Material Properties of Fire Ant Aggregations

David Hu

Authors: Michael Tennenbaum¹, Zhongyang Liu², David Hu², Alberto Fernandez-Nieves¹

Affiliation:
¹School of Physics, Georgia Institute of Technology, Atlanta, Georgia, USA, 
²School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA.

Link to Hu Laboratory for Biolocomotion >>

Michael Tennenbaum

Fire ants are an impressive species. A remarkable property is that they are able to build rafts to survive flooding. These rafts are only made of ants; they contain no twigs or leaves. The raft is solely linked together with ants. This ability to link together means that we can think of ant aggregations as condensed states of matter, like the common fluid or solid states. In this work [1] we begin to characterize the properties of the ant aggregation as a material. However, in contrast to the particles in conventional materials, ants are alive; they are out of equilibrium and also are self-propelled. As a result, ant aggregations are particular examples of active materials.

Alberto Fernandez-Nieves

In fact, the combination of being alive and being able to link together makes fire ants an excellent system to study active materials. Our work began with two simple experiments. The first is a penny that is dropped through a 2D column of fire ants, as shown in figure 1a-c. This behavior is reminiscent of what happens to a ball bearing falling through a viscous liquid. The second experiment in figure 1 shows what happens when an aggregation of fire ants is compressed by a Petri dish. Once compressed the ants spring back to their original shape. This is the classic behavior of elastic materials. We thus conclude that fire ant aggregations are both viscous and elastic. To more carefully study this viscoelastic behavior we employ rheology. We use a modified Anton Paar MCR 501 stress controlled rheometer to investigate the ants.

Figure 1: (a—c) A penny being dropped through a 2D column of ants. (d-f) Compression of an ant aggregation using Petri dishes. Videos are online at antphysics.gatech.edu .

In our recent paper we present the ant aggregation’s response to oscillations. This is called small amplitude oscillatory shear experiments. The premise is to apply a small sinusoidal strain and measure the stress necessary to maintain this strain. In elastic materials this stress is perfectly in phase with the strain. In contrast, for perfectly viscous materials it is completely out of phase. For viscoelastic materials, the response is in between. We can characterize how much energy is stored per cycle (Storage modulus) by the in phase component and how much energy is dissipated per cycle (Loss modulus) by the out of phase component.

Amazingly for ant aggregations these components are equal for the frequency range probed. This means that in each cycle the ants are dissipating energy and storing energy equally. The response is also power law with an exponent of ~0.5. This power law behavior implies that there is a lack of a unique timescale to relax. Polymer gels when they first percolate through the system show this same behavior [2]. In polymer gels this is attributed to the fractal nature of the gel. However, fire ants are not fractal as far as we have seen. The power law exponent of 0.5 combined with the equality of the Storage and Loss moduli is consistent with the Kramers-Kronig relations [3,4], which apply to systems near equilibrium, in the so-called linear regime. However, fire ant aggregations are far from equilibrium and thus it is not obvious as to why linear response works. This is an interesting open question.

Figure 2: Storage modulus G' and Loss modulus G" as a function of frequency (a) Live ant frequency sweeps, (b) Dead ant frequency sweeps.

We are nevertheless sure that our observations are due to the active nature of the ants. When we performed similar measurements using dead ants the result was completely different. Dead ants are elastic. Their storage modulus is always higher than their loss modulus and are frequency independent.

Interestingly, when we increase the density of the live ant aggregation, the behavior approaches that of dead ants and eventually the system becomes predominantly elastic. Looking closer at this we see that there are two regimes. The first is at lower densities and here the storage modulus increases linearly with the fraction of space taken up by ants or volume fraction. In this regime the ants are crowding and the addition of ants decreases the available possibilities for them to rearrange. After a certain point in volume fraction though, the addition of ants causes them to pull their legs in a little. This progressive compression of the ants characterizes the second regime.

A very different response is obtained when the ant aggregation is forced to flow. In this case there is no difference between live and dead ants, and the aggregation behaves as a shear thinning liquid like ketchup, which manifests a smaller viscosity the harder it is pushed. Remarkably though, the amount of shear thinning in the ants is more pronounced relative to that observed in materials like ketchup. This result can ultimately be related to how the energy input is dissipated in the aggregation. For dead ants, this mainly happens at the ants joints, when these give way due to the imposed flow state of the aggregation [5]. The similar behavior exhibited by live ants indicates that this mechanism is also at play for these aggregations.

In summary, we have found (i) that live ants at relatively “low” volume fractions are equally viscous and elastic, (ii) that they become predominantly elastic and approach dead-ant behavior as the volume fraction increases, and (iii) that when forced to flow, they do so with a viscosity that dramatically decreases as they are forced to flow faster. Our work opens the way to many more interesting studies where ants are used as model active particles. We thus hope to use them to address many more relevant problems.

References:
[1] Michael Tennenbaum, Zhongyang Liu, David Hu, Alberto Fernandez-Nieves, "Mechanics of fire ant aggregations", Nature Materials, 15, 54-59, doi:10.1038/nmat4450 (2016). Abstract.
[2] Horst Henning Winter, Marian Mours, "Rheology of Polymers Near Liquid-Solid Transitions" in 'Neutron spin echo spectroscopy viscoelasticity rheology' (Volume 134 of the series 'Advances in Polymer Science', pp 165-234, Springer, 1997). Abstract.
[3] R. Byron Bird, Robert C. Armstrong, Ole Hassager, "Dynamics of polymeric liquids. Vol. 1: Fluid mechanics" (Wiley, 1987).
[4] Michael Stone, Paul Goldbart, "Mathematics for physics: a guided tour for graduate students" (Cambridge University Press, 2009).
[5] Sasha N. Zill, Sumaiya Chaudhry, Ansgar Büschges, Josef Schmitz, "Directional specificity and encoding of muscle forces and loads by stick insect tibial campaniform sensilla, including receptors with round cuticular caps", Arthropod structure & development, 42, 455-467 (2013). Abstract.

All-Optical Reconstruction of Crystal Band Structure

Giulio Vampa

Paul Corkum

Authors: Giulio Vampa¹, Thomas Hammond¹, Nicolas Thiré², Bruno Schmidt², François Légaré², Chris McDonald¹, Thomas Brabec¹, Dennis Klug³,
Paul Corkum^1,3

Affiliation:
¹Department of Physics, University of Ottawa, Ontario, Canada,
²INRS-EMT, Varennes, Québec, Canada,
³National Research Council of Canada, Ottawa, Ontario, Canada.

The electronic band structure of solids determines their key properties, for example electrical conductivity and optical absorption. The energy bands are conventionally measured with Angle Resolved Photoemission Spectroscopy (ARPES), in which the kinetic energy and the momentum of electrons ionized by highly energetic photons are simultaneously measured [1]. The working principle is sketched in the left of Fig. 1. ARPES has been an incredibly successful method to probe conventional and less conventional materials, such as superconductors [2], graphene [3] and topological insulators [4].

However, electrons are not always accessible. Only high vacuum must oppose their propagation from the surface of the sample to the detector. This prevents measuring the band structure of the bulk, or of matter under extreme pressures, where the sample is enclosed in a diamond anvil cell, or in high magnetic fields, where electrons are deviated. Further, many surface chemical reactions that happen at ambient conditions, such as catalysis, are difficult to study with ARPES.

Figure 1: Comparison between photoemission and high harmonic generation. In photoemission experiments, an incoming photon (purple arrow) causes emission of an electron (black vertical arrow) with kinetic energy (K1 and K2) proportional to the initial binding energy (E1 and E2). In high harmonic generation, an electron first tunnels (marked by circled 1) to the conduction band. The electron-hole pair is then accelerated (circled 2) and recombines (circled 3) emitting a harmonic photon in the process. Electrons and holes are denoted by filled and empty blue circles, respectively. Two trajectories are identified by the wiggled solid black arrows, corresponding to different times of creation and recollision of the electron-hole pair.

In our recent letter [5], we report on an optical method to determine the band structure of solids. Because the technique does not detect electrons, it does not need high vacuum. The technique requires focusing a strong femtosecond laser pulse (1 fs = 10^-15 s), with a peak field strength of ~0.1-1 V/Ang – comparable to the force binding electrons to their atoms – with a central wavelength in the mid-infrared spectral region (therefore < 1 eV photon energy) inside the bulk of the solid sample to generate several new frequencies at odd multiples of the mid-infrared one. The process, known as High Harmonic Generation [6], proceeds through three steps that are depicted in the right of Fig. 1. First, when the field is close to a maximum, electrons tunnel from the top of the valence to the bottom of the conduction band, creating an electron-hole pair with zero initial crystal momentum (circled “1” in Fig. 1). Then, the laser field accelerates the electron-hole pair to high crystal momentum (it can reach the edge of the Brillouin Zone!) - marked “2” in Fig. 1 – in a way that depends on the shape of their respective bands. Then, at a specific time in the laser cycle, the electron can recombine with the hole, emitting a high harmonic photon in the process with energy equal to the band gap at the momentum of recombination (marked “3” in Fig. 1).

The process is highly coherent: ionization, propagation and recombination are perfectly synchronized with the laser filed. This allows to link each harmonic photon energy to a specific trajectory of the electron-hole pair, which is ultimately determined by when it was created about the peak of the laser field. Therefore, knowledge of the trajectory is sufficient to determine the momentum at recollision, the only ingredient required to determined the band structure – together with the harmonic photon energy. The technique relies on a second laser pulse, superimposed to the first, at twice the mid-infrared frequency, to perturb – and therefore measure – the trajectory.

In a simulated experiment, we are able to fully reconstruct the momentum-dependent band gap of a target model solid, chosen to approximate the band structure of a ZnO crystal. The technique requires measuring many harmonic orders, a task at the moment beyond the capabilities of our experimental setup. In a real experiment we conducted, we are able to measure only 20% of the Brillouin Zone. Even with this limited experimental data, we determine that the split-off valence band on ZnO is the one mostly contributing to tunnelling of electrons to the conduction band.

In conclusion, rather than using weak incoherent fields of high energy photons – as in photoemission experiments – we use intense coherent light of low energy photons to create, accelerate and probe electron-hole pairs in solids. The information about the energy of the bands in which the electron and the hole move is imprinted on a high harmonic photon upon their recombination. Like other spectroscopy techniques based on high harmonic generation in gases [7], the method has intrinsic sub-laser cycle temporal resolution. This could be used to track band structure modifications following laser excitation [8].

References:
[1] Andrea Damascelli, Zahid Hussain, Zhi-Xun Shen, "Angle-resolved photoemission studies of the cuprate superconductors", Review of Modern Physics, 75, 473 (2003). Abstract.
[2] A. Lanzara, P.V. Bogdanov, X.J. Zhou, S.A. Kellar, D.L. Feng, E.D. Lu, T. Yoshida, H. Eisaki, A. Fujimori, K. Kishio, J.-I. Shimoyama, T. Noda, S. Uchida, Z. Hussain, Z.-X. Shen, "Evidence for ubiquitous strong electron–phonon coupling in high-temperature superconductors", Nature, 412, 510 (2001). Abstract.
[3] Søren Ulstrup, Jens Christian Johannsen, Federico Cilento, Jill A. Miwa, Alberto Crepaldi, Michele Zacchigna, Cephise Cacho, Richard Chapman, Emma Springate, Samir Mammadov, Felix Fromm, Christian Raidel, Thomas Seyller, Fulvio Parmigiani, Marco Grioni, Phil D. C. King, Philip Hofmann, "Ultrafast Dynamics of Massive Dirac Fermions in Bilayer Graphene", Physical Review Letters, 112, 257401 (2014). Abstract.
[4] Y. L. Chen, J. G. Analytis, J.-H. Chu, Z.K. Liu, S.-K. Mo, X.L. Qi, H.J. Zhang, D.H. Lu, X. Dai, Z. Fang, S.C. Zhang, I.R. Fisher, Z. Hussain, Z.-X. Shen, "Experimental Realization of a Three-Dimensional Topological Insulator, Bi₂Te₃", Science 325, 178 (2009). Abstract.
[5] G. Vampa, T.J. Hammond, N. Thiré, B.E. Schmidt, F. Légaré, C.R. McDonald, T. Brabec, D.D. Klug, P.B. Corkum, "All-Optical Reconstruction of Crystal Band Structure", Physical Review Letters, 115, 193603 (2015). Abstract.
[6] Shambhu Ghimire, Anthony D. DiChiara, Emily Sistrunk, Pierre Agostini, Louis F. DiMauro, David A. Reis, "Observation of high-order harmonic generation in a bulk crystal", Nature Physics, 7, 138 (2011). Abstract.
[7] S. Baker, J.S. Robinson, C.A. Haworth, H. Teng, R.A. Smith, C.C. Chirilă, M. Lein, J.W.G. Tisch, J.P. Marangos, "Probing Proton Dynamics in Molecules on an Attosecond Time Scale", Science, 312, 424 (2006). Abstract.
[8] E. N. Glezer, Y. Siegal, L. Huang, E. Mazur, "Laser-induced band-gap collapse in GaAs", Physical Review B, 51, 6959 (1995). Abstract.

Topological Defect Lasers

From left to right: Sebastian Knitter, Seng Fatt Liew, Wen Xiong, Hui Cao

Authors: Sebastian Knitter, Seng Fatt Liew, Wen Xiong, Hui Cao

Affiliation: Department of Applied Physics, Yale University, New Haven, Connecticut, USA.

Topological defects have been widely studied in liquid crystals and colloids. One important application of topological defects to photonics is the manipulation of the orbital angular momentum of optical beams. However, they have not been incorporated into lasers. Inspired by the topological defects existing in nematic liquid crystal, we recently designed and fabricated a new type of laser – a topological defect laser [1].

Past 2Physics articles by this group:
April 03, 2011: "Time-reversed Lasing and Coherent Control of Absorption"
 by A. Douglas Stone, Yidong Chong and Hui Cao.

One essential component of a laser is a cavity that confines light. A microscale cavity can be made within a photonic crystal, e.g., a two-dimensional membrane containing a periodic array of circular air holes, as shown in Fig. 1(a). Light, of wavelength comparable to the lattice constant, may be confined in the central square region as a result of high reflectivity from the surrounding photonic crystal walls. Figure 1(b) shows a spatial field profile of a confined mode, and Fig. 1(c) is the spatial map of its energy flow [2].

Figure 1: Introducing topological defect to a photonic crystal with anisotropic unit cell. (a,c) A square lattice of air holes embedded in a dielectric membrane. In (a), the holes have circular cross-section. The 4×4 holes are removed from the center to from a cavity that confines light by high reflection from the surrounding photonic crystal walls. The lattice constant is a = 220nm, and the hole radius is 65nm. To introduce topological defect in (c), the air holes are deformed to ellipses. The major axis of each ellipse is rotated to an angle φ = kθ + c from the horizontal axis. θ is the polar angle of the center position of the ellipse. k = 1 and c = π/4. (b,d) Calculated spatial distribution of the magnetic field for a confined optical mode in (a,b). The wavelength of the mode is 880nm. The topological defect rotates the mode in (d). (c,e) The spatial map of the Poynting vector for the modes in (b,d). Each arrow points in the direction of local energy flux, and its length is proportional to the amplitude of the flux. In the photonic crystal structure, the energy flows out of the central defect region in all four directions. In the topological defect structure, the optical flux circulates in the central region.

To introduce the topological defect to this micro-cavity, we deform the air hole shape from circle to ellipse, and rotate the orientation of individual ellipses to form a vortex-like topological defect, as seen in Fig. 1(d). Light can still be confined in the central region, but the spatial field profile of confined mode is twisted as shown in Fig. 1(e). Figure 1(f) reveals an even more dramatic change in the energy flow: a tightly confined circulating flux pattern arises at the center, in contrast to the outward energy flow in Fig. 1(c). Such change is attributed to the spatial variation of the ellipse orientation in the topological defect structure, which creates the swirling vortex of light [2].

Experimentally we fabricated such structure in a free-standing gallium-arsenide membrane by molecular beam epitaxy, electron-beam lithography, reactive ion etching and wet chemical etching. Figure 2 is the scanning electron micrograph of a fabricated sample. The 190nm-thick membrane contains three layer of quantum dots made of indium arsenide. When pumped by an external laser, the quantum dots are excited to upper states. They subsequently decay to lower states by emitting photons to the confined modes such as the one shown in Fig. 1. When the amplification rate exceeds the leakage rate through the walls, lasing action starts. The laser light swirls around in a vortex.

Fig. 2: Scanning-electron micrograph (SEM) of a topological defect laser fabricated in a GaAs membrane. (a) Top-view SEM image of a square lattice of 32 × 32 air holes with elliptical shape. The ellipticity is ε = 1.4. The lattice constant is a = 220 nm. The air filling fraction is 0.27. At the array center, 4 × 4 air holes are removed. (b) Magnified SEM of a section in (a), highlighted by the gray rectangle. (c) Tilt-view SEM image showing the free-standing GaAs-membrane. Scale-bars in (b) and (c) represent a length of 500 nm.

The power-flow vortex persists beyond the membrane. Our calculation shows that the evanescent field above the top surface of the membrane possess circulating energy flows. These may transfer angular momentum to particles or molecules in the vicinity of the topological defect structure. Thus the optical vortex of the lasing mode may potentially be used for on-chip nanoparticle manipulation. Further experimental study is required to optimize the topological defect laser and exploit the unique potential for applications in areas such as microfluidics for particle sorting and separation. Finally, this work shows that the spatially inhomogeneous variation of the unit cell orientation adds another degree of freedom to the control of a lasing mode, enabling the manipulation of its field pattern and energy flow landscape.

References:
[1] Sebastian Knitter, Seng Fatt Liew, Wen Xiong, Mikhael I. Guy, Glenn S Solomon, Hui Cao, “Topological defect lasers”, Journal of Optics, 18, 014005 (2015). Full Article.
[2] Seng Fatt Liew, Sebastian Knitter, Wen Xiong, Hui Cao, “Photonic crystals with topological defects”, Physical Review A, 91, 023811 (2015). Abstract.

Using Phase Changes to Store Information in the Magnetic Permeability

Authors: Alan S. Edelstein^*, John Timmerwilke, Jonathan R. Petrie 

Affiliation: US Army Research Laboratory, Adelphi, Maryland, USA

*Email: aedelstein@cox.net

Finding better methods for storing information was a serious problem for the earliest computers; considerable effort is still being devoted to decreasing the cost and increasing the density and lifetime of stored information. Initial methods of storage included using acoustic delay lines and pixels on the display of cathode ray tubes [1]. Though the current methods for storing information, which include magnetic hard disks, magnetic tape, and various forms of random access memory (RAM) are far superior to these early methods, they still have significant limitations.

As an example, the information on hard disks or magnetic tape is written by a magnetic field and stored as regions, i.e. bits, having different directions for their remanent magnetization. Thus, this information can be erased by exposure to a magnetic field. Furthermore, to avoid thermal upsets of the spin direction of the bits there is a trade-off between how long the information can be stored without acquiring too many incorrect bits and the information density on hard disks. Maintaining a magnetic hard disk lifetime of about seven years has made it difficult to increase the information density in hard disk drives. Magnetic tape degrades in about 20 years.

To avoid these problems, we have been developing a new approach for storing information that we call Magnetic Phase Change Memory (MAG PCM). Instead of using the direction of magnetic remanance, information is stored in bits of soft ferromagnetic material having different values for their magnetic permeability. The initial magnetic permeability of a soft ferromagnetic material is reversible and dependent only on its atomic structure. Thus, it is independent of the magnetic field. The permeability of iron rich FeGa single crystal alloys [2]  is an interesting example of soft magnetic behavior.

The property we use is that high permeability bits attract magnetic fields and low permeability bits do not. To read the information stored in bits with high or low permeability we measure their effect on a probe field. We have primarily focused on writing and changing the permeability of bits of amorphous ferromagnet, 2826 MB Metglas, films by thermally heating with a laser. The nearest neighbor atoms in amorphous ferromagnets materials do not have long range order. Thus, they do not have much crystalline anisotropy or coercivity and are soft ferromagnets with large values for their permeability. When amorphous materials are heated above their glass temperature, they crystalize and have larger values for their coercivity and smaller values for their permeability. The glass temperature of 2826 MB Metglas is 410^oC. At temperatures as high as 200^oC, 2826 MB Metglas will retain its high permeability for hundreds of years.

Figure 1: a) Microscope view of three 50 micron wide crystallized lines written into amorphous Metglas. b) Voltage of the MTJ reader as it moved over the three crystalline lines written in the presence of a 32 Oe probe field.

We have read the effect on a probe magnetic field near each bit using both magnetic tunnel junction (MTJ) sensors [3,4], and spin transfer oscillators [5]. Figure 1a shows a microscope image of three crystalline lines in Metglas written by a focused 1.966 micron (Tm fiber) laser. The output voltage of an MTJ sensor is plotted in Figure 1b as it is swept over the crystallized Metglas lines shown in Figure 1a. One sees that the crystallized lines affect a 32 Oe probe field. The crystallized lines do not attract the probe field as much as the amorphous Metglas film does which causes the magnetic sensor to measure a larger field. Smaller nanometer-sized bits were created using e-beam lithography. Figure 2a is a microscope image of two square 0.9 mm arrays of 300 nm bits of amorphous Metglas. Figure 2b shows a scanning electron microscope (SEM) image of the 300 nm diameter bits. Laser heating was used to crystallize all of the bits in the left array. Figure 3 shows the voltage output of the MTJ sensor when it is moved over the two arrays before and after the laser heating. One sees that the bits in the left array no longer attract the magnetic field lines of the probe field.

Figure 2. (a) Microscope image of two square 0.9 mm arrays of 300 nm diameter bits of Metglas; (b) scanning electron microscope image of the 300 nm diameter bits of Metglas.

This new approach for storing information has several advantages. One can write bits with at least three different values [6]  for their permeability. The bits will not be corrupted by a magnetic field or thermal upsets and therefore should last decades. It should be possible to write nm sized bits economically by an adaption of heat assisted magnetic recording (HAMR) [7], a technology that is being developed by hard disk companies such as Seagate and Western Digital to cope with the problem mentioned above of maintaining stability against thermal upsets. In HAMR a laser and a near field transducer is used to heat nm sized regions to 710^oC to decrease the coercivity so that they can be written without using as large a magnetic field. What we need to do is simpler, in that we do not need a magnetic field and for archiving we do not need to rewrite.

Figure 3: Magnetic tunnel junctions scans before (red, o) and after (blue, x) the left array of 300nm Metglas bits in Fig. 2 were crystallized by heating with a laser.

MAG PCM has the potential for a combination properties not found in other storage technologies. It should have decades of longevity and the rapid access and high density of future hard disks. We have a clear path for developing MAG PCM into commercial products for long term storage applications such as archiving. Though it is unnecessary for archiving, we have found that we can rewrite our bit [8], i.e., return a crystallized bit to an amorphous state.

This work was done while we were at the US Army Research Laboratory.

References:
[1] D.R. Hartree, M.H.A. Newman, M.V. Wilkens, F.C. Williams, J.H. Wilkinson, A.D. Booth, ” A discussion on computing machines”, Proceedings of the Royal Society of London Series A- Mathematical and Physical Sciences, 195:1042, 265 (1948). Abstract.
[2] Harsh Deep Chopra, Manfred Wittig, “Non-Julian magnetostriction”, Nature, 521, 340-343 (2015). Abstract.
[3] J.R. Petrie, K.A. Wieland, R.A. Burke, G.A. Newburgh, J.E. Burnette, G.A. Fischer, A.S. Edelstein, “ A non-erasable magnetic memory based on the magnetic permeability”, Journal of Magnetism and Magnetic Materials, 361, 262 (2014). Abstract.
[4] John Timmerwilke, J.R. Petrie, K.A. Wieland, Raymond Mencia, Sy-Hwang Liou, C.D. Cress, G.A. Newburgh, A.S. Edelstein, “Using magnetic permeability bits to store information”, Journal of Physics D: Applied Physics, 48, 405002 (2015). Abstract.
[5] J.R. Petrie, S. Urazhdin, K.A. Wieland, A.S. Edelstein, “Using a spin torque nano-oscillator to read memory based on the magnetic permeability”, Journal of Physics D: Applied Physics, 47, 055002 (2014). Abstract.
[6] J.R. Petrie, K.A. Wieland, J.M. Timmerwilke, S.C. Barron, R.A. Burke, G.A. Newburgh, J.E. Burnette, G.A. Fischer, and A.S. Edelstein, “A multi-state magnetic memory dependent on the permeability of Metglas”, Applied Physics Letters, 106, 142403 (2015). Abstract.
[7] M.H. Kryder and Soo Kim Chang, “After hard drives—what comes next?” IEEE Transactions on Magnetics, 45, 3406 (2009). Abstract.
[8] Unpublished data.

A Quantum Gas Microscope for Fermionic Atoms

The Fermi gas microscope group: (from left) graduate students Katherine Lawrence and Melih Okan, postdoc Thomas Lompe, graduate student Matt Nichols, Professor Martin Zwierlein, and graduate student Lawrence Cheuk. Photo credit: Jose-Luis Olivares/MIT.

Authors: Lawrence Cheuk and Martin Zwierlein

Affiliation: 
Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA.

Link to Ultracold Quantum Gases Group >>

What do electrons, protons, neutrons and even quarks have in common? They all are fermions, particles with half-integer spin. Unlike their bosonic counterparts, integer spin particles, fermions cannot occupy one and the same quantum state. This simple fact leads to the structure of our elements, where electrons have to avoid each other and occupy different orbits around the atomic nucleus, or at least differ in their spin orientation.

When many fermions interact strongly with each other, they can form complex matter with exotic properties, from atomic nuclei to solid state materials, to distant neutron stars. Their collective behavior leads to diverse phenomena such as the structure of the elements, high-temperature superconductivity and colossal magneto-resistance.

Yet our understanding of strongly-interacting Fermi systems is limited. In recent years, ultracold atomic Fermi gases have emerged as a pristine platform to study many-fermion systems. In particular, fermionic atoms trapped in an optical lattice formed by standing waves of light can simulate the physics of electrons in a crystalline solid, shedding light on novel physical phenomena in materials with strong electron correlations.

Yet our understanding of strongly-interacting Fermi systems is limited. In recent years, ultracold atomic Fermi gases have emerged as a pristine platform to study many-fermion systems. In particular, fermionic atoms trapped in an optical lattice formed by standing waves of light can simulate the physics of electrons in a crystalline solid, shedding light on novel physical phenomena in materials with strong electron correlations.

In the present work, recently published in Physical Review Letters [3], we have realized quantum gas microscope that images ultracold fermionic ⁴⁰K atoms with single-lattice-site resolution. Similar results have also been achieved at about the same time by researchers at University of Strathclyde and Harvard University [4,5].

Figure Caption: Fermionic ⁴⁰K atoms in a 2D optical lattice with 541nm spacing imaged using Raman sideband cooling. Image taken from [3].

In our experiment, we prepare a two-dimensional layer of ⁴⁰K atoms via laser cooling and forced evaporation. The atoms are then trapped in an optical lattice formed by retro-reflected laser beams, which form a standing wave with 541nm spacing. In order to resolve atoms with single-lattice-site resolution, we utilize a novel setup that incorporates a solid immersion lens into the vacuum window. This allows an enhancement in the numerical aperture, leading to higher resolution and enhanced light collection. In addition, optical aberrations that arise from a planar window are minimized in this setup.

In order to detect the atoms, we perform fluorescence imaging while simultaneously cooling the atoms. To make the atoms fluoresce, they are illuminated with near-resonant light. However, as the atoms emit photons, they experience heating from the recoil of photons. As the atoms are heated up, they hop between lattice sites and can even hop out of the lattice. In order to faithfully measure the occupation of the lattice sites, one must therefore eliminate the heating that arises when atoms fluoresce. We accomplish this via a technique known as Raman sideband cooling.

Raman sideband cooling, a technique first demonstrated in the 1990s, selectively transfers atoms from high-energy states to lower energy states via a two-photon Raman process. Atoms that are already in the lowest energy state, however, remain “dark” to the Raman light. By collecting photons that are scattered during this cooling process, we extract the position of the atoms while cooling the atoms. Hopping and atom loss are thus avoided. Furthermore, we have found that even after imaging the atoms with Raman sideband cooling, the atoms are predominantly in the lowest energy state. This invites the possibility of assembling low-entropy many-fermion states atom by atom.

The advent of fermion microscope will allow new studies of many-fermion systems in optical lattices, such as measurement of high order correlations and detection of magnetic ordering. Such studies could shed light on the behavior of other fermions, in particular, electrons. This may one day advance our understanding of the diverse phenomena that arise in complex solid-state systems.

References:
[1] Waseem S. Bakr, Jonathon I. Gillen, Amy Peng, Simon Fölling, Markus Greiner, "A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice", Nature, 462, 74 (2009). Abstract.
[2] Jacob F. Sherson, Christof Weitenberg, Manuel Endres, Marc Cheneau, Immanuel Bloch, Stefan Kuhr, "Single-atom-resolved fluorescence imaging of an atomic Mott insulator", Nature, 467, 68 (2010). Abstract.
[3] Lawrence W. Cheuk, Matthew A. Nichols, Melih Okan, Thomas Gersdorf, Vinay V. Ramasesh, Waseem S. Bakr, Thomas Lompe, Martin W. Zwierlein, "Quantum-Gas Microscope for Fermionic Atoms", Physical Review Letters, 114, 193001 (2015). Abstract.
[4] Maxwell F. Parsons, Florian Huber, Anton Mazurenko, Christie S. Chiu, Widagdo Setiawan, Katherine Wooley-Brown, Sebastian Blatt, Markus Greiner, "Site-Resolved Imaging of Fermionic ⁶Li in an Optical Lattice", Physical Review Letters, 114, 213002 (2015). Abstract.
[5] Elmar Haller, James Hudson, Andrew Kelly, Dylan A. Cotta, Bruno Peaudecerf, Graham D. Bruce, Stefan Kuhr, "Single-atom imaging of fermions in a quantum-gas microscope", arXiv:1503.02005v2 [cond-mat.quant-gas] (2015).

Site-Dependent Evolution of Electrical Conductance from Tunneling to Atomic Point Contact

Howon Kim (left) and Yukio Hasegawa

Authors: Howon Kim and Yukio Hasegawa

Affiliation: The Institute for Solid State Physics, University of Tokyo, Japan.

In our recent work [1], the evolution of electrical conductance was investigated from tunneling to atomic point contact whose atomic geometry was precisely defined using scanning tunneling microscopy (STM). We found that the conductance evolution depends on the contact site; for instance, on-top, bridge, or hollow ('hexagonal close packed, hcp' and 'face centered cubic, fcc') site in the close-packed lattice of the substrate, indicating the importance of the atomic configuration in the conductance of the atomic junctions.

Electronic conduction through atomic-sized metal contacts is of fundamental interest as a transport mechanism though the ultimately squeezed conductor [2]. Several seminal phenomena, such as quantization and step-wise variation [3, 4] in the conductance, have been reported using a method called break junction in which the conductance is measured just before the breaking moment of a nanometer-width thin wire. Since atomic geometry of the point contact cannot be controlled and the measured conductance fluctuates at every breaking, therefore, the obtained conductances are usually analyzed in a statistical manner. Scanning tunneling microscopy (STM) has also been utilized for the study of atomic point contacts, in which the contact is formed by pushing the probe tip toward the sample surface. Because of plastic deformation of the tip by the contact formation, however, quantitatively reliable and reproducible measurements have been difficult.

Figure 1. schematic showing the atomic geometry of the atomic point contacts formed at an on-top site (left) and a 3-fold hollow site (right) of a close-packed surface.

Here, in our study, making most of the capability of the atomically resolved imaging of STM, we measured the conductance of the atomic point contact in an atomically controlled manner. We first positioned the probe tip on a specific site, for instance, on-top, bridge, or hollow (fcc and hcp) site, in the crystallographic lattice of the substrate surface (Fig. 1), and then measured the conductance while moving the tip toward the substrate from tunneling to contact regimes. It is found that the conductance evolution depends significantly on the contact site. When the contact is formed, the hollow site has the largest conductance, and among the two hollow sites the hcp site is more conductive than fcc. When the tip is pulled from the contact by just 20-30 pm, a crossover occurs and the conductance at on-top site becomes the largest.

Figure 2: electrical conductance measured from tunneling (Δz = -20 pm) to contact (Δz = -60 pm) regimes. The measured conductance G is normalized by the quantum conductance G₀ given by 2e²/h (~77.5 μS). For each conductance trace, 10 traces taken at the corresponding sites marked in the atomically-resolved STM image (inset) are averaged.

The traces of the electrical conductance measured from tunneling to contact at on-top, bridge, fcc, and hcp sites of the Pb(111) surface are shown in Fig. 2. For each plot, 10 traces obtained from the corresponding marked sites in the inset STM image are averaged. At the tip displacement Δz of -50 ~ -60 pm from the tunneling (Δz = 0), the atomic contact is formed as the conductance shows saturation around the quantum conductance G₀ given by 2e²/h (~77.5 μS). The contact conductance shows strong site dependence; the conductance at the hcp site is largest and more than 50 % larger than the one measured at the on-top site. Around Δz = -30 ~ -40 pm, that is, when the tip is located above the substrate by 20 ~ 30 pm from the contact, the plot indicates the largest conductance at on-top site.

Figure 3. Spatial mappings of the conductance at various tip displacements (upper left) topographic STM image (3.0 X 3.0 nm²) taken simultaneously with 64 X 64 conductance traces. (lower left) conductance mapping at Δz = -32pm, where the largest conductance at on-top site is enhanced (Lower right) conductance mapping at Δz = -60 pm, that is, the contact regime, where hollow site, particularly hcp site, has large conductance. (upper right) schematics explaining the site dependence of the conductance. The atoms on which the chemical interaction is exerted are marked red.

In order to spatially demonstrate the site dependence, we performed real-space mappings of the conductance in the on-top enhancement region and in the contact regime. The upper-left panel of Fig. 3 is an STM image showing the atomic contrast taken simultaneously with the conductance traces. At a tip displacement Δz of -32pm, the conductance mapping (lower-left of Fig. 3) exhibits bright contrast at the on-top site, similarly to that in the topographic image. As the conductance mapping at Δz = 0 does not have any contrast, the bright contrast indicates the conductance enhancement at the on-top site. On the other hand, the conductance mapping in the contact regime (lower right of Fig. 3, Δz = -60pm) has its contrast reversed from that of the topographic one, indicating a larger conductance at the hollow site than at the on-top site. These results clearly demonstrate that the point contact conductance is quite sensitive to the atomic configuration.

When the distance between the tip and substrate is reduced, the attractive chemical interaction is exerted between the surface and tip apex atoms. This interaction presumably opens up the conduction channel and contributes to the development of the conductance. Schematics in the upper right panel of Fig. 3 show how the chemical interaction works in the case of contacts formed at on-top and hollow sites. When the tip approaches from the tunneling regime, the attractive interaction is exerted first at the on-top site (the force-exerted atoms are marked red in the schematics) because the substrate atoms are closer at on-top site than at hollow sites, thus making the on-top conductance enhanced. In the contact regime, however, the attractive force becomes stronger at hollow sites because of the greater number of involved atoms than the on-top site. This is probably the reason why conductance becomes larger there at the contact. Obviously, theoretical studies [5], simultaneous measurements of force and conductance by atomic force microscopy [6], and/or conduction channel analysis of the atomic point contact [7] are needed to elucidate the observed conductance behaviors.

References :
[1] Howon Kim and Yukio Hasegawa, "Site-dependent evolution of electrical conductance from tunneling to atomic point contact", Physical Review Letters, 114, 206801 (2015). Abstract.
[2] Nicolás Agraı̈t, Alfredo Levy Yeyati, Jan M. van Ruitenbeek, "Quantum properties of atomic-sized conductors", Physics Reports, 377, 81 (2003). Abstract.
[3] J. M. Krans, J. M. van Ruitenbeek, V. V. Fisun, I. K. Yanson, L. J. de Jongh; "The signature of conductance quantization in metallic point contacts", Nature, 375, 767 (1995). Abstract.
[4] L. Olesen, E. Lægsgaard, I. Stensgaard, F. Besenbacher, J. Schiøtz, P. Stoltze, K. W. Jacobsen, J. K. Nørskov; "Quantized conductance in an atom-sized point contact", Physical Review Letters, 72, 2251 (1994). Abstract.
[5] Jose Manuel Blanco, Cesar González, Pavel Jelínek, José Ortega, Fernando Flores, Rubén Pérez, "First-principles simulations of STM images: From tunneling to the contact regime", Physical Review B, 70, 085405 (2004). Abstract.
[6] Yoshiaki Sugimoto, Keiichi Ueda, Masayuki Abe, Seizo Morita "Three-dimensional scanning force/tunneling spectroscopy at room temperature", Journal of Physics : Condensed Matter, 24, 084008 (2012). Abstract.
[7] Howon Kim and Yukio Hasegawa, "Site-dependent conduction channel transmission in atomic-scale superconducting junctions", arXiv:1506.05528 [cond-mat.mes-hall].

Tuning Superconductivity in a Molecular System: The Key Role of the Jahn-Teller Metallic State

Authors of the paper in Science Advances (reference [1]). Left to Right: (top row) R. H. Zadik, Y. Takabayashi, G. Klupp, R. H. Colman, A. Y. Ganin, A. Potočnik, (middle row) P. Jeglič, D. Arčon, P. Matus, K. Kamarás, Y. Kasahara, Y. Iwasa, (bottom row) A. N. Fitch, Y. Ohishi, G. Garbarino, K. Kato, M. J. Rosseinsky, K. Prassides.

Authors: Gyöngyi Klupp and Ruth H. Zadik

Affiliation: Department of Chemistry, Durham University, UK

In our recent work, published in the journal Science Advances [1], we have addressed the relationship between the parent insulating phase, the normal metallic state and the superconducting pairing mechanism, a key challenge for all unconventional superconductors, in a series of chemically-pressurized fulleride superconductors. This work has revealed a new state of matter straddling the Mott insulating and Fermi liquid states at the two extremes of the phase diagram: the Jahn-Teller metal, where localized electrons on the fullerene molecules coexist with metallicity.

Figure 1: Crystal structure of face-centred-cubic A₃C₆₀ (A = alkali metal) with C₆₀^3- anions in grey, and the alkali metal cations in colour; reproduced from ref. [1].

Alkali metal intercalated fullerene compounds with the stoichiometry A₃C₆₀ (Fig. 1) are superconducting, with the highest superconducting T_c found in a molecular material being 38 K in pressurised Cs₃C₆₀ [2]. This material is an unconventional superconductor; however, its Rb analogue, Rb₃C₆₀ exhibits conventional superconductivity. The question arises how the two types of behaviours are related both in the normal and in the superconducting state. The nature of the normal state from which the highest T_c emerges is also of key importance.

In order to address these questions, mixed bulk superconducting salts of C₆₀ were prepared with compositions Rb_xCs_3-xC₆₀ (0 < x < 3) [1]. In the isostructural face-centred-cubic- structured phases of this compositional series, tuning the ratio of cations with different diameters controls the distance between C₆₀^3- anions, without the need to apply external pressure, thus permitting a wide range of measurements to be employed. Variable temperature high-resolution synchrotron x-ray powder diffraction, SQUID (superconducting quantum interference device) magnetometry, nuclear magnetic resonance (NMR), infrared (IR) spectroscopy and specific heat measurements were undertaken. When the intermolecular separation is large, like in Cs₃C₆₀ at ambient conditions, the electrons of the C₆₀³⁻ anions cannot hop from one site to the other, and the material is a Mott insulator (Fig. 2). Electrons localised on the C₆₀^3- anions couple to intramolecular vibrations leading to the distortion of the molecule [3]. The Jahn-Teller distortion removes electronic as well as vibrational degeneracies. The latter results in splitting of vibrational lines in the IR spectrum, which provides an excellent way of detecting the Jahn-Teller effect. Thus the parent insulating state of A3C60 superconductors is a Mott-Jahn-Teller insulator, as has previously been demonstrated through IR spectroscopy for the most expanded member Cs₃C₆₀ [3].

Figure 2: The different electronic phases encountered in Rb_xCs_3-xC₆₀ fullerides ranging from the conventional metallic (green) through the Jahn-Teller metallic (orange) to the Mott-Jahn-Teller insulating regime (cyan). The top two rows show schematics of the molecular geometry together with the molecular electronic structure determined by the Jahn-Teller effect and the most characteristic region of the infrared spectrum. The middle panel is the electronic phase diagram; symbols represent the insulator-to-metal transitions and the superconducting T_cs as a function of the volume occupied by a C₆₀^3- anion, which is increasing as the intermolecular distance increases. The lower panel shows the variation in the superconducting gap normalised by T_c. Figure reproduced from ref. [1].

Decreasing the intermolecular distance from this state allows the hopping of the electrons, yielding metallicity. Thus an insulator-to-metal transition, or crossover, is observed on increasing the proportion of the smaller Rb⁺ ion in the material (Fig. 2). Signatures of this transition from the experimental techniques deployed include anomalous shrinkage of the unit cell size, cusps (or maxima) in the magnetic susceptibility and temperature-normalised spin-lattice relaxation rates as a function of temperature, and a step-wise decrease in IR spectral background transmittance.

However, the metallic state encountered close to the metal-insulator boundary is not conventional; the electrons are not forming the conventional bands of a Fermi liquid. Electron correlation results in some persisting localised features in the electron system, like the continued presence of the Jahn-Teller effect as evidenced by IR spectroscopy. The coexistence of the molecular Jahn-Teller effect with metallicity is reflected in the designation of the newly observed phase as a Jahn-Teller metal. The further decrease of intermolecular distances leads to the gradual disappearance of the localised features, like e.g. the Jahn-Teller effect, until a conventional metal is encountered in Rb₂CsC₆₀ and Rb₃C₆₀ (Fig. 2). When the electrons are delocalised over the whole crystal to provide a conventional band, they cannot induce Jahn-Teller distortion any more [4].

A similar crossover between the unconventional and the conventional behaviour is also present in the superconducting state. The superconducting gap probed by NMR spectroscopy at large intermolecular separations is much larger than that of conventional BCS (Bardeen, Cooper and Schrieffer)-type weakly-coupled superconductors (Fig. 2). As the localised character of the electronic structure fades away gradually with decreasing intermolecular distances, the size of the gap returns to the value characteristic for conventional superconductors. Decreasing the intermolecular separation in the unconventional region leads to a rise in T_c , while it leads to the long-known decrease in the conventional region. Thus the highest T_c emerges where the molecular and extended properties of the electronic structure are balanced.

The observed behaviour shows how the superconducting T_c can be tuned in fullerides, paving the way for the preparation of other molecular superconductors with enhanced T_c. Establishing the whole phase diagram of face-centered-cubic A₃C₆₀ superconductors and tracking the transition between conventional and unconventional states can provide important clues for the understanding of high-T_c superconductivity in other materials, as well. Our results are also expected to stimulate the development of improved theoretical descriptions of the A₃C₆₀ system [5], further advancing our understanding of the origins and mechanism of superconductivity in other strongly-correlated high-T_c superconductors.

References:
[1] Ruth H. Zadik, Yasuhiro Takabayashi, Gyöngyi Klupp, Ross H. Colman, Alexey Y. Ganin, Anton Potočnik, Peter Jeglič, Denis Arčon, Péter Matus, Katalin Kamarás, Yuichi Kasahara, Yoshihiro Iwasa, Andrew N. Fitch, Yasuo Ohishi, Gaston Garbarino, Kenichi Kato, Matthew J. Rosseinsky, Kosmas Prassides, “Optimized unconventional superconductivity in a molecular Jahn-Teller metal”. Science Advances, 1, e1500059 (2015). Abstract.
[2] Alexey Y. Ganin, Yasuhiro Takabayashi, Yaroslav Z. Khimyak, Serena Margadonna, Anna Tamai, Matthew J. Rosseinsky, Kosmas Prassides, “Bulk superconductivity at 38 K in a molecular system”. Nature Materials, 7, 367 (2008). Abstract.
[3] Gyöngyi Klupp, Péter Matus, Katalin Kamarás, Alexey Y. Ganin, Alec McLennan, Matthew J. Rosseinsky, Yasuhiro Takabayashi, Martin T. McDonald, Kosmas Prassides, “Dynamic Jahn-Teller effect in the parent insulating state of the molecular superconductor Cs₃C₆₀”. Nature Communications, 3, 912 (2012). Abstract.
[4] A. Wachowiak, R. Yamachika, K. H. Khoo, Y. Wang, M. Grobis, D.-H. Lee, S. G. Louie, M. F. Crommie, “Visualization of the molecular Jahn-Teller effect in an insulating K₄C₆₀ monolayer”, Science, 310, 468 (2005). Abstract.
[5] Yusuke Nomura, Shiro Sakai, Massimo Capone, Ryotaro Arita, “Unified understanding of superconductivity and Mott transition in alkali-doped fullerides from first principles”, arXiv:1505.05849v1 [cond-mat.supr-con] (2015).

Using Exciton-Polaritons as a Nonequilibrium Coolant Fluid

From left to right: Lesi Dang, Sebastian Klembt, Anna Minguzzi, Maxime Richard and Emilien Durupt.

Authors: Sebastian Klembt¹, Emilien Durupt¹, Sanjoy Datta², Thorsten Klein³, Yoan Léger⁴, Augustin Baas¹, Detlef Hommel³, Carsten Kruse³, Anna Minguzzi², Maxime Richard<sup>1

1</sup>Institut Néel, Université Grenoble Alpes and CNRS, Grenoble, France,
²Lab. de physique et modélisation des milieux condensés, Université Grenoble Alpes and CNRS, Grenoble, France,
³Universität Bremen, Bremen, Germany,
⁴Laboratoire FOTON, CNRS and INSA-Rennes, Rennes, France.

Exciton-polaritons are short-lived hybrid excitations that are obtained in solid-state (semiconductor) microcavities in the strong coupling regime. “Hybrid” stands here for the fact that polaritons have a mixed photonic and excitonic nature (excitons are hydrogenoid bound electron-hole pair excitations in semiconductors) [1]. As a result, they behave like photons interacting with each other and with their environment, like for instance thermal lattice vibrations.

From the thermodynamics point-of view, a typical gas of polaritons does not meet any criterion of thermodynamical equilibrium [2]: as particles, their lifetime is too short to reach a proper equilibration with their solid-state thermostat (i.e. thermal lattice vibrations); as waves, they cannot be considered as a black-body radiation since at the wavelength they display (in the visible), the electromagnetic vacuum can be considered as T=0K black-body, meaning that the polariton number at equilibrium is zero.

Figure: Principle of polaritonic cooling. The black curve is a typical lower polariton dispersion ω(k_||). The red spot and arrows figure the optically pumped polaritons (of energy ħω₀). Some of the pumped polaritons are scattered by thermal phonons (spring-like arrow) and thus pick up an average energy ħΩ_f(T) (i.e. the average thermal phonons energy) from the thermal phonons bath, and finally recombine by emitting photons in vacuum (yellow arrows).

In a recent experiment, we have studied how polaritons, with this nonequilibrium character, could be used as a coolant fluid to pick up heat from the surrounding thermal lattice vibrations and release it into the electromagnetic vacuum [3]. The principle of this mechanism is shown in Fig.1: polaritons are injected by resonant optical excitation in the lowest energy momentum state k_||=0 (red arrows). This state is the “ground-state” of the polaritonic subsystem, in the sense that polaritons cannot have a lower total energy.

It thus behaves as a “cold” fluid (an effective injected polariton temperature T_p=4K can be defined) [4] interacting with the much hotter gas (T= 20K to 150K) of thermal lattice vibrations (phonons). During its lifetime, a polariton can pick-up a thermal phonon’s energy by inelastic scattering, thus gaining in average an energy ħΩ_f(T) under the form of kinetic energy (yellow state in Fig.1), where ħΩ_f(T) is the average phonons energy. The most likely ensuing event is the annihilation of these excited polaritons into photons, which are emitted away from the microcavity. Thermodynamically, the net result is the transfer of local thermal vibrational energy into “escaping” electromagnetic energy. For bare photons (i.e. weakly “dressed” by the surrounding material), such an inelastic scattering with phonons is also used in the context of optical cooling [5,6] and known as anti-Stokes Raman scattering.

In our experiment we have measured the thermal flux between the microcavity thermal phonons bath in a volume and the electromagnetic vacuum by counting the number and energy of the photons emitted within this mechanism. We found some other mechanisms competing with that described above like two-photon absorption and bare excitons anti-Stokes excitation. Taking them carefully into account, we measured a net maximum positive cooling power of P_cool= 80±16µW/cm³ for a cryostat temperature T=50K.

This cooling power is still too weak to cause a sizeable temperature decrease in the present experiment which was not optimized for this purpose. However, in a better insulated environment, better optimized microcavity, and by removing every unwanted light absorbing layers (like the GaAs substrate in our case), it should be possible to increase this cooling power by orders of magnitude. This mechanism is an interesting alternative to more conventional optical cooling as for instance, it keeps on working in conditions where the latter usually turns off, like in for low temperatures. From a more fundamental point of view, this work shows that polaritons offer a unique playground to investigate the thermodynamics of nonequilibrium weakly interacting quantum fluids in contact with some environments at equilibrium (e.g. electromagnetic vacuum, phonons, and excitons).

References:
[1] Iacopo Carusotto, Cristiano Ciuti, "Quantum fluids of light". Review of Modern Physics, 85, 299 (2013). Abstract.
[2] J. Kasprzak, D.D. Solnyshkov, R. André, Le Si Dang, G. Malpuech, "Formation of an Exciton Polariton Condensate: Thermodynamic versus Kinetic Regimes". Physical Review Letters, 101, 146404 (2008). Abstract.
[3] Sebastian Klembt, Emilien Durupt, Sanjoy Datta, Thorsten Klein, Augustin Baas, Yoan Léger, Carsten Kruse, Detlef Hommel, Anna Minguzzi, Maxime Richard, "Exciton-Polariton Gas as a Nonequilibrium Coolant". Physical Review Letters, 114, 186403 (2015). Abstract.
[4] For polaritons, the terms “hot” and “cold” are not refereeing to a proper equilibrium temperature, but rather, by analogy, to the polaritons steady-state energy distribution.
[5] Mansoor Sheik-Bahae, Richard I. Epstein, "Optical refrigeration". Nature Photonics, 1, 693 (2007). Abstract.
[6] Jun Zhang, Dehui Li, Renjie Chen, Qihua Xiong "Laser cooling of a semiconductor by 40 kelvin". Nature, 493, 504 (2013). Abstract.

Core-shell Hybrid Nanostructure Based High Performance Supercapacitor Electrode

Ashutosh Kumar Singh (left) and Kalyan Mandal

Authors: Ashutosh Kumar Singh, Kalyan Mandal

Affiliation: Department of Condensed Matter Physics and Material Sciences,
S.N. Bose National Centre for Basic Sciences, Kolkata, India.

Background:

Since last decade, energy crisis has been one of the vital problems in the society due to the excessive use of fossil-fuel resources and environmental pollution. Therefore, the development of very light-weight and environment-friendly proficient energy storage devices has become the priority of the researchers and scientists for satisfying the demand of modern consumer’s hybrid electric and portable electronics devices [1,2]. In this progression, researchers have developed new type of energy storage devices called supercapacitors, also known as electrochemical capacitors which offer high power and eneergy density, high rate capability as well as superb cycle stability as compared to conventional battery and capacitors [3,4].

The supercapacitors are classified in two groups based on their charge storage method. The first group is called pseudocapacitor which involves the redox reactions of the electrode materials at the interface of electrode and electrolyte, whereas the second group is known as electric double layer capacitor which holds charge separation at the interface of electrode and electrolyte [5,6]. By changing the morphology of the electrode materials, one can manipulate the performance of a supercapacitor. The performance and quality of the supercapacitors are very much dependent on the materials and morphology used in the preparation of their electrodes. Recently, many metal oxide based materials (like RuO₂, NiO, Fe₂O₃, MnO₂, Co₃O₄, TiO₂, etc.) have been used for the fabrication of pseudocapacitor electrodes; among them NiO and Fe₂O₃ have been widely used as redox active materials for the fabrication of supercapacitor electrodes of different morphologies, such as Fe₂O₃-nanotube, Fe₂O₃-thinfilm, electrospun Co₃O₄-nanostrtuctures, porous Fe₂O₃-nanostrtuctures, NiO–nanobelts, NiO–nanoballs, NiO–nanoflowers, NiO–nanoflakes. The reasons behind the extensive use of NiO and Fe₂O₃ as supercapacitor electrode materials are: they are very stable in nature, they are non-toxic as well as environment friendly and they are very cheap and easily available.

Aim:

After having so many of supportive properties for being used as electrode materials in supercapacitors, still their reported specific capacitance values are very low compared to their own theoretical specific capacitance value and other metal oxide based electrodes. The only problem restricts them to be used as an electrode material for high performance supercapaitor is their bad electrical conductivity and we all are aware of the fact that electrode material must have high electrical conductivity for high performance supercapacitor.

Scope:

In the recent development process of supercapacitor performance, it has been found that the electrical conductivity could be improved by introducing impurities via doping of one metal oxide material with other metal oxide material. This doping process enhances the charge movement which affects the reactions at the interface of electrode and electrolyte. So far in the literature we have not found any work based on NiO and Fe₂O₃ as mixed component transition metal oxides for supercapacitor electrodes. However, keeping all the above research facts in the mind, still there exist a plenty of remarkable opportunities to enhance the electrochemical properties of NiO and Fe₂O₃ based electrodes.

Unique features of the approach:

Therefore, we report a simple fabrication technique and unique electrochemical properties of the electrode based on core/shell Fe-Ni/Fe₂O₃-NiO hybrid nanostructures (HNs). This core-shell HNs have very high aspect ratio with a porous thin nanolayer of redox active oxides which would provide a very large surface area for redox reactions at the interface of electrode and electrolyte. This would contribute to the enhancement of the ion and electron movement and performance of the supercapacitor. In addition, the core material consists of conductive FeNi nanowires (NWs) which provides the expressway for the electrons to transport to the current collector via core material.

This would automatically improve the rate capability and power density of the supercapacitor. The electrical conductivity of the electrode could be improved by introducing impurities via doping of one metal oxide (NiO) material with another metal oxide (Fe₂O₃) material. The unique feature of this electrode fabrication technique is that it doesn’t contain any extra binder material. As a result, there would be enhancement in the charge transfer kinetics [7]. This kind of fabrication technique could be applied in the fabrication process of electrodes of all energy storage devices in general.

Significant Results:

According to our anticipations, the core/shell Fe-Ni/Fe₂O₃-NiO hybrid nanostructure shows high quality supercapacitive performance in terms of specific capacitance (1415 F/g), energy density (27.6 Wh/kg), power density (10.3 kW/kg), cycling stability (remain 95% of initial specific capacitance after 3000 charge/discharge cycle) and rate capability [7]; these profound results made it a very good and unique alternative for the next generation supercapacitor electrodes.

References:
[1] Patrice Simon, Yuri Gogotsi, "Materials for electrochemical capacitors". Nature Materials, 7, 845 (2008).  Abstract.
[2] John R. Miller, Patrice Simon, Electrochemical Capacitors for Energy Management". Science 321, 651 (2008). Abstract.
[3] Zhibin Lei, Li Lu, X.S. Zhao, "The electrocapacitive properties of graphene oxide reduced by urea". Energy & Environmental Science, 5, 6391 (2012). Abstract.
[4] Sheng Chen, Junwu Zhu, Xiaodong Wu, Qiaofeng Han, Xin Wang, "Graphene Oxide−MnO2 Nanocomposites for Supercapacitors". ACS Nano 4, 2822 (2010). Abstract.
[5] Wei Chen, R.B. Rakhi, Liangbing Hu, Xing Xie, Yi Cui, H.N. Alshareef, "High-Performance Nanostructured Supercapacitors on a Sponge". Nano Letters, 11, 5165 (2011). Abstract.
[6] Raghavan Baby Rakhi, Wei Chen, Dongkyu Cha, H. N. Alshareef, "Nanostructured Ternary Electrodes for Energy-Storage Applications". Advanced Energy Materials, 2, 381 (2012). Abstract.
[7] Ashutosh K. Singh, Kalyan Mandal, "Engineering of high performance supercapacitor electrode based on Fe-Ni/Fe2O3-NiO core/shell hybrid nanostructures". Journal of Applied Physics, 117, 105101 (2015). Abstract.

Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor

From Left to Right: (top row) Stevan Nadj-Perge, Ilya K. Drozdov, Jian Li, Hua Chen ; (bottom row) Sangjun Jeon, Allan H. MacDonald, B. Andrei Bernevig, Ali Yazdani.

Authors: Stevan Nadj-Perge¹, Ilya K. Drozdov¹, Jian Li¹, Hua Chen², Sangjun Jeon¹, Jungpil Seo¹, Allan H. MacDonald², B. Andrei Bernevig¹, Ali Yazdani¹.

Affiliation
¹Joseph Henry Laboratories and Dept of Physics, Princeton University, USA.
²Department of Physics, University of Texas at Austin, USA.

Link to Yazdani Lab >>
Link to Allan H. MacDonald's Group >>

In 1937 Italian scientist Ettore Majorana, one of the most promising theoretical physicists at that time, proposed a hypothetical fermionic excitation, now called Majorana fermion, which has a property that it is its own anti-particle [1]. Ever since significant efforts were invested in finding an elementary particle described by Majorana. While present for many years in particle physics community, it was only in 2001 that Alexei Kitaev suggested an intriguing possibility that a type of a quasi-particle, a condensed matter analog of the Majorana fermion could exist [2]. Such quasi-particle would emerge as a zero energy excitation localized at the boundary of a one dimensional topological superconductor. Following his seminal work various systems were proposed as a potential platform for realization of Majorana quasi-particles. Apart from fundamental scientific interest, the motivation for investigating Majorana bound states partly relies on their potential for use for quantum computing [3,4].

Past 2Physics article by Ali Yazdani :
August 25, 2013: "Visualizing Nodal Heavy Fermion Superconductivity"
by Brian Zhou, Shashank Misra, and Ali Yazdani.

Previous to our experiments, the most promising experimental route to realize these elusive bound states was based on semiconductor-superconductor interfaces in which Majorana fermions would appear as conductance peaks at zero energy [5,6]. Indeed experiments in 2012 reported zero energy conductance peaks suggesting presence of Majorana modes in these type of systems [7,8], however, alternative explanations related to disorder and Kondo phenomena proposed latter could not be fully ruled out. It is worth noting that in these interfaces spatial information about localized excitations is very hard to obtain.

Fig. 1: (A) Schematic of the proposal for realization and detection of Majorana states: A ferromagnetic atomic chain is placed on the surface of strongly spin-orbit–coupled superconductor and studied using STM. (B) Band structure of a linear suspended Fe chain before introducing spin-orbit coupling or superconductivity. The majority spin-up (red) and minority spin-down (blue) d-bands labeled by azimuthal angular momentum m are split by the exchange interaction J (degeneracy of each band is noted by the number of arrows). a, interatomic distance. (C) Regimes for trivial and topological superconducting phases are identified for the band structure shown in (B) as a function of exchange interaction in presence of SO coupling. The value J for Fe chains based on density functional calculations is noted. μ is the chemical potential.

Building upon previous proposal to realize Majorana modes in an array of magnetic nanoparticles [9], we proposed to use a chain of magnetic atoms coupled to a superconductor [10]. The key advantage of this platform is that the experimentally properties of this system can easily be studied using standard scanning tunneling microscopy (STM) technique. While ours and other follow-up initial proposals [11-16] consider specific orientation of the magnetic moments, the approach works also for ferromagnetic atomic chains as long as it is coupled to a superconductor with strong spin-orbit coupling (Fig. 1A) [17]. In this case, the large exchange interaction results in a band structure of the chains such that majority spin band is fully occupied while the Fermi level is in the minority spin bands. For example the electronic structure of a linear Iron (Fe) ferromagnetic atomic chain is shown in Fig. 1B. Considering only d-orbitals which are spin-polarized it is easy to show that many of the bandstructure degeneracies are lifted and that for large range of parameters, chemical potential and the exchange energy, such chains are in topologically non-trivial regime characterized by the odd number of crossing at the Fermi level (Fig 1C). When placed on the superconducting substrate with strong-spin orbit coupling the resulting superconductivity on the chain will necessarily be topological in nature resulting in zero energy Majorana bound states located at the chain ends.

Fig. 2: (A) Topograph of the Pb(110) surface after growth of Fe, showing Fe islands and chains indicated by white arrows and atomically clean terraces of Pb (regions with the same color) with size exceeding 1000 Å. (Lower-right inset) Anisotropic atomic structure of the Pb(110) surface (Upper-left insets) images of several atomic Fe chains and the islands from which they grow (scale bars, 50 Å). (B) Topography of the chain colorized by the conductance at H= ±1 T from low (dark blue) to high conductance (dark red). (C) Difference between conductance on and off the chain showing hysteresis behavior. (D and E) Atomic structure of the zigzag chain, as calculated using density functional theory. The Fe chain structure that has the lowest energy in the calculations matches the structural features in the STM measurements, a_B is the Bohr radius.

We have developed a way to grow iron atomic chains on the surface of lead (Pb) which, due to heavy atomic mass, is expected to have strong spin-orbit coupling. For this purpose we used Pb(110) crystallographic surface orientation which has characteristic anisotropy (Fig. 2(A) lower left inset). When a sub-monolayer of Fe is evaporated and slight annealing, the anisotropy of the substrate could trigger growth of one-dimensional atomic chains. We investigated the resulting structures by using STM at cryogenic temperatures (temperature was 1.4K in the experiment). On relatively large atomically ordered regions of the Pb(110) surface we observed self-assembled islands as well as single atom wide chains of Fe. Depending on growth conditions, we find Fe chains as long as 500 Å with ordered regions approaching 200 Å. In order to confirm ferromagnetic order on the chain we have performed spin-polarized measurements using bulk antiferromagnetic Chromium STM tips. Tunneling conductance (dI/dV) at a low bias voltage as a function of the out-of-plane magnetic field shows contrast for opposite fields (Fig. 2B) and a hysteresis behavior (Fig. 2C, note that no hysteresis is observed on the Pb substrate). The observed hysteresis loop corresponds to the tunneling of electrons between two magnets with the field switching only one of them at around 0.25 T.

We also observed the variation of the spin-polarized STM signal along the chain which is likely due to its electronic and structural properties. Indeed, both topographic features and periodicity of signal variation could be very well explained by our theory collaborators who performed density functional theory modeling. Their calculations suggested that our chains have zig-zag structure which explains both topographic information obtained using STM and matches well with our spin-polarized measurements (Fig. 2D and 2E).

Fig. 3: (A) STM spectra measured on the atomic chain at locations corresponding to those indicated in (B) and (C). For clarity, the spectra are offset by 100 nS. The red spectrum shows the zero-bias peak at one end of the chain. The gray trace measured on the Pb substrate can be fitted using thermally broadened BCS superconducting density of states (dashed gray line, fit parameters Δs = 1.36 meV, T = 1.45 K). (B and C) Zoom-in topography of the upper (B) and lower end (C) of the chain and corresponding locations for spectra marked (1 to 7). Scale bars, 25 Å. (D and E) Spectra measured at marked locations, as in (B) and (C). (F) Spatial and energy-resolved conductance maps of another atomic chain close to its end, which shows similar features in point spectra as in (A). The conductance map at zero bias (middle panel) shows increased conductance close to the end of the chain. Scale bar, 10 Å.

After establishing basic properties of our chains we investigated low-energy excitations using spatial spectroscopic mapping, see Fig 3. While on the surface of bare Pb(110), there is clear structure of the superconducting gap on the Fe atomic chain, the presence of the in-gap states is predominant (Fig. 3A). Most notably a peak close to zero bias voltage is observed near the chain end together with asymmetric less-developed gap-like structure in the middle of the chain (Fig. 3D and Fig. 3E). Both spatially resolved spectra and the spectroscopic maps at low bias voltage show signatures expected from Majorana bound states (Fig. 3F). The ability to correlate the location of the zero bias conductance peak with the end of the atomic chains is one of the main experimental results of our work. This is one of the basic requirements for interpreting that this feature is associated with the predicted Majorana bound state of a topological superconductor. In addition to robust observation of the zero bias peaks in many chains, we have performed several control experiments to eliminate other potential effects which may give similar looking signatures. For example, when superconductivity is suppressed by applying small magnetic field, the spectrum on the chain becomes featureless in contrast to what would be expected for Kondo effect. Also for very short chains zero biased peaks were not observed, ruling out trivial effects related to the chain ends. Furthermore, in order to increase experimental resolution we took measurements with superconducting tip which also confirm the over picture consistent with Majorana bound states in this system.

The observed spectroscopic signatures are consistent with the existence of Majorana bound states in our system. An obvious extension of our experiments is to create two dimensional islands and search for propagating Majorana modes or, for example, investigate other systems with both even and odd number of band crossing at Fermi level in order to further test the concept behind our study. Ultimately the future experiments will focus on manipulation of Majorana bound states in this system [18].

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