

Affiliation:
¹Instituto de Nanociencia de Aragón, Universidad de Zaragoza, Spain
²Departamento de Física de la Materia Condensada, Universidad de Zaragoza, Spain
³A.V. Rzhanov Institute of Semiconductor Physics SB RAS, Novosibirsk, Russia
⁴Materials Science Division, Argonne National Laboratory, Illinois, USA
⁵Instituto de Ciencia de Materiales de Aragón, Universidad de Zaragoza-CSIC, Facultad de Ciencias, Spain
⁶Laboratorio de Bajas Temperaturas, Departamento de F´ısica de la Materia Condensada, Instituto de Ciencia de Materiales Nicol´as Cabrera, Facultad de Ciencias, Universidad Autónoma de Madrid, Spain
⁷H.H. Wills Physics Laboratory, University of Bristol, United Kingdom
⁸IMEC, Leuven, Belgium
⁹Departamento de Física de la Materia Condensada, Instituto de Ciencia de Materiales Nicolás Cabrera, Facultad de Ciencias, Universidad Autónoma de Madrid, Spain

Corresponding author: Hermann.suderow@uam.es

A recent collaboration of the US, Russian and Spanish researchers finds a new method to improve current carrying capability of superconductors. Usually, superconducting vortices induced by the magnetic field move under the applied current and dissipate the energy degrading thus the ability of superconductors to carry electrical current with zero resistance. To recover superconductivity one has to pin vortices down stopping their motion[1]. However all pinning mechanisms known so far become inefficient at technologically important temperatures and magnetic fields, and this constitutes the major problem restricting applications of superconductivity[2,3,4]. The international team demonstrates the method to immobilize vortices at elevated temperatures and magnetic fields, reversing the deleterious effect of vortex motion as the applied magnetic field is increased[5].

Figure 1: Resistance as a function of the magnetic field in perforated nanostructures.

To achieve this, the authors have carved patterns in superconductors using advanced nanofabrication tools. They have revealed geometrical structures, which impede vortex motion just when it is most harmful for applications, at high magnetic fields and temperatures. The work provides a new avenue for research on blocking vortex motion using nano-patterns[7,8]. The science involved brings new concepts to light: vortices confined on a row dig for themselves a deep potential well which suppresses their capability to move. Being tightly squeezed together vortices join into large clusters so that even the combined action of temperature and current fails to destroy them and move vortices. The result is truly surprising: the resistance drops down when increasing the magnetic field, even if temperature is high and close to the critical one, and remains zero over a broad range. It is exactly opposite to what the conventional wisdom in superconductors would have expected.

Figure 2: Magnetic field dependence of the resistance in a nanowire with a single vortex row.

The to-do list of researchers includes now imaging these immobile clusters and developing a quantitative theory of the effect in order to achieve complete understanding and fully utilize the potential technological promise of their discovery. One of the directions of the future work is the extension of the novel approach to pinning to other materials including high-temperature superconductors[4], where nanopatterning is expected to bring a dramatic improvement of their performance[8]. For example, while many researchers are optimistic about synthesizing the room temperature superconductors, they remain skeptical about their usefulness for applications, since at elevated temperatures mobile vortices would anyway destroy the ability of superconductors to carry current without resistance. The novel approach developed by the team promises to meet this challenge of pinning vortices at high temperatures thus breaking ground for ‘quantum leap’ of superconducting materials into industrial and technological applications.

Figure 3: Perforated superconducting thin film.

References:
[1] P.W. Anderson & Y.B. Kim. "Hard superconductivity-theory of motion of Abrikosov flux lines". Review of Modern Physics, 36, 39-43 (1964). Abstract.
[2] V.V. Moshchalkov, R. Wördenweber and W. Lang, "Nanoscience and engineering in superconductivity" [Springer, ISBN: 9783642151361, 2010].
[3] A.M. Campbell & J.E. Ivetts, "Critical Currents in Superconductors - Monographs on Physics" [Taylor & Francis Ltd., London, 1972].
[4] David Larbalestier, Alex Gurevich, D. Matthew Feldmann & Anatoly Polyanskii. "High-Tc superconducting materials for electric power applications". Nature 414, 368-377 (2001). Abstract.
[5] R. Córdoba, T.I. Baturina, J. Sesé, A. Yu. Mironov, J.M. De Teresa, M.R. Ibarra, D.A. Nasimov, A.K. Gutakovskii, A.V. Latyshev, I. Guillamón, H. Suderow, S. Vieira, M.R. Baklanov, J.J. Palacios and V.M. Vinokur. "Magnetic field-induced dissipation-free state in superconducting nanostructures". Nature Communications, 4, 1437 (2013). Abstract.
[6] M. Baert, V. V. Metlushko, R. Jonckheere, V. V. Moshchalkov, and Y. Bruynseraede. "Composite flux-line lattices stabilized in superconducting films by a regular array of artificial defects". Physical Review Letters, 74, 3269-3272 (1995). Abstract.
[7] J. I. Martín, M. Vélez, A. Hoffmann, Ivan K. Schuller, J. L. Vicent, "Temperature dependence and mechanisms of vortex pinning by periodic arrays of Ni dots in Nb films". Physical Review B, 62, 9110-9116 (2000). Abstract.
[8] A. Llordés, A. Palau, J. Gázquez, M. Coll, R. Vlad, A. Pomar, J. Arbiol, R. Guzmán, S. Ye, V. Rouco, F. Sandiumenge, S. Ricart, T. Puig, M. Varela, D. Chateigner, J. Vanacken, J. Gutiérrez, V. Moshchalkov, G. Deutscher, C. Magen and X. Obradors. "Nanoscale strain‐induced pair suppression as a vortexpinning mechanism in high‐temperature superconductors". Nature Materials, 11, 329 (2012). Abstract.

Evidence of Majorana States in an Al Superconductor – InAs Nanowire Device

[From left to right] Moty Heiblum, Yuval Oreg, Anindya Das, Yonathan Most, Hadas Shtrikman, Yuval Ronen

Authors: Yuval Ronen, Anindya Das, Yonatan Most, Yuval Oreg, Moty Heiblum, and Hadas Shtrikman

Affiliation: Dept. of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel

When a bridge between fields in physics is created, exciting physics can emerge. In 1962 Anderson walked on a bridge connecting condensed matter physics with particle physics, by introducing the Anderson mechanism in superconductivity to explain the Meissner effect. A similar idea was used on the other side of the bridge by Higgs in 1964, to explain the mechanism that generates the mass of elementary particles known as the Higgs mechanism. Nowadays, another bridge is formed between these two fields emanating from an idea first originated by Ettore Majorana in 1937 – where spin 1/2 particles can be their own anti-particles[1]. Back then, Majorana suggested the neutrino as a possible candidate for his prediction, and experiments such as double-beta decay are planned to test his prediction.

A link between Majorana’s prediction of new elementary particles and the field of condensed matter physics was formed already more than a decade ago. Quasi-particle excitations, which are equal to their anti-quasi-particle excitations, are predicted to be found in the solid. Specifically, in vortices that live in an esoteric two-dimensional P-wave spinless superconductor. Moreover, these excitations are expected to be inherently different from their cousins the elementary particles: they have non-abelian statistics. The non-abelian statistics is one of the beautiful triumphs of the physics of condensed matter.

This so far unobserved quasi-particle, that has non-abelian statistics, has for a while been a ‘holy grail’ in the fractional quantum Hall effect regime; with filling factor 5/2 being the most promising candidate for its observation. Lately, another realization of Majorana quasi-particles is pursued. It follows a 1D toy model presented by Kitaev in 2001, showing how one can isolate two Majorana states at two widely separated ends of a 1D P-wave spinless superconductor [2]. These two Majorana states are expected to sit in the gap of the superconductor (at the Fermi energy) for a wide range of system parameters. Seven years later, Fu and Kane [3] found that a P-wave spinless superconductor can be induced by an S-wave superconductor in proximity to a topological insulator, occurring in a semiconductor with an inversion gap. It was thus not long before two theoretical groups [4,5] provided a prescription for how to turn a 1D semiconductor nanowire into an effective Kitaev 1D spinless P-wave superconductor.

The prescribed system is a semiconductor nanowire, with strong spin-orbit coupling, coupled to an S-wave superconductor (a trivial superconductor, with Cooper pairs in a singlet state). Electrons from the semiconductor undergo Andreev reflections, a process which induces S-wave superconductivity in the nanowire. The induced superconductivity opens gaps in the nanowire spectrum around the Fermi energy, at momentums k=0 and k=k_F (the Fermi momentum), due to the two spin bands being separated by spin-orbit coupling. An applied magnetic field quenches the gap at k=0 while hardly affecting the gap at k_F (the Zeeman splitting competes with superconductivity at k=0, where spin-orbit coupling, being proportional to k, plays no role), creating an effective gap different from the one induced by superconductivity. A gate voltage is used to tune the chemical potential into the effective gap. When the Zeeman energy is equal to the induced superconducting gap, the effective gap at k=0 closes; it then reopens upon further increase of the magnetic field, bringing the nanowire into a so called ‘topological phase’. Kitaev’s original toy model of a 1D P-wave superconductor is then implemented (Fig. 1).

Figure 1: Energy dispersion of the InAs nanowire excitations (Bogoliubov-de Gennes spectrum), in proximity to the Al superconductor. Heavy lines show electron-like bands and light lines show hole-like bands. Opposite spin directions are denoted in blue and magenta (red and cyan) for the spin-orbit effective field direction (perpendicular direction), where a relative mixture denotes intermediate spin directions. (a) Split electronic spin bands due to spin-orbit coupling in the InAs wire. Spin-orbit energy defined as Δ_so, with the chemical potential μ measured with respect to the spin bands crossing at p=0. (b) With the application of magnetic field, B, perpendicular to the spin-orbit effective magnetic field, B_so a Zeeman gap, E_z= gμ_BB/2, opens at p=0. (c) Light curves for the hole excitations are added, and bringing into close proximity a superconductor opens up superconducting gaps at the crossing of particle and hole curves. The overall gap is determined by the minimum between the gap at p=0 and the gap at p_F, while for μ=0 and E_z close to Δ_ind the gap at p=0 is dominant. (d) As in (c) but E_z is increased so that the gap at p_F is dominant. (e) B is rotated to a direction of 30^o with respect to B_so. The original spin-orbit bands are shifted in opposite vertical directions, and the B component, which is perpendicular to B_so is diminished. (f) The evolution of the energy gap at p=0 (dotted blue), at p_F (dotted yellow), and the overall energy gap (dashed black) with Zeeman energy, E_z, for μ=0. The overall gap is determined by the minimum of the other two, where the p=0 gap is dominant around the phase transition, which occurs at E_z=Δ_ind. At high E_z the p_F gap, which is decreasing with E_z, becomes dominant.

Seventy five years after Majorana’s monumental paper, we may be close to a realization of a quasi-particle that is identical to its anti-quasi-particle, possessing non-abelian statistics. Several experimental groups [6,7,8] follow the prescribed recipe for a 1D P-wave spinless superconductor[4,5], with our group being one of them. A zero energy conductance peak, at a finite Zeeman field, had been seen now in InSb and InAs nanowires in proximity to Nb and Al superconductors, respectively. This peak is considered a signature for the existence of a Majorana quasi-particle, since the Majorana resides at the Fermi energy.

Figure 2: Structure of the Al-InAs structures suspended above p-type silicon covered with 150nm SiO₂. (a) Type I device, the nanowire is supported by three gold pedestals, with a gold ‘normal’ contact at one edge and an aluminum superconducting contact at the center. The conductive Si substrate serves as a global gate (GG), controlling barrier as well as the chemical potential of the nanowire. Two narrow local gates (RG and LG), 50nm wide and 25nm thick, displaced from the superconducting contact by 80nm, also strongly influence the barrier height as well as the chemical potential in the wire. (b) Type II device, similar to type I device, but without the pedestal under the Al superconducting contact. This structure allows control of the chemical potential under the Al contact. (c) SEM micrograph of type II device. A voltage source, with 5 Ohm resistance, provides V_SD, and closes the circuit through the ‘cold ground’ (cold finger) in the dilution refrigerator. Gates are tuned by V_GG and V_RG to the desired conditions. Inset: High resolution TEM image (viewed from the <1120> zone axis) of a stacking faults free, wurtzite structure, InAs nanowire, grown on (011) InAs in the <111> direction. TEM image is courtesy of Ronit Popovitz-Biro. (d) An estimated potential profile along the wire. The two local gates (LG and RG) and global gate (GG) determine the shape of the potential barriers; probably affect the distance between the Majoranas.

Our work, with MBE grown InAs nanowire in proximity to an Al superconductor [8] (Fig 2), demonstrated a zero bias peak and several more interesting features in the parameters' space. First, the closing of the gap at k=0 was clearly visible when the Zeeman energy was equal to the induced gap. Second, splitting of the zero-bias-peak was observed at low and high Zeeman field; likely to result from spatial coupling of the two Majorana states. Third, the zero-bias-peak was found to be robust in a wide range of chemical potential (assumed to be within the k=0 gap). While these observations agree with the presence of a Majorana quasi-particle (though the peak height is much smaller than expected, maybe due to the finite temperature of the experiment), the available data does not exclude other effects that may result with a similar zero bias peak (such as, interference, disorder, multi-bands, Kondo correlation).

Quoting Wilczek: “Whatever the fate of these particular explorations, there is no doubt that Majorana's central idea, which long seemed peripheral, has secured a place at the core of theoretical physics"[9].

References:
[1] Ettore Majorana, "Teoria simmetrica dell’elettrone e del positrone", Il Nuovo Cimento, 171 (1937). Abstract.
[2] A. Yu. Kitaev, "Unpaired Majorana fermions in quantum wires". Physics Uspekhi, 44, 131 (2001). Full Article.
[3] Liang Fu and Charles Kane, "Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator", Physical Review Letters 100, 096407 (2008). Abstract.
[4] Roman M. Lutchyn, Jay D. Sau and Sankar Das Sarma, "Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures", Physical Review Letters, 105, 077001 (2010). Abstract.
[5] Yuval Oreg, Gil Refael, and Felix von Oppen, "Helical Liquids and Majorana Bound States in Quantum Wires", Physical Review Letters, 105, 177002 (2010). Abstract.
[6] V. Mourik, K. Zuo, S.M. Frolov, S.R. Plissard, E.P.A.M. Bakkers, L.P. Kouwenhoven, "Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices", Science 336, 1003 (2012). Abstract. 2Physics Article.
[7] M. T. Deng, C. L. Yu, G. Y. Huang, M. Larsson, P. Caroff, H. Q. Xu, "Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device", arXiv: 1204.4130 (2012).
[8] Anindya Das, Yuval Ronen, Yonathan Most, Yuval Oreg, Hadas Shtrikman, Moty Heiblum, "Zero-bias peaks and splitting in an Al–InAs nanowire topological superconductor as a signature of Majorana fermions", Nature Physics, 8, 887–895 (2012). Abstract.
[9] Frank Wilczek, "Majorana Returns", Nature Physics, 5, 614 (2009). Abstract.

Imperfections, Disorder and Quantum Coherence

Steve Rolston [Image courtesy: University of Maryland, USA]

A new experiment conducted at the Joint Quantum Institute (JQI, operated jointly by the National Institute of Standards and Technology in Gaithersburg, MD and the University of Maryland in College Park, USA) examines the relationship between quantum coherence, an important aspect of certain materials kept at low temperature, and the imperfections in those materials. These findings should be useful in forging a better understanding of disorder, and in turn in developing better quantum-based devices, such as superconducting magnets. The new results are published in the New Journal of Physics [1].

Most things in nature are imperfect at some level. Fortunately, imperfections---a departure, say, from an orderly array of atoms in a crystalline solid---are often advantageous. For example, copper wire, which carries so much of the world’s electricity, conducts much better if at least some impurity atoms are present.

In other words, a pinch of disorder is good. But there can be too much of this good thing. The issue of disorder is so important in condensed matter physics, and so difficult to understand directly, that some scientists have been trying for some years to simulate with thin vapors of cold atoms the behavior of electrons flowing through solids trillions of times more dense. With their ability to control the local forces over these atoms, physicists hope to shed light on more complicated case of solids.

That’s where the JQI experiment comes in. Specifically, Steve Rolston and his colleagues have set up an optical lattice of rubidium atoms held at temperature close to absolute zero. In such a lattice atoms in space are held in orderly proximity not by natural inter-atomic forces but by the forces exerted by an array of laser beams. These atoms, moreover, constitute a Bose Einstein condensate (BEC), a special condition in which they all belong to a single quantum state.

This is appropriate since the atoms are meant to be a proxy for the electrons flowing through a solid superconductor. In some so called high temperature superconductors (HTSC), the electrons move in planes of copper and oxygen atoms. These HTSC materials work, however, only if a fillip of impurity atoms, such as barium or yttrium, is present. Theorists have not adequately explained why this bit of disorder in the underlying material should be necessary for attaining superconductivity.

The JQI experiment has tried to supply palpable data that can illuminate the issue of disorder. In solids, atoms are a fraction of a nanometer (billionth of a meter) apart. At JQI the atoms are about a micron (a millionth of a meter) apart. Actually, the JQI atom swarm consists of a 2-dimensional disk. “Disorder” in this disk consists not of impurity atoms but of “speckle.” When a laser beam strikes a rough surface, such as a cinderblock wall, it is scattered in a haphazard pattern. This visible speckle effect is what is used to slightly disorganize the otherwise perfect arrangement of Rb atoms in the JQI sample.

In superconductors, the slight disorder in the form of impurities ensures a very orderly “coherence” of the supercurrent. That is, the electrons moving through the solid flow as a single coordinated train of waves and retain their cohesiveness even in the midst of impurity atoms.

In the rubidium vapor, analogously, the slight disorder supplied by the speckle laser ensures that the Rb atoms retain their coordinated participation in the unified (BEC) quantum wave structure. But only up to a point. If too much disorder is added---if the speckle is too large---then the quantum coherence can go away. Probing this transition numerically was the object of the JQI experiment. The setup is illustrated in figure 1.

Figure 1: Two thin planes of cold atoms are held in an optical lattice by an array of laser beams. Still another laser beam, passed through a diffusing material, adds an element of disorder to the atoms in the form of a speckle pattern. [Image courtesy: Matthew Beeler]

And how do you know when you’ve gone too far with the disorder? How do you know that quantum coherence has been lost? By making coherence visible.

The JQI scientists cleverly pry their disk-shaped gas of atoms into two parallel sheets, looking like two thin crepes, one on top of each other. Thereafter, if all the laser beams are turned off, the two planes will collide like miniature galaxies. If the atoms were in a coherent condition, their collision will result in a crisp interference pattern showing up on a video screen as a series of high-contrast dark and light stripes.

If, however, the imposed disorder had been too high, resulting in a loss of coherence among the atoms, then the interference pattern will be washed out. Figure 2 shows this effect at work. Frames b and c respectively show what happens when the degree of disorder is just right and when it is too much.

Figure 2: Interference patterns resulting when the two planes of atoms are allowed to collide. In (b) the amount of disorder is just right and the pattern is crisp. In (c) too much disorder has begun to wash out the pattern. In (a) the pattern is complicated by the presence of vortices in the among the atoms, vortices which are hard to see in this image taken from the side. [Image courtesy: Matthew Beeler]

“Disorder figures in about half of all condensed matter physics,” says Steve Rolston. “What we’re doing is mimicking the movement of electrons in 3-dimensional solids using cold atoms in a 2-dimensional gas. Since there don’t seem to be any theoretical predictions to help us understand what we’re seeing we’ve moved into new experimental territory.”

Where does the JQI work go next? Well, in figure 2a you can see that the interference pattern is still visible but somewhat garbled. That arises from the fact that for this amount of disorder several vortices---miniature whirlpools of atoms---have sprouted within the gas. Exactly such vortices among electrons emerge in superconductivity, limiting their ability to maintain a coherent state.

Another of the JQI scientists, Matthew Beeler, underscores the importance of understanding the transition from the coherent state to incoherent state owing to the fluctuations introduced by disorder: “This paper is the first direct observation of disorder causing these phase fluctuations. To the extent that our system of cold atoms is like a HTSC superconductor, this is a direct connection between disorder and a mechanism which drives the system from superconductor to insulator.”

Reference:
[1] M C Beeler, M E W Reed, T Hong, and S L Rolston, "Disorder-driven loss of phase coherence in a quasi-2D cold atom system", New Journal of Physics, 14, 073024 doi:10.1088/1367-2630/14/7/073024 (2012). Abstract. Full Article.

Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices

Authors: Vincent Mourik¹, Kun Zuo¹, Sergey Frolov¹, Sébastien Plissard², Erik Bakkers^1,2, Leo Kouwenhoven¹

Affiliation:
¹Kavli Institute of Nanoscience, Delft University of Technology, Netherlands.
²Dept of Applied Physics, Eindhoven University of Technology, Netherlands.

Particle Predictors:
Paul Dirac was the very first particle predictor. In 1927, Dirac developed a formula that linked two new theories: Einstein’s special theory of relativity and quantum mechanics. Dirac’s equation, however, had several solutions. The first solution described the familiar electron: a particle with a negative charge holding a certain amount of positive energy. Another solution actually constituted its very opposite: a positively charged particle holding a certain amount of negative energy. Rather than ignoring the contradiction raised by his additional solution, Dirac surmised that there must be a particle in nature with a positive electrical charge and negative energy [1]. This particle therefore has properties that would exactly mirror the properties of an electron. Several years later, this particle was indeed found, and was named positron. Together, the electron and the positron form a particle and antiparticle pair.

A pure genius, Paul Dirac was utterly convinced of the veracity of his formula. If his equation offered a certain solution, then a corresponding particle simply had to exist in nature. Since that time, numerous other particles have been predicted and identified this way. For example, the ongoing search for the Higgs boson is set up just like that, based on a prediction from the Standard Model.

Ettore Majorana was a physicist and a contemporary of Dirac. Majorana had an enigmatic biography that formed the topic of many books and films in Italy. At some point in the 1930s, Majorana was playing around with Dirac’s equation and after slightly modifying it he found a new solution: a particle that is identical to its antiparticle. And something can only be identical to its counterpart if it has properties that are all zero. Ettore Majorana, too, had a firm belief in formulas and in 1937 he published a paper [2] predicting his new particle, which has since become known as the Majorana fermion.

For decades the Majorana particle received little attention, but in the 1970s the search began afresh. Using large accelerators and detectors, scientists started hunting for neutrino particles with Majorana properties. Indeed, these elementary Majorana particles might even solve the mystery of dark matter that fills our Universe. So far, the elementary Majorana particles have remained elusive, but this important quest is still being pursued by CERN in Geneva.

Particle Creators:

In addition to elementary particles, composite or collective particles (see box) also exist in the world of condensed matter physics. We know of heat particles (phonons), electron density waves (plasmons), magnetic waves (magnons) and a long list of other collective particles. These collective particles are particularly convenient for making the physics of materials a lot simpler. Materials hold a distinct place in physics because by combining materials we can create objects that did not exist before. Technology, for instance, abounds with remarkable material combinations, such as silicon and silicon oxide forming the backbone of electronics. But material combinations can also be used in fundamental physics to create something new. This prompted a number of theoretical physicists to reflect on whether we could combine materials in such a way that the collective particles inside them will acquire the properties of Majorana fermions.

The one-dimensional lattice proposed by Alexei Kitaev in 2001 was still highly mathematical and abstract [3]. A number of propositions then followed based on (p-wave superconducting) materials that did not yet exist. In 2008, Liang Fu and Charles Kane’s theory [4] was the first to be based on existing materials, but was still difficult to put into practice. The year 2010 saw the publication, in Physical Review Letters of two similar theories by two groups of theorists, independently of each other, which for the first time looked feasible in practice. One of the publications [5] came from theorists at the University of Maryland (Roman Lutchyn, Jay Sau and Sankar Das Sarma); the other [6] was a collaborative effort between theorists at the Weizmann Institute in Israel, California Institute of Technology of USA and the Free University of Berlin in Germany (Yuval Oreg, Gil Rafael and Felix von Oppen). The importance of the aforementioned theoretical developments was that it shifted the focus from what is found in nature to the artificial creation of Majorana particles.

Prior knowledge: there are particles and then there are particles…

If you blow into your hand, what you will primarily feel are oxygen and nitrogen molecules. Those molecules are minute, subnanometer-scale particles that are composed, in this case, of two atoms each. In turn, each atom is made up of an atomic nucleus encircled by electrons. The electrons cannot be divided into smaller particles - they are ‘elementary’ particles. However, the protons and neutrons inside the nucleus can be shattered to create even smaller particles. This shattering process is generated in accelerators such as the one at CERN in Geneva, where the search for the Higgs particle continues unabated. Other popular particles are the neutrinos (which for a short period were believed to travel even faster than light) and the Majorana fermions. These Majorana fermions have not yet been found at CERN.The Majorana fermions may well be the key to explaining the dark matter mystery. In the universe, there is five times as much dark matter as ordinary matter, and so Majorana fermions could be the most widespread particles in the universe.

CERN are engaged in the study of fundamental particles. Each of these particles are smaller than the smallest atom, hydrogen. Our world of matter is based on atoms and clusters of atoms that form molecules. The glue that binds these atoms to molecules is described by quantum mechanics. Our bodies, for instance, are chemical factories in which atoms are stuck together with quantum glue. Apart from complex biological materials, there are also crystals that frequently hold the same atoms stacked inside a grid. Even the smallest materials may contain large numbers of atoms. For example, a nanowire with a diameter of 100 nm and a length of 1000 nm (1000 nm = 1 micrometer) alone contains some 10 billion atoms.

Next to fundamental particles and atoms there are also collective particles. The ‘wave’ in a stadium is a good example. The ‘wave’ is simply a group of spectators jumping up and down to create a wave. If we wanted to describe this wave in mathematical terms, we might do that by including everyone in a large formula. Then again, we could also approach it more simply by forgetting about all those individuals and only describe their collective behavior, that is, the wave. And for simplicity’s sake we could call the ‘wave’ a particle, in this case, a collective particle. This reduction to collective particles simplifies matters enormously and is often highly successful. An example: heat in a material is not described in terms of a bunch of vibrating atoms but, far more easily, as heat particles that are known as phonons.

You may think that ‘collective particles’ is a rather imprecise way of describing what actually happens. This may be true of the wave but phonons, for example, can in fact provide us with a very exact, realistic description. What is perhaps the most surprising fact is that collective particles can actually behave in accordance with the laws of quantum mechanics. A phonon can find itself in the superposition of both hot and cold. Such a quantum superposition may sound absurd enough for elementary particles, but is really stretching our imagination where collective particles are concerned.

The Majorana fermions in crystals are not only interesting from a fundamental viewpoint, but also have unique properties that can be used to build a quantum computer. Field medalist Michael Freedman works at Microsoft and has been carrying out active research into topological quantum computers with a team of scientists since 2005. This computer works by moving Majorana particles around each other and forming space-time braids.

The proposals put forward by Lutchyn et al [5] and Oreg et al [6] are both based on bringing semiconducting nanowires into contact with a superconducting material. We had already successfully accomplished this combination in Delft, which resulted in publications in Science (2005) and Nature (2006). Combining these specific materials suddenly made us the experimental specialists in the search for Majorana fermions.

Note that the Majorana quest had already been described at an early stage in the journal 'Science' [7].

Majorana in Delft:

How do you create a Majorana fermion? Based on the condition that the particle is identical to its antiparticle, you can do some reverse engineering. It cannot, for instance, have an electrical charge, nor have energy or spin. The theoretical proposals argue that those properties are created by combining materials consisting of a superconductor with a special semiconductor that has strong spin-orbit coupling. This semiconductor should take the form of a one-dimensional nanowire. If a magnetic field is also applied, the Majorana fermion should appear at low temperatures, just above absolute zero temperature. We combined these materials on a microchip. We developed InSb (Indium Antimonide) nanowires for the semiconductor. InSb has strong spin-orbit coupling. We used a Nb alloy as a superconductor. This material will retain its superconductive properties also in the presence of an external magnetic field. For this material we were granted permission to use the technology available in Teun Klapwijk’s group in Delft. Using nanotechnology, we produced an electronic chip that, admittedly, looks rather messy (top right). Zooming down to sub-micrometre scale, we can see the nanowire thread and the electrical contacts (below right).

In this device, the superconductor is larger than the semiconductor. The diameter of the nanowire is so small that it actually becomes a one-dimensional conductor. A portion of the superconductor is covering the nanowire, which causes the superconductivity to leak into the semiconductor, effectively creating a one-dimensional superconductor. These do not exist in nature but can be induced this way. The strong spin-orbit coupling in the InSb nanowire makes this one-dimensional superconductor particularly unique. It has a so-called p-symmetry, which again has also not been found in nature. This p-superconductor extends across the entire section where the nanowire is in contact with the superconductor. At the end points, where the p-superconductor ends, two Majorana fermions appear, one on each end point.

Image: The microchip used with three different Majorana devices. This chip is cooled down to almost absolute zero point (-273 degrees Celsius). The electrical wires are connected to measuring equipment at room temperature.
 
We can measure the Majorana fermions in the electrical conductivity. From the gold contact we send electrons into the nanowire, towards the lower Majorana fermion. Only when we send electrons inside with precisely zero energy can we measure a current. If we add voltage to the electrons to energise them further, they are reflected at the p-superconductor and we measure zero conductivity. The presence of the Majorana fermion in our system is therefore visible as a conductance peak at a voltage that is precisely zero.

In the 'Science' publication [8] we also included various control experiments, which demonstrate that each single ingredient from the original theory is essential for this observation. The results can only be interpreted if we assume the presence of Majorana fermions. The article is published online on 12 April in 'Science Express' [8].

Image: The nanowire, shown vertically in this photo, is lying flat on a substrate. Hidden in the substrate are different gate electrodes (the horizontal ‘stripes’ below the nanowire and the contacts), which can change the conductivity of the nanowire. The lower electrical contact to the nanowire is madefrom gold, a normal conductor. The contact on the top is covering half of the nanowire. This is the superconductor. The total length of the nanowire is three micrometres. The anticipated positions of two Majorana fermions are indicated with red stars. 

We have since been carrying out new experiments. As the title of our article ‘Signatures of …’ suggests, we also want to demonstrate other unique properties of Majorana fermions. And our Majorana fermions are literally one of a kind. Nature has two types of particles: fermions (such as electrons, positrons, neutrons, etc.) and bosons (photons, Higgs particles, phonons, etc.). Our Majorana particles are likely to have other properties than fermions and bosons. In terms of physics, their behaviour is described by non-Abelian statistics. If we can demonstrate these statistics in our new experiments, we add a completely new chapter to the book of physics. This new round of experiments is based on a highly theoretical approach using new concepts that are not yet quite understood. To translate abstract concepts into experiments we are working with Carlo Beenakker’s theory group from Leiden. The non-Abelian statistics also make Majorana particles useful for a topological quantum computer.

References:
[1] P. A. M. Dirac, "The Quantum Theory of the Electron". Proceedings of the Royal Society of London: Series A 117, 610–624 (1928). Full Article.
[2] Ettore Majorana, "Teoria simmetrica dell’elettrone e del positrone", Il Nuovo Cimento, 171 (1937). Abstract. 
[3] A. Yu. Kitaev, "Unpaired Majorana fermions in quantum wires". Physics Uspekhi, 44, 131 (2001). Full Article. 
[4] Liang Fu and Charles Kane, "Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator", Phys. Rev. Lett. 100, 096407 (2008). Abstract.   
[5] Roman M. Lutchyn, Jay D. Sau and Sankar Das Sarma, "Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures", Physical Review Letters, 105, 077001 (2010). Abstract.
[6] Yuval Oreg, Gil Refael, and Felix von Oppen, "Helical Liquids and Majorana Bound States in Quantum Wires", Physical Review Letters, 105, 177002 (2010). Abstract.
[7] Robert F. Service, "Search for Majorana Fermions Nearing Success at Last?", Science, 332, 193 (2011). Abstract.
[8] V. Mourik, K. Zuo, S.M. Frolov, S.R. Plissard, E.P.A.M. Bakkers, L.P. Kouwenhoven, "Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices", Science Express, DOI: 10.1126/science.1222360 (Published Online April 12 2012). Abstract.

Unveiling the Unconventional Pairing in Iron-based Superconductor: Direct Observation of the Nodal Gap Structure in Ferropnictide Superconductor

Yan Zhang (left) and Zirong Ye (right), leading authors of the Nature Physics paper





Authors: Yan Zhang, Dong-Lai Feng

Affiliation: State Key Laboratory of Surface Physics, Advanced Materials Laboratory, and Department of Physics, Fudan University, Shanghai 200433, China

Link to Feng Group: Research Group of Complex Quantum Systems >>

Pairing symmetry is a pivotal characteristic of a superconductor. In the conventional BCS superconductors, the formation of Cooper pairs is due to the attractive interaction between electrons mediated by the electron-phonon interaction. Such pairing interaction results in an isotropic s-wave pairing symmetry, which is manifested as finite-sized energy gap called superconducting gap in single particle excitations throughout the entire Fermi surface. However, for many unconventional superconductors, since Coulomb repulsive interaction between electrons is often rather strong, Cooper pairs favor a non-zero angular momentum to minimize the total energy. For example, the cuprate high temperature superconductors take the d-wave pairing symmetry, which would cause superconducting gap diminishes at certain locations called nodes on the Fermi surface. Such gap nodes will have significant effects on the low temperature properties.

Four years after the discovery of the iron-based superconductors in 2008, the mechanism of this new class of high temperature superconductors is still under debate, because of their diversified structure, composition, and electronic structure. Scientists are still struggling to construct a unified picture for the basic phenomenology of different iron-based superconductors. One central issue is the exact nature of the superconducting gap. For example, in the superconducting state, some iron-based superconductors, such as Ba_1-xKFe₂As₂, BaFe_2-xCo_xAs₂, K_xFe_2-ySe₂, FeTe_1-xSe_x, etc., exhibit a nodeless behavior [1, 2], while others like LaOFeP, LiFeP, KFe₂As₂, BaFe₂(As_1-xP_x)₂, BaFe_2-xRu_xAs₂, and FeSe exhibit a nodal behavior with zero energy excitations [2].

This discrepancy on superconducting gap raises serious challenges, questions and debates. For example, one could ask whether the nodal behavior is due to d-wave pairing; and if so, why there are two types pairing symmetries or mechanisms in iron-based superconductors? Many theories have been proposed to address these fundamental questions, but no consensus has been reached. The main obstacle is that all the previous measurements do not provide detailed information of the gap structure in the momentum space, and are somewhat indirect. We have no knowledge on the location of the nodes, as to which band does it belong, and where is it in the Brillouin zone, etc.

Figure 1. (a) The three-dimensional Fermi surface of BaFe₂(As_0.7P_0.3)₂. (b) k_z dependence of the symmetrized spectra measured on the α hole FSs. (c) The superconducting gaps on the α FSs as a function of k_z.

Recently, these mysteries regarding the nature of the superconducting gap in iron-based superconductors have been resolved by our angle resolved photoemission spectroscopy (ARPES) study [3]. We have successfully determined the nodal gap structure of BaFe₂(As_1-xP_x)₂, which is a prototypical iron-based superconductor with nodal behaviors established by many transport studies. As shown in Fig. 1a, the Fermi surface of BaFe₂(As_0.7P_0.3)₂ consists of three hole Fermi surface sheets (FSs) (α, β and γ) surrounding the central Γ–Z axis of the Brillouin zone, and two electron FSs (δ and η) around the corner. Detailed survey on the electron FSs found a nodeless superconducting gap with little k_z dependence. However, for the α hole FSs, the experimental data clearly showed a zero superconducting gap or nodes located around the Z point (Fig. 1b and 1c).
























Figure 2. False-color plots of the gap distribution on the Fermi surface of BaFe₂(As_0.7P_0.3)₂.

The gap distribution of BaFe₂(As_0.7P_0.3)₂ is summarized in Fig. 2. The node is located on a ring around Z, which immediately rules out the d-wave pairing symmetry, since it would give four vertical line nodes in the diagonal directions (θ = ± 45°, ± 135°) as in the cuprates. The horizontal ring node around Z is not forced by symmetry, as it is fully symmetric with respect to the point group. Therefore, the node is an “accidental” one under the s-wave pairing symmetry, which is likely induced by the strong three-dimensional nature of the α band, and its sizable d_3z2−r2 orbital character near Z. This finding provides a general explanation as to why the gap is nodal for certain compounds and nodeless for others, and thus helps build a universal picture of the pairing symmetry in iron-based superconductors.

References:
[1] Y. Zhang, L. X. Yang, M. Xu, Z. R. Ye, F. Chen, C. He, H. C. Xu, J. Jiang, B. P. Xie, J. J. Ying, X. F. Wang, X. H. Chen, J. P. Hu, M. Matsunami, S. Kimura, and D. L. Feng, "Nodeless superconducting gap in A_xFe₂Se₂ (A=K,Cs) revealed by angle-resolved photoemission spectroscopy". Nature Materials, 10, 273–277 (2011). Abstract.
[2] J. Hirschfeld, M. M. Korshunov, and I. I. Mazin, "Gap symmetry and structure of Fe-based superconductors". Reports on Progress in Physics, 74, 124508 (2011). Abstract.
[3] Y. Zhang, Z. R. Ye, Q. Q. Ge, F. Chen, Juan Jiang, M. Xu, B. P. Xie and D. L. Feng, "Nodal superconducting-gap structure in ferropnictide superconductor BaFe₂(As_0.7P_0.3)₂". Nature Physics, doi:10.1038/nphys2248 (Published online Mar 04, 2012). Abstract.

Iron-Based Superconductor at Highest Known Temperature for a Material in Its Class

Jeffrey W. Lynn of NIST Center for Neutron Research (left) and Johnpierre Paglione of Center for Nanophysics and Advanced Materials, University of Maryland (right)

The interplay between structural, magnetic and superconducting properties in the newly discovered iron-based superconducting compounds has been a central theme in attempts to elucidate the nature of Cooper pairing in this new family of high-temperature superconductors. Now, a team from the National Institute of Standards and Technology (NIST) and the University of Maryland has found an iron-based superconductor that operates at the highest known temperature for a material in its class [1]. The discovery inches iron-based superconductors—valued for their ease of manufacturability and other properties—closer to being useful in many practical applications.

Iron-based superconductors, which were discovered only about four years ago, are a hot research topic, in part because they are more amenable to commercial applications than copper-based superconductors, which are more difficult to make and are frequently brittle. Of the four broad classes of iron-based superconductors, the 1:2:2 class—so named because their crystals are built around a hub of one atom of calcium, two of iron and two of arsenic—is particularly promising because these superconductors’ properties can be custom-tailored by substituting other atoms for these basic elements.

Magnets made with low-temperature superconductors have already found use in hospital MRI machines, but less expensive MRI machines and other applications, such as superconducting cables for resistance-free power transmission over long distances, become closer to reality the more choices manufacturers have among superconductors.

Working at the NIST Center for Neutron Research (NCNR) and the University of Maryland, the team found that a particular type of 1:2:2 superconductor possesses some unexpected properties. Of perhaps greatest value to manufacturers is that its threshold temperature of superconductivity is 47 degrees Kelvin, the highest yet for the 1:2:2 class, whose previous record was 38K.

[Image credit: NIST] When calcium atoms (yellow spheres) in these iron-based crystals (left) are replaced on some occasions with praseodymium (blue sphere in right image), the crystals are able to superconduct at up to 47K - but the crystals can also collapse, shrinking by about 10 percent in size. Adding a sufficient amount of praseodymium is necessary to avoid the collapse, which compromises the materials usability in electronics applications.

But the crystal also has a highly curious property: It can superconduct at this record temperature when a smaller atom is substituted for the crystal’s original calcium in some of its hubs, and when this substitution is performed, the overall crystal actually shrinks by about 10 percent, a dramatic size change. “It’s almost like what would happen if you cut off a few inches from the bottom of your chair’s legs,” says the NCNR’s Jeff Lynn. “The crystal just collapses. The change is quite visible in neutron scans.”

This effect is likely one that manufacturers will want to avoid. But Lynn says the group’s research has determined how to make the substitution while eluding the collapsed state altogether, so that as it is cooled, the potential mechanical instabilities associated with the collapse are sidestepped. “This understanding should enable manufacturers to use the superconductor in electronic devices,” he says.

Reference:
[1] S.R. Saha, N.P. Butch, T. Drye, J. Magill, S. Ziemak, K. Kirshenbaum, P.Y. Zavalij, J.W. Lynn and J. Paglione. "Structural collapse and superconductivity in rare-earth-doped CaFe₂As₂". Physical Review B, vol. 85, pp 024525 (2012). Abstract. ArXiv:1105.4798.

“Dressing” Atoms with Laser Allows High Angular Momentum Scattering : Could Reveal Ways to Observe Majorana Fermions

Ian Spielman (photo courtesy: Joint Quantum Institute, USA)

Scientists at the Joint Quantum Institute (JQI, a collaborative enterprise of the 'National Institute of Standards and Technology' and the University of Maryland) have for the first time engineered and detected the presence of high angular momentum collisions between atoms at temperatures close to absolute zero. Previous experiments with ultracold atoms featured essentially head-on collisions. The JQI experiment, by contrast, is able to create more complicated collisions between atoms using only lasers that dramatically influences their interactions in specific ways.

Such light-tweaked atoms can be used as proxies to study important phenomena that would be difficult or impossible to study in other contexts. Their most recent work, appearing in Science [1] demonstrates a new class of interactions thought to be important to the physics of superconductors that could be used for quantum computation.

Particle interactions are fundamental to physics, determining, for example, how magnetic materials and high temperature superconductors work. Learning more about these interactions or creating new “effective” interactions will help scientists design materials with specific magnetic or superconducting properties.Because most materials are complicated systems, it is difficult to study or engineer the interactions between the constituent electrons. Researchers at JQI build physically analogous systems using supercooled atoms to learn more about how materials with these properties work.

The key to the JQI approach is to alter the atoms’ environment with laser light. They “dress” rubidium atoms by bathing them in a pair of laser beams, which force the atoms to have one of three discrete values of momentum. In the JQI experiment, rubidium atoms comprise a Bose-Einstein condensate (BEC). BECs have been collided before. But the observation of high-angular-momentum scattering at such low energies is new.

The paper in 'Science Express' [1] includes a variety of technical issues which require some explanation:

Collisons

One of the cardinal principles of quantum science is that matter must be simultaneously thought of as both particles and waves. When the temperature of a gas of atoms is lowered, the wavelike nature of the atom emerges, and the idea of position becomes fuzzier. While an atom at room temperature might spread over a hundredth of a nm, atoms at nano-kelvin temperatures have a typical wavelength of about 100 nm. This is much larger than the range of the force between atoms, only a few nm. Atoms generally collide only when they meet face to face.

However, to study certain interesting quantum phenomena, such as searching for Majorana particles---hypothetical particles that might provide a robust means of encoding quantum information---it is desirable to engineer inter-atomic collisions beyond these low-energy, head-on type. That’s what the new JQI experiment does.

Partial Waves

Scattering experiments date back to the discovery of the atomic nucleus 100 years ago, when Ernest Rutherford shot alpha particles into a foil of gold. Since then other scattering experiments have revealed a wealth of detail about atoms and sub-atomic matter such as the quark substructure of protons.

A convenient way of picturing an interaction between two particles is to view their relative approach in terms of angular momentum. Quantized angular momentum usually refers to the motion of an electron inside an atom, but it necessarily pertains also to the scattering of the two particles, which can be thought of as parts of a single quantum object.

If the value of the relative angular momentum is zero, then the scattering is designated as “s-wave” scattering. If the pair of colliding particles has one unit of angular momentum, the scattering is called p-wave scattering. Still more higher-order scattering scenarios are referred to by more letters: d-wave, f-wave, g-wave, and so on. This model is referred to as the partial waves view.

In high energy scattering, the kind at accelerators, these higher angular-momentum scattering scenarios are important and help to reveal important structure information about the particles. In atomic scattering at low temperatures, the s-wave interactions completely swamp the higher-order scattering modes. For ultralow-temperature s-wave scattering, when two atoms collide, they glance off each other (back to back) at any and all angles equally. This isotropic scattering doesn’t reveal much about the nature of the matter undergoing collision; it’s as if the colliding particles were hard spheres.

This has changed now. The JQI experiment is the first to create conditions in which d-wave and g-wave scattering modes in an ultracold experiment could be seen in otherwise long-lived systems.

Quantum Collider

Ian Spielman and his colleagues at the National Institute for Standards and Technology (NIST) chill Rb atoms to nano-kelvin temperatures. The atoms, around half a million of them, have a density about a millionth that of air at room temperature. Radiofrequency radiation places each atom into a superposition of quantum spin states. Then two (optical light) lasers impart momentum (forward-going and backward-going motion) to the atoms.

Schematic drawing of collision between two BECs (the gray blobs) that have been “dressed” by laser light (brown arrows) and an additional magnetic field (green arrow). The fuzzy halo shows where atoms have been scattered. The non-uniform projection of the scattering halo on the graph beneath shows that some of the scattering has been d-wave and g-wave [image courtesy: JQI]

If this were a particle physics experiment, we would say that these BECs-in-motion were quantum beams, beams with energies that came in multiples of the energy kick delivered by the lasers. The NIST “collider” in Gaithersburg, Maryland is very different for the CERN collider in Geneva, Switzerland. In the NIST atom trap the particles have kinetic energies of a hundred pico-electron-volts rather than the trillion-electron-volt energies used at the Large Hadron Collider.

At JQI, atoms are installed in their special momentum states, and the collisions begin. Outward scattered atoms are detected after the BEC clouds are released by the trap. If the atoms hadn’t been dressed, the collisions would have been s-wave in nature and the observed scattered atoms would have been seen uniformly around the scattering zone.

The effect of the dressing is to screen the atoms from s-wave scattering in the way analogous to that in some solid materials, where the interaction between two electrons is modified by the presence of trillions of other electrons nearby. In other words, the laser dressing effectively increased the range of the inter-atom force such that higher partial wave scattering was possible, even at the lowest energies.

In the JQI experiment, the observed scattering patterns for atoms emerging from the collisions was proof that d-wave and g-wave scattering had taken place. “The way in which the density of scattered atoms is distributed on the shell reflects the partial waves,” said Ian Spielman. “A plot of scattered-density vs. spherical polar angles would give the sort of patterns you are used to seeing for atomic orbitals. In our case, this is a sum of s-, p-, and d- waves.”

Simulating Solids Using Gases

Ultracold atomic physics experiments performed with vapors of atoms are excellent for investigating some of the strongly-interacting quantum phenomena usually considered in the context of condensed matter physics. These subjects include superconductivity, superfluids, the quantum Hall effect, and topological insulators, and some things that haven’t yet been observed, such as the “Majorana” fermions.

Several advantages come with studying these phenomena in the controlled environment of ultracold atoms. Scientists can easily manipulate the landscape in which the atoms reside using knobs that adjust laser power and frequency. For example, impurities that can plague real solids can be controlled and even removed, and because (as in this new JQI experiment) the scattering of atoms can now (with the proper “dressing”) reveal higher-partial-wave effects. This is important because the exotic quantum effects mentioned above often manifest themselves under exactly these higher angular-momentum conditions.

“Our technique is a fundamentally new method for engineering interactions, and we expect this work will stimulate new directions of research and be of broad interest within the physics community, experimental and theoretical,” said Spielman. “We are modifying the very character of the interactions, and not just the strength, by light alone.”

On To Fermions

The JQI team, including Nobel Laureate William Phillips, is truly international, with scientists originating in the United Kingdom (lead author Ross Williams), Canada (Lindsay LeBlanc), Mexico (Karina Jiménez-García), and the US (Matthew Beeler, Abigail Perry, William Phillips and Ian Spielman).

The researchers now will switch from observing bosonic atoms (with a total spin value of 1) to fermion atoms (those with a half-integral spin). Combining the boson techniques demonstrated here with ultracold fermions offers considerable promise for creating systems which are predicted to support the mysterious Majorana fermions. “A lot of people are looking for the Majorana fermion,” says lead author and JQI postdoctoral fellow Ross Williams. “It would be great if our approach helped us to be the first.”

Reference
[1] R. A. Williams, L. J. LeBlanc, K. Jiménez-García, M. C. Beeler,A. R. Perry, W. D. Phillips, I. B. Spielman, "Synthetic partial waves in ultracold atomic collisions”, Science Express, (December 7, 2011). DOI: 10.1126/science.1212652. Abstract.