A Current-Driven Single-Atom Memory

Top row: (left to right): Christian Schirm, Manuel Matt, Fabian Pauly. Bottom row (left to right): Elke Scheer, Juan Carlos Cuevas, Peter Nielaba.

Authors: Christian Schirm¹, Manuel Matt¹, Fabian Pauly¹, Juan Carlos Cuevas², Peter Nielaba¹, Elke Scheer¹

Affiliation:
¹Department of Physics, University of Konstanz, Germany.
²Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Spain.

Building functional devices at the atomic scale is a central vision of nanotechnology. Recently we demonstrated a two-state electrical switch with basically a single atom acting as moving part [1]. The switch consists of an aluminum atomic contact that is connected to electrodes at each side. Applying positive or negative currents above a certain threshold will change the state. Lower currents can be used to read out the switching status by simply measuring the resistance. This qualifies the device for future potential applications in high-density solid-state memories.

The single-atom switch was analyzed in close collaboration between experimental and theoretical physicists. Quantum mechanical transport channels of the electrical conductance served as an important link between experiment and theory. (The conductance is the inverse of the electrical resistance.) On the one hand these channels could be determined experimentally by measuring non-linear current-voltage characteristics in the superconducting state at very low temperatures [2]. On the other hand the channels could be calculated through a combination of molecular dynamics simulations, electronic structure theory, and transport theory expressed in terms of non-equilibrium Green's functions [4]. The theory enabled us to identify atomic configurations for both states of the experimentally realized switches. The comparison showed that in some cases the observed switching effect can be attributed to the geometrical rearrangement of a single atom.

Fig 1: Aluminum bridge with a 100 nm constriction, fabricated by electron beam lithography (see left panel). Due to the use of an elastic substrate, the aluminum structure can be stretched by carefully bending the sample. Since we measure the conductance continuously, we can stop the breaking procedure at a constriction narrowed to a single atom (see sketch in the right panel).

In the experiment we created an atomic contact of aluminum by the mechanically controllable break-junction technique using a lithographically fabricated bridge with a 100 nm wide constriction [3]. Fig. 1 shows a scanning electron micrograph (in false colors) of such an aluminum sample on an elastic substrate and illustrates the breaking process to reach an atomic-sized contact. Next, as shown in the graph in Fig. 2, we applied a slowly increasing electrical current and measured the conductance simultaneously. At some threshold current an electromigration process takes place, which can be observed as a jump in the conductance. The current is now decreased until the next jump is detected, then increased and so on. After some rearrangements the system may reversibly switch between two conductance states. A comparison of the conduction channel signatures verifies that these states remain exactly the same.

Fig 2: Applying a careful electromigration protocol when an atom-size contact has formed, a two-state atomic switch may develop. For this the current through the contact is increased slowly with time. When a jump in the conductance is detected, the current is reversed. After some time the system may switch reversibly between two conductance states. The inset shows the rectangular conductance-current hysteresis of a successfully generated two-level switch. The unit of conductance is G₀=2e²/h, also called the “quantum of conductance”.

In molecular dynamics simulations we performed a stretching procedure similar to the preparation of the contact in the experiment. The simulations generate realistic contact geometries and transport data as we verified by comparing experimental and theoretical conductance histograms [4,5]. Fig. 3 shows two atomic geometries as obtained in a stretching process. The calculated total conductance and individual conductance channels were in good agreement with several experimentally realized switches.

Fig 3: Molecular dynamics simulation of geometries corresponding to conductance values and channel signatures found in the experiment. The primary difference between both geometries is a relocation of the central atom and the breaking of two bonds to move from state “1” to state “0” (symbolized by the red scissors). The conductance and the individual channels are given in units of G₀.

The project demonstrates how theory and experiment can work hand in hand to advance nanotechnology. The atomic switch fulfills several technological requirements. For instance, it is relatively easy to fabricate due to the two-terminal configuration. Our work can be considered as a feasibility study of a one-bit atomic-size memory [6]. Potentially, an array of such switches can be implemented in a cross-bar architecture of solid-state memories when further technological issues, such as the stable operation at room temperature, can be solved.

References:
[1] C. Schirm, M. Matt, F. Pauly, J. C. Cuevas, P. Nielaba, E. Scheer, "A current-driven single-atom memory", Nature Nanotechnology 8, 645–648 (2013). Abstract. 
[2] E. Scheer, P. Joyez, D. Esteve, C. Urbina, M. H. Devoret, “Conduction channel transmissions of atomic-size aluminum contacts”, Physical Review Letters, 78, 3535–3538 (1997). Abstract. 
[3] J. M. van Ruitenbeek, A. Alvarez, I. Piñeyro, C. Grahmann, P. Joyez, M. H. Devoret, D. Esteve, C. Urbina, "Adjustable nanofabricated atomic size contacts", Review of Scientific Instruments, 67, 108 (1996). Abstract. 
[4] F. Pauly, M. Dreher, J. K. Viljas, M. Häfner, J. C. Cuevas, P. Nielaba, "Theoretical analysis of the conductance histograms and structural properties of Ag, Pt, and Ni nanocontacts", Physical Review B, 74, 235106 (2006). Abstract. 
[5] See supplementary information in reference [1].
[6] Sense Jan van der Molen, "Single-atom switches: Toggled with electrical current", Nature Nanotechnology, 8, 622 (2013). Abstract. 

Deterministic Quantum Teleportation with Feed-Forward in a Solid State System

[From left to right] Andreas Wallraff, Christopher Eichler, Yves Salathe, Markus Oppliger, Philipp Kurpiers, Lars Steffen

Authors: Lars Steffen, Yves Salathe, Markus Oppliger, Philipp Kurpiers, Matthias Baur^*, Christian Lang, Christopher Eichler, Gabriel Puebla-Hellmann, Arkady Fedorov^*, Andreas Wallraff

Affiliation: Department of Physics, ETH Zurich, Switzerland

^*Present address: ARC Centre for Engineered Quantum Systems, University of Queensland, Brisbane, Australia

Link to QUDEV-Lab >>

Transferring the state of an information carrier between two parties is an essential primitive in both classical and quantum communication and information processing. Quantum teleportation [1] describes the concept of transferring an unknown quantum state from a sender to a physically separated receiver without transmitting the physical carrier of information itself. To do so, teleportation makes use of the non-local correlations provided by an entangled pair shared between the sender and the receiver and the exchange of classical information.

In our recent publication [2] we report the first teleportation of information in a solid state system. We use a chip-based superconducting circuit architecture [3, 4] (Fig. 1) with three superconducting transmon qubits [5] and three superconducting coplanar waveguide resonators [6] which serve as a quantum bus [7, 8] and allow to perform qubit state readout [9, 10]. We have realized the full deterministic quantum teleportation protocol using quantum-limited parametric amplifiers [11] for single-shot readout, a crossed quantum bus technology and flexible real-time digital electronics.

Figure 1: In our chip-based superconducting circuit three qubits are coupled to three resonators to realize deterministic quantum teleportation.

The success of the teleportation protocol in every instance with unit fidelity is counterintuitive from a classical point of view [12]. The receiver’s quantum bit (qubit) does not interact with any other qubit after it has been entangled with one of two qubits in the sender’s possession. The input state (|ψ_in>) is prepared at a later time at the sender. The classical information sent by the sender is not sufficient to recreate |ψ_in> perfectly at the receiver. Indeed, assuming no entanglement between sender and receiver one can replicate the sender’s state at best with a process fidelity of 1/2. To always recover the original state |ψ_in> the sender performs a measurement in the basis of the Bell states, which projects the two qubits in the sender’s possession randomly onto one of the four Bell states. As a consequence the receiver’s qubit is projected instantaneously into a state related to |ψ_in> without ever having interacted with the sender’s qubit. The receiver’s qubit only differs from the input state by a single-qubit rotation which depends on the four possible measurement results. In the final step, the sender communicates the Bell measurement result as two bits of classical information via a classical channel and therefore the receiver can always obtain the original input state |ψ_in>. This final step is frequently referred to as feed-forward.

Figure 2: a) Standard protocol of quantum teleportation. The protocol starts with the preparation of a Bell state between Q2 and Q3 (blue box) followed by the preparation of an arbitrary state |ψ_in> (green box) and a Bell state measurement of Q1 and Q2 (red box). The classical information extracted by the measurement of Q1 and Q2 is transferred to the receiver to perform local gates conditioned on the measurement outcomes. At the end of the protocol Q3 is in a state |ψ_out> which ideally is identical to |ψ_in> (also colored in green). Here, H is the Hadamard gate, X and Z are Pauli matrices σ_x and σ_z, respectively. The cnot-gate is represented by a vertical line between the control qubit (•) and the target qubit (⊕). b) The protocol implemented in the experiment presented here uses controlled-phase gates indicated by vertical lines between the relevant qubits (•), and single qubit rotations R^θ_±y of angle θ about the ±y-axis. To finalize the teleportation we either post-select on any single one of the four measurement outcomes (00, 01, 10 and 11) acquired in a single shot, or we deterministically use all four outcomes, which we then may use to implement feed-forward. The feed-forward operators R^π_x and R^π_y are applied to Q3 conditioned on the four measurement outcomes according to the table presented in the framed box.

Our implementation of the protocol (Fig. 2b) uses single qubit rotations and controlled-phase gates [13, 14] and is equivalent to the original protocol shown in Fig. 2a. The teleportation process succeeds with order unit probability for any input state, as we reliably prepare entangled states as a resource and are able to distinguish all four maximally entangled Bell states in a single measurement.

Figure 3: The solid bars show the experimentally obtained process matrix describing the state transfer from the sender to the receiver. The ideal process matrix, which is the identity operation, is shown in wire frames.

To identify simultaneously the four outcomes of the Bell-state measurement in a deterministic way we use two-qubit single-shot read-out [15, 16] for which we achieve a success probability of (81.8±0.5) %. In the teleportation protocol we analyze the Bell-state measurement in real time by using fast electronics based on a field programmable gate array (FPGA) and realize the feed-forward step in about 500 ns. We have achieved an average process fidelity of (62.2±0.3) % for the full quantum teleportation algorithm, which is clearly above the classical threshold (Fig. 3). We have demonstrated teleportation at a rate of 10,000 quantum bits per second between two macroscopic systems separated by 6 mm.

The low transmission loss of superconducting waveguides is likely to enable the range of this and other schemes to be extended to significantly larger distances, enabling tests of non-locality and the realization of elements for quantum communication at microwave frequencies. The demonstrated feed-forward may also find application in error correction schemes.

References:
[1] Charles H. Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, and William K. Wootters. "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels". Physical Review Letters, 70, 1895 (1993). Abstract.
[2] L. Steffen, Y. Salathe, M. Oppliger, P. Kurpiers, M. Baur, C. Lang, C. Eichler, G. Puebla-Hellmann, A. Fedorov, and A. Wallraff. "Deterministic quantum teleportation with feed-forward in a solid state system". Nature, 500, 319 (2013). Abstract.
[3] A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf. "Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics". Nature, 431, 162 (2004). Abstract.
[4] F. Helmer, M. Mariantoni, A. G. Fowler, J. von Delft, E. Solano, and F. Marquardt. "Cavity grid for scalable quantum computation with superconducting circuits". Europhysics Letters, 85, 50007 (2009). Abstract.
[5] Jens Koch, Terri M. Yu, Jay Gambetta, A. A. Houck, D. I. Schuster, J. Majer, Alexandre Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf. "Charge-insensitive qubit design derived from the Cooper pair box". Physical Review A, 76, 042319 (2007). Abstract.
[6] M. Göppl, A. Fragner, M. Baur, R. Bianchetti, S. Filipp, J. M. Fink, P. J. Leek, G. Puebla, L. Steffen, and A. Wallraff. "Coplanar waveguide resonators for circuit quantum electrodynamics". Journal of Applied Physics, 104, 113904 (2008). Abstract.
[7] J. Majer, J. M. Chow, J. M. Gambetta, J. Koch, B. R. Johnson, J. A. Schreier, L. Frunzio, D. I. Schuster, A. A. Houck, A. Wallraff, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf. "Coupling superconducting qubits via a cavity bus". Nature, 449, 443 (2007). Abstract.
[8] Mika A. Sillanpää, Jae I. Park, Raymond W. Simmonds. "Coherent quantum state storage and transfer between two phase qubits via a resonant cavity". Nature, 449, 438 (2007). Abstract.
[9] R. Bianchetti, S. Filipp, M. Baur, J. M. Fink, M. Göppl, P. J. Leek, L. Steffen, A. Blais, and A. Wallraff. "Dynamics of dispersive single-qubit readout in circuit quantum electrodynamics". Physical Review A, 80, 043840 (2009). Abstract.
[10] S. Filipp, P. Maurer, P. J. Leek, M. Baur, R. Bianchetti, J. M. Fink, M. Göppl, L. Steffen, J. M. Gambetta, A. Blais, and A. Wallraff. "Two-qubit state tomography using a joint dispersive readout". Physical Review Letters, 102, 200402 (2009). Abstract,
[11] Bernard Yurke and Eyal Buks. "Performance of cavity-parametric amplifiers, employing Kerr nonlinearites, in the presence of two-photon loss". Journal of Lightwave Technology, 24, 5054 (2006). Abstract.
[12] S. Massar and S. Popescu. "Optimal extraction of information from finite quantum ensembles". Physical Review Letters, 74, 1259 (1995). Abstract.
[13] Frederick W. Strauch, Philip R. Johnson, Alex J. Dragt, C. J. Lobb, J. R. Anderson, and F. C. Wellstood. "Quantum logic gates for coupled superconducting phase qubits". Physical Review Letter, 91, 167005 (2003). Abstract.
[14] L. DiCarlo, J. M. Chow, J. M. Gambetta, Lev S. Bishop, B. R. Johnson, D. I. Schuster, J. Majer, A. Blais, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf. "Demonstration of two-qubit algorithms with a superconducting quantum processor". Nature, 460, 240 (2009). Abstract.
[15] François Mallet, Florian R. Ong, Agustin Palacios-Laloy, François Nguyen, Patrice Bertet, Denis Vion & Daniel Esteve. "Single-shot qubit readout in circuit quantum electrodynamics". Nature Physics, 5, 79 (2009). Abstract.
[16] R. Vijay, D. H. Slichter, and I. Siddiqi. "Observation of quantum jumps in a superconducting artificial atom". Physical Review Letters, 106, 110502 (2011). Abstract.

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.

Mesoscopic Interference and Light Trapping in Semiconductor Nanowire Mats

[From left to right clockwise] Claire Blejean, Otto Muskens, Tom Strudley, Tilman Zehender, Erik Bakkers

Authors: Tom Strudley¹, Claire Blejean¹, Tilman Zehender², Erik P.A.M. Bakkers^2,3, Otto L. Muskens¹,

Affiliation: 
¹Faculty of Physical and Applied Sciences, University of Southampton, UK
²Dept of Applied Physics, Eindhoven University of Technology, Netherlands
³Kavli Institute of Nanoscience, Delft University of Technology, Netherlands.

For many years the field of mesoscopic physics, defined as the interface between the microscopic and macroscopic worlds, has been the domain of solid state electronics. Amongst the most prominent of such mesoscopic effects are those of universal conductance fluctuations [1] and Anderson localization [2]. The case of localization, in which transport is completely halted due to interference effects in the presence of sufficiently strong disorder, has been of considerable interest over the years. Indeed it was one of the two pieces of work for which Anderson was jointly awarded a Nobel prize in 1977, and its complexity has prompted many to quote Anderson’s Nobel lecture: “Very few believed it at the time…among those who failed to fully understand it at first was certainly its author.” [3]

Past 2Physics articles by Erik Bakkers:
May 20, 2012: "Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices" by Vincent Mourik, Kun Zuo, Sergey Frolov, Sébastien Plissard, Erik Bakkers, Leo Kouwenhoven.

Due to the strong analogy between electron and wave transport, such phenomena should also occur for wave transport in random media. However this presents a significant challenge, as mesoscopic effects occur when the probability of a diffusion scattering back to the same point and interfering with itself becomes significant. Intuitively this break down of the traditional ‘random walk’ description requires scattering mean free paths significantly lower than the wavelength. As a consequence, demonstrations of Anderson localization of light in three dimensions have proved difficult, with most observations being for other systems such as microwaves in a waveguide [4], acoustic waves [5] and even cold atoms [6]. A couple of pioneering studies have reported localization of light in three dimensional media [7,8], however the interpretation of their results is complicated by absorption and fluorescence, which can mimic certain localization effects.

Figure 1: (left) The process of Vapour-liquid-solid growth starting from a gold nanoparticle catalyst is used to grow nanowires on a substrate. A lateral growth step increases the diameter of the wires, without affecting their length. (right) A typical high-density nanowire mat used in our experiments.

In our recent work published in Nature Photonics [9], we presented experimental results obtained using densely packed disordered mats of semiconductor nanowires. We demonstred strong mesoscopic effects using visible light in these layers. The nanowire mats were fabricated at the University of Eindhoven using the method of metallo-organic vapour phase epitaxy (MOVPE), see Fig. 1. By using a recipy of alternating cycles of vapour-liquid-solid (VLS) nanowire growth, followed by lateral growth to increase the wire diameter, precise control could be achieved over the length and diameters of the wire. A very high nanowire density of up to 50% area percentage was necessary to achieve the strong scattering strength required for observing the mesoscopic effects. These nanowire mats are remarkable as they have optical mean free paths as low as 0.2 micrometres, which along with their low intrinsic absorption make them ideal candidates for exploring Anderson localization.

Figure 2 [click on image to see higher resolution]: (left) typical intensity images of light transmitted through a nanowire mat, for a tight laser focus ('in focus') and for a laser illumination out of focus. Total image size ~20 μm. (middle) Intensity distribution normalized to ensemble average, showing the speckle fluctuations in space at the exit plane of the nanowire mat. (right) the total intensity fluctuations are enhanced for a tigthly focused laser, see Ref. [9].

By examining the intensity statistics of the transmitted light we found that it exhibited the large intensity fluctuations and long range correlations (both spatial and spectral) typical of mesoscopic interference (Fig. 2). Fitting these fluctuations with predictions from theory, we found an average of only 4 independent transmission channels through our sample, which is several orders of magnitude lower than previously reported values. These measurements unambiguously show for the first time that strong mesoscopic interference corrections can be achieved in three-dimensional nanomaterials and at optical wavelengths.

Mesoscopic transport corrections are a precursor of the strong or Anderson localization transition, where transport of light is halted by self-interference of many light paths returning to the same position in the medium. We are now in the exciting position where we can probe in detail the mesoscopic physics of light, as well as tuning our nanowire growth parameters further in a bid to observe localization itself. For practical applications, semiconductor nanowires have great potential in solar cell and light generation. A deep understanding of light transport in such materials is of great importance for further optimizing these applications. Ultimately, it may be possible for mesoscopic effects to be harnessed and turned into a new design tool for maximizing performance of real-world devices.

References:
[1] P.A. Lee and A. Douglas Stone, “Universal Conductance Fluctuations in Metals”, Physical Review Letters, 55, 1622-1625 (1985). Abstract.
[2] P.W. Anderson, “Absence of diffusion in certain random lattices”, Physical Review, 109, 1492-1505 (1958). Abstract.
[3] Philip W. Anderson, Nobel lecture (1977).
[4] A.A. Chabanov, M. Stoytchev, A.Z. Genack, “Statistical Signatures of Photon Localization”, Nature 404, 850-853 (2000). Abstract.
[5] Hefei Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, B. A. van Tiggelen, “Localization of Ultrasound in a Three-Dimensional Elastic Network”, Nature Physics, 4, 945-948 (2008). Abstract.
[6] Juliette Billy, Vincent Josse, Zhanchun Zuo, Alain Bernard, Ben Hambrecht, Pierre Lugan, David Clément, Laurent Sanchez-Palencia, Philippe Bouyer, Alain Aspect, “Direct Observation of Anderson localization of matter waves in a controlled disorder”, Nature, 453, 891-894 (2008). Abstract. 2Physics Article.
[7] Diederik S. Wiersma, Paolo Bartolini, Ad Lagendijk, Roberto Righini, “Localization of light in a disordered medium”, Nature 390, 671-673 (1997). Abstract.
[8] Martin Störzer, Peter Gross, Christof M. Aegerter, and Georg Maret, “Observation of the Critical Regime Near Anderson Localization of Light”, Physical Review Letters, 96, 063904 (2006). Abstract.
[9] Tom Strudley, Tilman Zehender, Claire Blejean, Erik P. A. M. Bakkers, Otto L. Muskens, “Mesoscopic Light Transport by Very Strong Collective Multiple Scattering in Nanowire Mats”, Nature Photonics, 7, 413-418 (2013). Abstract.

Edgy Photonics

[From Left to Right] Mordechai Segev, Julia M. Zeuner, Mikael C. Rechtsman, Yaakov Lumer, Yonatan Plotnik.

Authors: Mikael C. Rechtsman¹, Julia M. Zeuner², Yonatan Plotnik¹, Yaakov Lumer¹, Mordechai Segev¹ and Alexander Szameit²

Affiliation: 
¹Department of Physics and the Solid State Institute, Technion – Israel Institute of Technology, Haifa, Israel
²Institute of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-Universität Jena, Germany

There is a topological revolution going on in solid-state physics. At its heart are ‘topological insulators’ (TIs), a class of materials that have electrical properties unlike anything else that has been seen before [1–4]. In TIs, electrical current flows only on the edges or surfaces and not through the bulk of the material: this is why the titles of many popular science articles on the topic are variants of “Physics on the edge.” The atoms making up these materials are, for example, Bismuth Selenide (for the three-dimensional case), and Mercury Telluride (for the two-dimensional case).

Alexander Szameit of Friedrich-Schiller-Universität Jena

The two-dimensional TI has perhaps the most bizarre behavior: electrical current flowing on its edge does not get obstructed by imperfections of the lattice. Any kind of defect or disorder cannot scatter the electrons – allowing them to flow in a smooth and seamless way. Essentially because of this robustness, the condensed matter and solid-state physics community has been convinced that these are going to be the materials at the core of futuristic technologies like robust quantum computation and spintronic devices.

Just as electronics uses the flow of electrons to manipulate information, the field of photonics explores the use of light to do the same thing. Examples of photonic technologies are optical fibers (which transmit internet signals across oceans) and DVD players (think “optical drives”), among many, many others. Physicists in the 1980s realized that light could be manipulated with incredible control in “photonic crystals" [5,6], which are lattices made out of some transparent material (for example, glass, polystyrene, or even silicon). Photonic crystals are central in many emerging photonic technologies, and have the ability to manipulate light in much the same way that semiconductors can control and manipulate electrons in computer chips.

This begs the question: can photons be topologically protected from disorder the same way that electrons can in TIs? Can topological robustness be realized photonic crystals just as it was in solids? As Raghu and Haldane showed in a theoretical paper in 2008 [7], the answer is yes – all you need to do is make a photonic crystal out of a gyromagnetic material (like, for example, Yttrium Iron Garnet - YIG), and apply an external constant magnetic field. The external field acts to break “time-reversal symmetry,” meaning that if light is flowing forward, it could be prevented from being scattered (due to the unavailability of a backwards-propagating wave).

 Raghu and Haldane’s theory was proven correct by an experiment carried out in Marin Soljacic’s group in 2009 [8,9]. But there was a catch: because of the weakness of the gyromagnetic effect at optical wavelengths, their experiment could only be done at microwave frequencies. That meant that the photonic crystals involved could be (roughly) no smaller than the metallic grating you can find on the front cover of your microwave oven. Another scheme – in other words, different physics – would have to be found in order to scale down to micron scales and beyond.

There were quite a number of ideas put forward on how to exactly to scale down in order to make photonic topological insulators with light [10–12]. Our team of researchers (a collaboration between the Segev group at the Technion – Israel Institute of Technology in Haifa and the Szameit group at Friedrich-Schiller University in Jena, Germany) conceived of a new way of doing exactly this, and then implemented it in the lab [13]. The group used an array of waveguides made of fused silica – i.e., glass – to create a honeycomb lattice. The waveguides – which are essentially wires for light – were made to propagate in a helical fashion, rather than straight (see Fig. 1). The helicity is the key ingredient – it allows the light to differentiate between diffracting off to the left or to the right, and only thus can topological protection be achieved. An animation of a simulation in which light misses a defect and then goes around a corner is included below. Full experimental results are available in a recent publication in the journal Nature [13].

Figure 1: This is a schematic diagram of a photonic topological insulator realized in Ref. 13. Each helix represents a waveguide that guides light just as a wire guides electrical current. Each waveguide is about 6μm in diameter and the spacing between waveguides is 15μm.

Caption for Animation: This animation is a simulation of how light propagates through a photonic topological insulator. As light travels down the waveguides, it encounters a defect in the form of a missing waveguide and simply bypasses it without getting scattered. Then, light encounters the corner of the array and simply goes up along the edge because it cannot go back. The reason that the whole array is spinning in a circular way is due to the helicity of the waveguides.

The realization of topological protection of light will impact photonic crystal science and beyond – especially by making photonic devices more robust to disorder, and hence – hopefully – cheaper to manufacture. The optical setting will also enable probing new topological physics that may never have been accessed otherwise. Perhaps the most beautiful aspect of photonic TIs is that they are another example of “emergent physics” [14] – the idea that in complex systems, physics can be much more than the sum of its parts.

References:
[1] C. L. Kane and E. J. Mele. "Quantum Spin Hall Effect in Graphene". Physical Review Letters, 95, 226801 (2005). Abstract.
[2] Markus König, Steffen Wiedmann, Christoph Brüne, Andreas Roth, Hartmut Buhmann. "Quantum Spin Hall Insulator State in HgTe Quantum Wells". Science, 318, 766–770 (2007). Abstract.
[3] D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, M. Z. Hasan. "A topological Dirac insulator in a quantum spin Hall phase". Nature, 452, 970–974 (2008). Abstract.
[4] M.Z. Hasan, C.L. Kane. "Colloquium: Topological insulators". Review of Modern Physics, 82, 3045–3067 (2010). Abstract.
[5] Eli Yablonovitch. "Inhibited Spontaneous Emission in Solid-State Physics and Electronics". Physical Review Letters, 58, 2059–2062 (1987). Abstract.
[6] Sajeev John. "Strong localization of photons in certain disordered dielectric superlattices". Physical Review Letters, 58, 2486–2489 (1987). Abstract.
[7] F.D.M. Haldane and S. Raghu. "Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry". Physical Review Letters, 100, 013904 (2008). Abstract.
[8] Zheng Wang, Y. D. Chong, John D. Joannopoulos, Marin Soljačić. "Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal". Physical Review Letters, 100, 013905 (2008). Abstract.
[9] Zheng Wang, Yidong Chong, J. D. Joannopoulos, Marin Soljačić. "Observation of unidirectional backscattering-immune topological electromagnetic states". Nature, 461, 772–775 (2009). Abstract.
[10] Mohammad Hafezi, Eugene A. Demler, Mikhail D. Lukin, Jacob M. Taylor. "Robust optical delay lines with topological protection". Nature Physics, 7, 907–912 (2011). Abstract.
[11] Kejie Fang, Zongfu Yu, Shanhui Fan. "Realizing effective magnetic field for photons by controlling the phase of dynamic modulation". Nature Photonics, 6, 782–787 (2012). Abstract.
[12] Alexander B. Khanikaev, S. Hossein Mousavi, Wang-Kong Tse, Mehdi Kargarian, Allan H. MacDonald, Gennady Shvets. "Photonic topological insulators". Nature Materials, 12, 233–239 (2013). Abstract.
[13] Mikael C. Rechtsman, Julia M. Zeuner, Yonatan Plotnik, Yaakov Lumer, Daniel Podolsky, Felix Dreisow, Stefan Nolte, Mordechai Segev & Alexander Szameit. "Photonic Floquet topological insulators". Nature, 496, 196–200 (2013). Abstract.
[14] P.W. Anderson. "More Is Different". Science 177, 393–396 (1972). Abstract.

How a New Angle on the Imaging of Nanoscale Metamaterials Resulted in the Discovery of a Novel Crystal Structure

[Top left] Wiel Evers, [top right] Daniel Vanmaekelbergh, [bottom] Mark Boneschanscher

Authors:
M.P. Boneschanscher¹, W.H. Evers² and D. Vanmaekelbergh¹

Affiliation:
¹Condensed Matter and Interfaces, Debye Institute for Nanomaterials Science, Utrecht University, Netherlands.
²Opto-electronic Materials, Delft University of Technology, Netherlands.

In the field of nanotechnology, we are concerned with materials that are larger than atoms, but significantly smaller than what we call ‘bulk’ materials. As the name indicates these nanoparticles have at least one dimension in the nanometre regime. Interestingly, materials within this size regime have physical properties that are not only determined by its chemical constituents (which atoms make up the structure?) but also by their size and shape. The classical rules of physics are not applicable anymore. Instead quantum mechanics dictates how size, shape and chemical composition influence the materials’ properties like adsorption, emission, conduction and magnetism [1].

It is nice that we can design materials at the nanometre scale to have certain desired properties, but in the end we would of course like to use these materials in devices. The trick is to assemble the nanoscale materials in such a way that the engineered material properties due to the nanometre scale of the building blocks are maintained. This process has very aptly been compared to the assembly of LEGO bricks into a LEGO building: the building bricks are still identifiable within the superstructure [2]. The way this assembly is commonly achieved is by means of self-assembly: a suspension containing the nanoparticles is dried under specific circumstances, in order to let the nanoscale building blocks crystallize into a superstructure (see Figure 1). In this superstructure the properties of the nanoscale building blocks are maintained. Moreover, different building blocks can be combined into one superstructure giving rise to synergetic properties [3].

Figure 1: Formation of the nanoparticle superstructures. a, Schematic of the evaporation process during which the nanoparticle superstructures form. b, TEM image of the resulting superstructure. Even though this is a transmission image of a 3D superstructure, the different building blocks (nanoparticles) are still visible.

Since the material properties depend on the way that they can couple to each other in the superstructure, it is of major importance that the exact crystal structure of the superstructure is known. Fully resolving these superstructures however is not an easy task. The usual way this is done in the field is the comparison of transmission electron microscopy (TEM) images (2D projection information) to crystal structures known from the atomic world. This approach has a number of drawbacks, since all information along the 3rd dimension (along the electron beam) is lost. We have addressed this issue before, when we used electron tomography to study superstructures and their defects [4].

In the latest edition of Nano Letters we describe how we have used this technique once more to study a superstructure with a crystal structure not observed in nature before [5]. But let us first have a look into electron tomography. As stated before, TEM creates 2D projection images of our 3D superstructure. Using electron tomography we take multiple TEM images while rotating our sample under the electron beam. In this way we create a tilt series, e.g. a series of transmission images at different angles. Movies of these tilt series can be found here (files si_002 to si_004 are tilt series on different samples). If we now combine all transmission images along the angles under which they were obtained we can reconstruct a 3D image of our superstructure. Movies where we slice through the 3D image can be found here (files si_005 to si_007 are the 3D images corresponding to the tilt series si_002 to si_004). After this it is a question of (rather difficult) computer-aided image analysis to extract the exact coordinates of the nanomaterials making up the superstructure. See Figure 2 for an overview of this process.

Figure 2: Electron tomography process. a, transmission images at different angles are taken and combined into a tilt series. b, after back projection of these transmission images along their respective angles a 3D image reconstruction is acquired, which can then be used for computer-aided image analysis. c, the final crystal structure of the nanoparticle superstructure as extracted from the 3D reconstructed image.

Our particular interest in the structure presented in this work was raised due to the formation process behind these structures. We established in earlier work that in most cases the formation of nanoparticle superstructures can be modelled using hard spheres [6]. This hard sphere model worked very well in predicting the crystal structures of the nanoparticle superstructures formed by a combination of two differently sized nanoparticles. However, there is a certain window of size ratios between the two different nanoparticles where the hard sphere model does not predict any superstructures at all. Therefore we were quite surprised to find that actually quite some different superstructures formed when we combined nanoparticles with just such a size ratio. That is, we did observe quite some different TEM images of what appeared to be different superstructures. The TEM patterns could not be attributed to any projection of a known crystal structure.

Figure 3: Three totally different TEM pictures originating from one and the same crystal structure. a, the [PbSe]₆[CdSe]₁₉ structure imaged along the [0001] direction. b, another crystallite where there is a planar stacking fault. Half of the TEM contrast is caused by the one orientation, the other half by the other orientation. c, yet another crystallite where the crystal growth appeared with the [0001] direction tilted 43^o with respect to the TEM grid.

Therefore we took 3 of such superstructures and performed tomography on them. The TEM images of these 3 structures all appeared to be very different (Figure 3). However, using electron tomography we resolved all three and found that they, in fact, resemble the same crystal structure. This however was a crystal structure not observed in nature before, nor in any artificial crystal structure (although we found an alloy having a similar – but not the same – crystal structure). Its unit cell is made up by 6 PbSe nanocrystals and 19 CdSe nanocrystals, and has a hexagonal symmetry (no. 178 P6m2). The different TEM pictures that we observed appeared to be caused by different orientations of that particular crystal structure and by one structure with a planar defect (Figure 3). This is once more a warning to the field that what you see in TEM is not always what you get.

Finally this discovery will have some implications in the field. First, the structure itself is built from a kagomé lattice, a type of symmetry that is of high interest in the field of condensed matter for its curious spin properties. Secondly the fact that this crystal structure is found in a size regime where no crystal structure was expected implies that either the hard-sphere model is not always valid for nanoparticles, or that this particular crystal structure is overlooked in the hard sphere modelling community. And finally, we hope to have set a new standard in the research to these nanocrystal superstructures: the use of electron tomography to fully resolve structures of interest.

References:
[1] Celso de Mello Donegá, "Synthesis and properties of colloidal heteronanocrystals", Chemical Society Reviews, 40, 1512-1546 (2011). Abstract.
[2] Dmitri V. Talapin, "Is it possible to form much larger ordered nanocrystal assemblies and to transfer them to different substrates?" ACS Nano 2, 1097-1100 (2008). Abstract.
[3] D. Vanmaekelbergh, "Self-assembly of colloidal nanocrystals as route to novel classes of nanostructured materials". Nano Today 6, 419-437 (2011). Abstract.
[4] Heiner Friedrich, Cedric J. Gommes, Karin Overgaag, Johannes D. Meeldijk, Wiel H. Evers, Bart de Nijs, Mark P. Boneschanscher, Petra E. de Jongh, Arie J. Verkleij, Krijn P. de Jong, Alfons van Blaaderen and Daniel Vanmaekelbergh, "Quantitative Structural Analysis of Binary Nanocrystal, Superlattices by Electron Tomography". Nano Letters, 9, 2719-2724 (2009). Abstract.
[5] Mark P. Boneschanscher, Wiel H. Evers, Weikai Qi, Johannes D. Meeldijk, Marjolein Dijkstra, and Daniel Vanmaekelbergh, "Electron Tomography Resolves a Novel Crystal Structure in a Binary Nanocrystal Superlattice". Nano Letters, 13, 1312-1316 (2013). Abstract.
[6] Wiel H. Evers, Bart De Nijs, Laura Filion, Sonja Castillo, Marjolein Dijkstra and Daniel Vanmaekelbergh, "Entropy-Driven Formation of Binary Semiconductor-Nanocrystal Superlattices". Nano Letters, 10, 4235-4241 (2010). 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.

Oxide Heterostructures for Efficient Solar Cells

Elias Assmann (left) and Giorgio Sangiovanni (right)













Authors: Elias Assmann¹, Peter Blaha², Robert Laskowski², Karsten Held¹, Satoshi Okamoto³, Giorgio Sangiovanni^1,4

Affiliation: 
¹Institute of Solid State Physics, Vienna University of Technology, Austria
²Institute of Materials Chemistry, Vienna University of Technology, Austria
³Materials Science and Technology Division, Oak Ridge National Laboratory, USA
⁴Institut fuer Theoretische Physik und Astrophysik, Universitaet Wuerzburg, Germany

Sunlight is a very promising source of renewable energy, but a number of  "structural'' upper bounds limit the efficiency of solar cells in principle and in practice. The most important effect concerns the band gap of the absorber material: Those photons with energy smaller than the gap cannot be absorbed and are wasted. At the same time, relaxation effects come into play, and energy in excess of the gap is released to the lattice by the electrons and holes excited by photons. Including further losses from smaller effects like black-body radiation and radiative recombination, the efficiency of single-junction solar cells is limited to about 34%, a number known as the Shockley-Queisser limit [1,2].

However, considering the scale of solar cell production and of global photovoltaic installations [3], even small improvements on the final efficiency of the devices have a huge economical and environmental impact and are intensively pursued by industry. In particular, a big effort concentrates on the reduction of the so-called Shockley-Read-Hall electron-hole recombination due to "trap'' states provided by lattice defects and, in general, of any other intrinsic mechanism opposing electron-hole separation.

Working to achieve higher efficiencies, the community is on the one hand trying to further optimize established technologies, such as those based on crystalline silicon, but on the other hand the search for new, more efficient absorber materials goes on.

Figure 1

In a recent publication[4], we have proposed an unexplored alternative, namely to build photovoltaic cells from oxide heterostructures. Lanthanum vanadate, LaVO₃ grown on strontium titanate, SrTiO₃ (shown in Fig. 1) has a direct band gap in the optimal range for photovoltaics, and can be engineered to have an intrinsic electric field. This field can help electron-hole separation and reduce the recombination rate, one of the key problems of solar cells. A third feature is the conducting interface between LaVO₃ and SrTiO₃ and the ultra-thin conducting surface layer, providing for naturally built-in contacts for the solar cell. Furthermore, oxide heterostructures make it possible to design multijunction cells in unprecedented, extremely flexible ways.

Oxide heterostructures are artificial crystals combining different materials. The excitement about them stems from the fact that, using techniques such as pulsed laser deposition (PLD) or molecular beam epitaxy (MBE), scientists can combine a wide range of different compounds with atomic precision like Lego blocks. A ground-breaking discovery was made a decade ago by Ohtomo and Hwang [5,6]: The interface between the insulators SrTiO₃ and LaAlO₃ can be conducting. Thereafter, an intense research concentrated on layered oxide heterostructures. The aim has been not only to engender new physical effects that are absent in the constituent bulk materials, but also to design tailor-made materials and tune specific properties for desired functionalities.

As pointed out by one of us [7], if materials with partially filled d-shells are involved, this flexibility becomes even stronger and therefore potentially more useful. Electrons in d and f shells are strongly correlated, i.e. their mutual interaction effects cannot be described within the standard framework of band-structure theory. Materials containing electrons of this kind often display very pronounced responses to external perturbations, even if these are small. This makes them ideal for use in tailor-made devices. For instance, it is well known that in some bulk oxide materials, like for example V₂O₃, a tiny change in external pressure triggers a first-order transition between a metallic and a Mott insulating phase, i.e. a phase in which electrons are localized because of strong mutual repulsion.

Lanthanum vanadate, the active material in the LaVO₃|SrTiO₃ heterostructure that we consider here, is such a strongly correlated material. Our proposal rests on four key points, which we back up in the paper [4] by ab-initio calculations based on Density Functional Theory (DFT):

1) The heterostructure intrinsically develops a large electric field (about 0.3 eV per atomic layer, or in more familiar units: 8 million Volts per centimeter) which will drive negatively charged electrons and positively charged holes in opposite directions, inhibiting their recombination and the losses associated therewith.

2) The electrical contacts to extract the electrons and holes are provided by the material in a natural manner. First, the interface between SrTiO₃ and LaVO₃ becomes conducting above a certain "critical thickness'' of the (ultra-thin) LaVO₃ film. This conducting layer (or "two-dimensional electron gas, 2DEG'') will serve as a back-contact for the solar cell. Second, our calculations show that the LaVO₃ surface should similarly develop a conducting layer. However, this conducting surface has to date not been observed in experiments (this could be due to localization by surface defects, for example). If it cannot be realized, an additional metallic layer such as strontium vanadate may be an expedient.

3) LaVO₃ (in bulk or in the heterostructure) has a band gap of 1.1 eV, which is near the optimum for single-junction solar cells. In fact, this is the same value as for silicon, but silicon has a so-called indirect band gap. This means that the valence band maximum and the conduction band minimum do not occur at the same k-vector ("momentum'' of the electrons or holes). Therefore, and because photons carry very little momentum, the optical absorption is strongly suppressed (the lattice has to provide the missing momentum in the form of a phonon), and silicon solar cells have to be rather thick. On the contrary, the gap of LaVO₃ is  "direct'', and its optical absorption is large; in fact, it is large not only compared to silicon, but also to the direct-gap absorbers cadmium telluride CdTe and gallium arsenide GaAs, two industry standard materials for thin-film solar cells, see Fig. 2.

Figure 2

4) The most important way of surpassing the Shockley-Queisser limit quoted above is to combine different materials to create a "tandem'' or multijunction solar cell. As mentioned before, oxide heterostructures can be grown very flexibly; in terms of solar cells, this will allow designing a multijunction cell layer by layer.

These four points are also illustrated in Fig. 3.

Figure 3

Our theoretical study suggests that layered oxide heterostructures hold great promise as absorber materials for solar cells. We have shown that they can provide a new concept for designing efficient solar cells, including gap grading and reduction of electron-hole recombination. We have reached this conclusion using calculations from first principles.

While important theoretical work remains to be done (such as a careful analysis of the excitonic properties and correlation effects), the crucial next step will be experimental work. In order to test whether or not our proposal actually works, experiments have necessarily to be performed. Experimental colleagues from the University of Wuerzburg are already working on that, using existing and new samples of layered heterostructures. We are looking forward to the first results of these experiments.

References:
[1] William Shockley and Hans J. Queisser, "Detailed Balance Limit of Efficiency of p-n Junction Solar Cells". Journal of Applied Physics, 32, 510 (1961). Abstract.
[2] Albert Polman & Harry A. Atwater. "Photonic design principles for ultrahigh-efficiency photovoltaics". Nature Materials, 11, 174-177 (2012). Abstract.
[3] EPIA report, "Global Market Outlook for Photovoltaics until 2016". Full Report.
[4] Elias Assmann, Peter Blaha, Robert Laskowski, Karsten Held, Satoshi Okamoto and Giorgio Sangiovanni, "Oxide Heterostructures for Efficient Solar Cells". Physical Review Letters, 110, 078701 (2013). Abstract.
[5] A. Ohtomo, D. A. Muller, J. L. Grazul and H. Y. Hwang, "Artificial charge-modulation in atomic-scale perovskite titanate superlattices". Nature, 419, 378-380 (2002). Abstract.
[6] A. Ohtomo and H. Y. Hwang, "A high-mobility electron gas at the LaAlO₃|SrTiO₃ heterointerface". Nature 427, 423-426 (2004). Abstract.
[7] Satoshi Okamoto & Andrew J. Millis, "Electronic reconstruction at an interface between a Mott insulator and a band insulator". Nature 428, 630-633 (2004). Abstract.
[8] Naoyuki Nakagawa, Harold Y. Hwang & David A. Muller, "Why some interfaces cannot be sharp". Nature Materials, 5, 204-209 (2006). Abstract.
[9] Guneeta Singh-Bhalla, Christopher Bell, Jayakanth Ravichandran, Wolter Siemons, Yasuyuki Hikita, Sayeef Salahuddin, Arthur F. Hebard, Harold Y. Hwang & Ramamoorthy Ramesh, "Built-in and induced polarization across LaAlO₃|SrTiO₃ heterojunctions". Nature Physics, 7, 80-86 (2011). Abstract.
[10] Y. Hotta, Y. Susaki and H. Y. Hwang, "Polar Discontinuity Doping of the LaVO₃|SrTiO₃ Interface". Physical Review Letters, 99, 236805 (2007). Abstract.