Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session Z46: Theory of Majorana States in Superconductors |
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Chair: Greg Boyd, Georgetown University Room: Mile High Ballroom 4E |
Friday, March 7, 2014 11:15AM - 11:27AM |
Z46.00001: Majorana surface and vortex states in three dimensional nodal noncentrosymmetric superconductors Po-Yao Chang, Shunji Matsuura, Andreas Schnyder, Shinsei Ryu We investigate Majorana surface and vortex states in three dimensional noncentrosymmetric superconductors (NCSs) that have antisymmetric spin-orbit coupling and exhibit an admixture of spin singlet and triplet superconducting pairings. By exact diagonalization of Bogoliubov-de Gennes Hamiltonians, we show different scenarios of Majorana surface and vortex states, which coexist with the surface flat bands originated from the nodal rings in the bulk: (i) there are no additional surface and vortex states; (ii) there are a Fermi arc on the surface and a flat band localized at the core of a vortex line; (iii) there are a Majorna cone state protected by a ${Z}_2$ topological invariant on the surface and a helical state localized at the core of a vortex line. By turning off the singlet superconducting pairing, these three different scenarios adiabatically connect to a trivial gapped superconductor, a nodal superconductor with two nodal points (a superconducting and time-reversal symmetric analogue of Weyl semimetal), and a fully gapped topological superconductor, respectively. The latter indicates NCSs can share interesting topological properties with fully gapped topological superconductors and widens the possibility of searching physics of topological superconductors in NCSs. [Preview Abstract] |
Friday, March 7, 2014 11:27AM - 11:39AM |
Z46.00002: Spin texture of topological superconductor surface states Philip Brydon, Andreas Schnyder, Carsten Timm Noncentrosymmetric superconductors (NCS), where singlet and triplet pairing coexist, are examples of topologically non-trivial gapless systems, and hence display nondegenerate flat-band surface states at certain surfaces [1]. Using quasiclassical methods, we construct the edge-state wavefunctions and calculate the edge-state spectra [2]. We show that the edge states, in particular the flat bands, generically show strong spin polarization which is odd in the surface momentum [3]. The spin polarization is mostly fixed by the spin-orbit coupling, but also depends upon the relative strength of singlet to triplet pairing. Not only does the spin polarization suppress the effect of impurity scattering, but it also is responsible for strong edge currents at interfaces with ferromagnets [3]. [1] A. P. Schnyder and S. Ryu, Phys. Rev. B {\bf 84}, 060504(R) (2011). [2] P. M. R. Brydon, A. P. Schnyder, and C. Timm, Phys. Rev. B {\bf 84}, 020501(R) (2011); A. P. Schnyder, P. M. R. Brydon, and C. Timm, Phys. Rev. B {\bf 85}, 024522 (2012). [3] A. P. Schnyder, C. Timm, and P. M. R. Brydon, Phys. Rev. Lett. {\bf 111}, 077001 (2013). [Preview Abstract] |
Friday, March 7, 2014 11:39AM - 11:51AM |
Z46.00003: Magnetic Field Response and Chiral Symmetry of Time Reversal Invariant Topological Superconductors Eugen Dumitrescu, Jay D. Sau, Sumtanta Tewari We study the magnetic ?eld response of the Majorana Kramers pairs of a one-dimensional time-reversal invariant (TRI) superconductors (class DIII) with or without a coexisting chirality symmetry. For unbroken TR and chirality invariance the parameter regimes for nontrivial values of the ($Z_2$) DIII-invariant and the ($Z$) BDI chiral invariant coincide. However, broken TR may or may not be accompanied by broken chirality, and if chiral symmetry is unbroken the pair of Majorana fermions (MFs) at a given end survives the loss of TR symmetry in an entire plane perpendicular to the spin-orbit coupling field. Conversely, we show that broken chirality may or may not be accompanied by broken TR, and if TR is unbroken, the pair of MFs survives the loss of broken chirality. In addition to explaining the anomalous magnetic field response of all the DIII class TS systems proposed in the literature, we provide a realistic route to engineer a ``true'' TR-invariant TS, whose pair of MFs at each end is split by an applied Zeeman field in arbitrary direction. We also prove that, quite generally, the splitting of the MFs by TR-breaking fields in TRI superconductors is highly anisotropic in spin space, even in the absence of the topological chiral symmetry. [Preview Abstract] |
Friday, March 7, 2014 11:51AM - 12:03PM |
Z46.00004: Planar tunneling spectroscopy of topological insulators and superconductors Wan Kyu Park, C. Jones, L. Sun, M. Worek, R. Tapping, L.H. Greene, J. Schneeloch, R.D. Zhong, Z.J. Xu, G. Gu Tunneling spectroscopy has been widely adopted for the study of electronic density of states. Using this technique, we investigate topological surface states and superconducting proximity effect in topological insulators and superconductors. Planar tunnel junctions are prepared via sputter deposition of Nb and/or AlO$_{\mathrm{x}}$ tunnel barrier onto cleaved or polished ({\&} ion-beam cleaned) surfaces of these materials. Interplay between superconducting pair potential in Nb and spin-momentum locking in the surface states of (Bi,Sb)$_{2}$Se$_{3}$, a confirmed topological insulator, is studied as a function of the Nb layer thickness. Our results have shown that tunneling conductance does not reveal any new features down to 150 {\AA} of Nb. Further investigations are under way to clarify the influence of interface cleanliness as well as the location of the chemical potential. Measurements of tunneling conductance into the surface states of some known and candidate topological insulators will also be discussed. [Preview Abstract] |
Friday, March 7, 2014 12:03PM - 12:15PM |
Z46.00005: BDI Class Topological Superconductors and Generating Correlated Spin Currents in Quantum Anomalous Hall insulators James He, Jiansheng Wu, Ting-Pong Choy, Xiong-Jun Liu, Y. Tanaka, K.T. Law In this work, we show that a one dimensional AIII class topological insulator, which supports fermionic end states, can be turned into a BDI class topological superconductor (TS) through proximity effect. The resulting BDI TS has two topological phases with one or two Majorana end states at each end of the wire respectively. Interestingly, in the phase with two Majorana end states, the BDI TS causes zero-bias conductance dips in tunneling spectroscopy experiments due to destructive interference of Andreev reflection amplitudes caused by the two Majorana end states. More importantly, this BDI TS can induces resonant crossed Andreev reflections in a normal lead/BDI TS/ normal lead junction, in which an electron from one lead is reflected as a hole in the other lead with probability of unity. Moreover, we show that the currents in the two normal leads are perfectly correlated and spin polarized with opposite spin-polarization. Therefore, BDI TS can be used to generate correlated spin currents. We demonstrate that a quantum Anomalous Hall insulator in proximity to a superconductor can be used to realize the proposed BDI TS. [Preview Abstract] |
Friday, March 7, 2014 12:15PM - 12:27PM |
Z46.00006: Majorana Fermion induced Selective Equal Spin Andreev Reflections Kam Tuen Law, James He, Tai Kai Ng, Patrick Lee It is known that a Majorana fermion end state of a topological superconductor can induce resonant Andreev reflections at a normal lead/topological superconductor junction. However, the details of the Andreev reflection processes have not been studied before. Surprisingly, in this work, we show that Majorana fermions induce a special type of Andreev reflections we call \textit{selective equal spin Andreev reflections }(SESARs). In SESAR processes, incoming electrons with certain spin polarization in the normal lead are reflected as counter-propagating holes with the same spin. More importantly, the spin polarization direction of the electrons, which can undergo Andreev reflections, is selected by the Majorana fermion end state. On the contrary, electrons with opposite spin polarization are always reflected as electrons with unchanged spin and they cannot undergo Andreev reflections. Due to SESARs, the current in the normal lead is spin-polarized. Therefore, a topological superconductor, which supports Majorana fermions, can be used as a novel device to create fully spin-polarized currents in paramagnetic leads. We point out that SESARs can also be used to detect Majorana fermions in topological superconductors. [Preview Abstract] |
Friday, March 7, 2014 12:27PM - 12:39PM |
Z46.00007: Realizing Majorana zero mode by Proximity Effect between Topological Insulator and d-wave Superconductor Zixiang Li, Cheung Chan, Hong Yao We study the proximity effect between a topological insulator (TI) and a d-wave superconductor systematically. We find that because of the difference of lattice structures between the topological insulator and the d-wave superconductor, a finite s-wave component, coexisting with d-wave component, in superconducting pairing emerges in the surface states of topological insulators. Moreover, we show that disorder has significant effects on suppressing d-wave pairing and enhancing s-wave pairing in topological insulators. This result qualitatively explains the recent experimental work, which reports the nearly isotropic pairing gap on the TI's surface states induced by proximity with a d-wave superconductor [Nature Physics 9, 621-625 (2013)]. Finally, we consider the system of TI and d-wave superconductor in presence of vortices and find evidences of Majorana zero mode in the vortex core, which may be detectable in future experiments. [Preview Abstract] |
Friday, March 7, 2014 12:39PM - 12:51PM |
Z46.00008: Zero-bias peak and soft superconducting gap in differential conductance calculations of semiconductor-based Majorana nanostructures John Stenger, Tudor Stanescu Recent experiments on semiconductor wire-superconductor hybrid structures aiming to realize and detect zero-energy Majorana bound states have revealed the presence of a substantial sub-gap conductance, in addition to the predicted zero-bias anomaly that appears, as expected, above a certain critical magnetic field. The origin of this soft gap is controversial and remains highly problematic. It has recently been suggested [1] that the coupling of the semiconductor nanowire to a large normal-metal lead is, in fact, the reason for the soft gap. Here, we confirm this mechanism by explicitly calculating the differential conductance of a normal metal -- semiconductor wire -- superconductor hybrid structure and we discuss the dependence of the soft gap on the relevant system parameters. \\[4pt] [1] Tudor D. Stanescu, Roman M. Lutchyn, and S. Das Sarma, arXiv:1311.2075 (2013). [Preview Abstract] |
Friday, March 7, 2014 12:51PM - 1:03PM |
Z46.00009: Local Adiabatic Mixing of Majorana Kramers pairs in DIII wires Konrad W\"{o}lms, Ady Stern, Karsten Flensberg We consider coherence of localized Kramers pairs of Majorana fermions in a DIII topological superconductors and show that they get mixed by adiabatic processes, even if the instantaneous Hamiltonian stays in the DIII class at each instant of time. In particular, we compute the associated Berry curvature analytically for an illustrative toy model as well as numerically for a simple DIII wire model and discuss the general conditions for the mixing to be finite. The mixing occurs for a wide range of perturbations, for example even by electrical noise alone. Our calculation thus shows that quantum information stored in time-reversal symmetric Majorana Kramers pairs are not topologically protected. [Preview Abstract] |
Friday, March 7, 2014 1:03PM - 1:15PM |
Z46.00010: Experimental search for Majorana fermions in chains of magnetic atoms on a superconductor Stevan Nadj-Perge, Ilya Drozdov, Sangjun Jeon, Jungpil Seo, Andrei Bernevig, Ali Yazdani The ongoing search for Majorana fermions (MF) is currently hindered by various disorder effects which can mimic signatures of MF modes. To overcome this problem, cleaner systems are needed in which MF modes can be readily distinguished from disorder induced effects. In this talk I will present novel experimental approach to realize MF modes in chains of magnetic atoms on the surface of an s-wave superconductor. Our experimental efforts are motivated by model calculations which show that such chains can support topological superconductivity with MF end modes [1]. Surprisingly, even short chains consisting of tens of atoms can host well resolved Majorana modes under suitable conditions depending on the relative spin orientations of adjacent atoms. We realize magnetic chains using self-assembled growth technique and probe their electronic structure using scanning tunneling microscopy. Results from spatially resolved spectroscopic mapping reveal zero energy modes at the chain ends, consistent with the existence of MF modes in this system. [1] S. Nadj-Perge, I. K. Drozdov, B. A. Bernevig., Ali Yazdani, Phys. Rev. B 88, 020407(R) (2013). [Preview Abstract] |
Friday, March 7, 2014 1:15PM - 1:27PM |
Z46.00011: Majorana bound states in two-channel time-reversal-symmetric nanowire systems Erikas Gaidamauskas, Jens Paaske, Karsten Flensberg In this work consider time-reversal-symmetric two-channel semiconducting nanowires proximity coupled to the s-wave superconductor. We made an analysis for the conditions for a topologicaly non-trivial phase, and find that necessary requirements are 1) the determinant of the pairing matrix in channel space must be negative, 2) spatial inversion symmetry must be broken, and 3) the two channels must have different spin-orbit couplings. The first condition can be realized in semiconducting nanowire systems with different tunnel couplings between the channels and superconductor, while the parity can be broken by tuning the chemical potentials of the channels. For the case of parallel spin-orbit directions, we derive the expression for the topological invariant applying the block diagonalization of the Hamiltonian into the two chiral symmetric blocks. Making the projection to the low-energy sector we solve for the bound states explicitly and investigate the influence of the magnetic field. [Preview Abstract] |
Friday, March 7, 2014 1:27PM - 1:39PM |
Z46.00012: Tunneling spectroscopy of a spiral Luttinger liquid in contact with superconductors Dong E. Liu, Alex Levchenko One-dimensional wires with Rashba spin-orbit coupling, magnetic field, and strong electron-electron interactions are described by a spiral Luttinger liquid model. We develop a theory to investigate the tunneling density of states into a spiral Luttinger liquid in contact with superconductors at its two ends. This approach provides a way to disentangle the delicate interplay between superconducting correlations and strong electron interactions. If the wire-superconductor boundary is dominated by Andreev reflection, we find that in the vicinity of the interface the zero-bias tunneling anomaly reveals a power law enhancement with the unusual exponent. This zero-bias due to Andreev reflections may coexist and thus mask possible peak due to Majorana bound states. Far away from the interface strong correlations inherent to the Luttinger liquid prevail and restore conventional suppression of the tunneling density of states at the Fermi level, which acquires a Friedel-like oscillatory envelope with the period renormalized by the strength of the interaction. [Preview Abstract] |
Friday, March 7, 2014 1:39PM - 1:51PM |
Z46.00013: Competitive pairing effects on interacting fermions: superconductivity, topology, and entanglement entropy Jiansheng Wu, Ching-Kai Chiu, Kuei Sun, Hsiang-Hsuan Hung We study spin-half fermions in one-dimensional chain lattices in which we identify three triplet and one singlet channels independently tunable for the Cooper pairing. We conduct a comprehensive analysis on the model, including a mean-field treatment on a large-size case and an exact-diagonalization method on a finite-size case. We find that the competitive pairing effects can lead to singlet, triplet and mixed superconducting states in both cases. The mean-field Hamiltonian has $Z_2$ topological invariant for symmetry class DIII determined by these pairings. The tunability of our model makes it particularly interesting for studying the interaction effects on one-dimensional topological superconductors in search for Majorana fermions. Furthermore, we consider a two-dimensional interacting model, the mean-field Hamiltonian of which corresponds to a topological superconductors. Its topological order can be confirmed by length-independent entanglement entropy. [Preview Abstract] |
Friday, March 7, 2014 1:51PM - 2:03PM |
Z46.00014: Majorana states in helical Shiba chains and ladders Teemu Ojanen, Kim Poyhonen, Alex Westsrom, Joel Rontynen Motivated by recent proposals to realize Majorana bound states in chains and arrays of magnetic atoms deposited on top of a superconductor, we study the topological properties of various chain structures, ladders and two-dimensional arrangements exhibiting magnetic helices. We show that magnetic domain walls where the chirality of a magnetic helix is inverted support two protected Majorana states giving rise to a tunneling conductance peak twice the height of a single Majorana state. Multiple overlapping Majorana states are protected by chiral symmetry which is present in systems exhibiting planar magnetic textures. Thus the topological properties of coupled chains exhibit nontrivial behaviour as a function of the number of chains beyond the even-odd dichotomy expected from ${Z}_2$ classification. In addition, it is possible that a ladder of two or more coupled chains exhibit Majorana edge states even when decoupled chains are trivial. [Preview Abstract] |
Friday, March 7, 2014 2:03PM - 2:15PM |
Z46.00015: Superconductor with intrinsic topological order induced by Coloumb repulsion Evelyn Tang, Xiao-Gang Wen We study a lattice system which at commensurate fillings supports fractional quantum Hall states; here we explore what happens at incommensurate fillings. As excitations are believed to be anyons, we assume that doping the system creates a finite density of anyon excitations. The presence of a lattice allows access to a new regime in which the anyon kinetic energy dominates. This leads to a gas of anyons which can condense to form a charged superfluid, driven by repulsive interactions and time-reversal symmetry breaking. We find ground states including those with intrinsic topological order, i.e. containing fractionalized quasiparticles. The relative stability of these states are compared using different flux-attachment approaches; lastly we discuss their physical properties and methods for experimental detection. [Preview Abstract] |
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