Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session Y45: Topological Superconductivity: TheoryFocus

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Sponsoring Units: DMP Chair: Lukasz Fidowski, State University of New York, Stony Brook Room: 392 
Friday, March 17, 2017 11:15AM  11:51AM 
Y45.00001: Edge quantum criticality and emergent supersymmetry in topological phases. Invited Speaker: Hong Yao, ZiXiang Li, YiFan Jiang Proposed as a fundamental symmetry describing our universe, spacetime supersymmetry (SUSY) has not been discovered yet in nature. Nonetheless, it has been predicted that SUSY may emerge in lowenergy physics of quantum materials such as topological superconductors and Weyl semimetals. Here, by performing stateoftheart signproblemfree Majorana quantum Monte Carlo (QMC) simulations of an interacting 2D topological superconductor, we show convincing evidences that the N$=$1 SUSY emerges at its edge quantum critical point (EQCP) while its bulk remains gapped and topologically nontrivial. Remarkably, near the EQCP, we find that the edge Majorana fermion acquires a mass which is identical with that of its bosonic superpartner. To the best of our knowledge, this is the first observation that fermions and bosons have equal dynamicallygenerated masses, a hallmark of emergent SUSY. We further discuss experimental signatures of such EQCP and the associated edge SUSY. Ref: ZiXiang Li, YiFan Jiang, Hong Yao, arXiv:1610.04616. [Preview Abstract] 
Friday, March 17, 2017 11:51AM  12:03PM 
Y45.00002: ThreeDimensional Majorana Fermions in Chiral Superconductors Vladyslav Kozii, Jorn Venderbos, Liang Fu Through a systematic symmetry and topology analysis we establish that threedimensional chiral superconductors with strong spinorbit coupling and oddparity pairing generically host lowenergy nodal quasiparticles that are spinnondegenerate and realize Majorana fermions in three dimensions. By examining all types of chiral Cooper pairs with total angular momentum $J$ formed by Bloch electrons with angular momentum $j$ in crystals, we obtain a comprehensive classification of gapless Majorana quasiparticles in terms of energymomentum relation and location on the Fermi surface. We show that the existence of bulk Majorana fermions in the vicinity of spinselective point nodes is rooted in the nonunitary nature of chiral pairing in spinorbitcoupled superconductors. We address experimental signatures of Majorana fermions, and find that the nuclear magnetic resonance spin relaxation rate is significantly suppressed for nuclear spins polarized along the nodal direction as a consequence of the spinselective Majorana nature of nodal quasiparticles. Furthermore, Majorana nodes in the bulk have nontrivial topology and imply the presence of Majorana bound states on the surface that form arcs in momentum space. [Preview Abstract] 
Friday, March 17, 2017 12:03PM  12:15PM 
Y45.00003: Characterization of Intrinsically Fermionic Topological Phases in MajoranaDimer models Brayden Ware, Jun Ho Son, Meng Cheng, Ryan Mishmash, Jason Alicea, Bela Bauer In this talk, we explore an exactly solvable model of resonating dimers decorated with Majorana modes. The model realizes an intriguing Isinglike topological order yet possesses a fully gapped edgea possibility that is unique to fermions and has no analogue in bosonic systems. Based on an analysis of fermionparity defects and fermionparity twisted boundary conditions, we argue that this phase can be described as the product of a chiral Ising theory and a topological $p_x  ip_y$ superconductor. We also discuss an eightfold hierarchy of such phases and show how to unambiguously determine the topological order in numerical calculations using modular transformations of minimally entangled ground states on the torus. [Preview Abstract] 
Friday, March 17, 2017 12:15PM  12:27PM 
Y45.00004: Ising Anyons in frustrationfree MajoranaDimer models: Construction and Spectrum Jun Ho Son, Brayden Ware, Meng Cheng, Ryan Mishmash, Jason Alicea, Bela Bauer Dimer models have long been a fruitful playground for understanding topological physics. This talk introduces a new class—termed Majoranadimer models—wherein bosonic dimers are decorated with pairs of Majorana modes. We show that it is possible to construct a gapped, frustrationfree, and analytically tractable Majoranadimer Hamiltonians on the triangular and Fisher lattices. By analyzing the lowenergy spectrum, we establish the following properties: (1) edges are fully gapped, (2) the bulk supports deconfined Ising anyons, and (3) on a torus the system admits threefold groundstate degeneracy. From these, we suggest that these Hamiltonians possess nonAbelian Ising topological order that generalizes the $Z_2$ topological order familiar from pure dimer models. [Preview Abstract] 
Friday, March 17, 2017 12:27PM  12:39PM 
Y45.00005: Majoranadecorated domain wall construction of fermionic SPTs Nicolas Tarantino, Lukasz Fidkowski A decorated domain wall construction generates a symmetryprotected topological phase (SPT) by begin in a symmetrybroken phase with multiple domains, binding a nontrivial lower dimensional phase to the domain boundary, and then restoring the symmetry by proliferating the domain walls. In this talk, I will sketch how this technique was used to build a commuting projector model of a unitary $\mathbb{Z}_2$ protected fermionic SPT\footnote{NT and L. Fidkowski, "Discrete spin structures and commuting projector models for twodimensional fermionic symmetryprotected topological phases", Phys. Rev. B 94, 115115 (2016)}. The symmetry fluxes in this phase, which can be thought of as open ends of domain walls, support Majorana zero modes, and so the domain walls should support a 1D phase which supports Majoranas on open boundaries, the Kitaev chain. Curiously, implementing this consistently requires the introduction of a Kasteleyn orientation, a lattice equivalent of a spin structure, to avoid accidentally breaking fermion parity. Time permitting, I will discuss known and possible generalizations of this construction. [Preview Abstract] 
Friday, March 17, 2017 12:39PM  12:51PM 
Y45.00006: Duality of a compact topological superconductor model and the Witten effect Flavio Nogueira, Zohar Nussinov, Jeroen van den Brink We consider a compact abelian Higgs model in 3+1 dimensions with a topological axion term and construct its dual theories for both bulk and boundary at strong coupling. The model may be viewed as describing a superconductor with magnetic monopoles, which can also be interpreted as a field theory of a topological Mott insulator. We show that this model is dual to a noncompact topological field theory of particles and vortices. It has exactly the same form of a model for superconducting cosmic strings with an axion term. We consider the duality of the boundary field theory at strong coupling and show that in this case $\theta$ is quantized as $8\pi n/m$ where $n$ and $m$ are the quantum numbers associated to electric and magnetic charges. These topological states lack a noninteracting equivalent.\\ \\F. S. Nogueira, Z. Nussinov, and J. van den Brink, Phys. Rev. D {\bf 94}, 085003 (2016). [Preview Abstract] 
Friday, March 17, 2017 12:51PM  1:03PM 
Y45.00007: Boundary Green's function of topological phases Yimu Bao, Yang Peng, Felix von Oppen We study the properties of the boundary Green’s function of topological electronic systems by a recursive approach. The recursion flows to the boundary Green’s function of the infinite system and can be implemented analytically in simple cases. We show how the recursion yields the topologically protected edge mode and describes the phase diagram as well as the topological phase transition. We explore the uniqueness of the resulting boundary Green functions. [Preview Abstract] 
Friday, March 17, 2017 1:03PM  1:15PM 
Y45.00008: Exactly solvable Majoranalike ground states in numberconserving models Zhiyuan Wang, Youjiang Xu, Han Pu, Kaden Hazzard Majorana fermions have sparked interest in condensed matter and cold atoms as emergent quasiparticles with fundamentally new properties, in particular nonAbelian statistics. However, most theoretical calculations start with a Bogoliubov mean field approximation from which they show that the resulting model possesses Majorana states. It then remains an open question whether and when this mean field approximation is valid. We make progress towards this question in two ways. First, we demonstrate a model in which mean field theory incorrectly predicts a gapped phase with Majorana ground states, in contrast to the gapless phase that we find from numerically exact DMRG calculations. Secondly, we construct new families of interacting models where the mean field treatment happens to be exact. Significantly, these exactly solvable models are numberconserving but nevertheless can be shown to host robust Majoranalike degenerate ground states and exhibit nonabelian statistics. These results give a deeper conceptual understanding of how Majorana fermions can be realized in nature. [Preview Abstract] 
Friday, March 17, 2017 1:15PM  1:27PM 
Y45.00009: NonAbelian Majorana modes protected by an emergent 4D topological invariant Cheung Chan, XiongJun Liu The search for topological superconductors and nonAbelian Majorana modes ranks among the most fascinating topics in condensed matter physics. There now exist several fundamental superconducting phases which host symmetry protected or chiral Majorana modes. The latter, namely the chiral Majorana modes are protected by topological Chern numbers in even dimensions. Here we propose to observe a new type of chiral Majorana modes by realizing FFLO state in a Weyl semimetal which breaks timereversal symmetry. Without symmetry protection, the 3D gapped FFLO phase is topologically trivial. However, we find that a vortex line generated in such phase can host chiral Majorana modes, which are shown to be protected by an emergent 4D topological invariant, namely the second Chern number of a synthetic 4D system generalized from the current FFLO phase. We further show that these chiral modes in the vortex rings obey nonAbelian statistics, similar as the vortices in a $p+ip$ superconductor. This work opens a new avenue in search for new type Majorana modes and nonAbelian loop braiding statistics which can be applied to topological quantum computation. [Preview Abstract] 
Friday, March 17, 2017 1:27PM  1:39PM 
Y45.00010: SYK model on the surface of 3d TI Dmitry Pikulin, Marcel Franz I will present the study of SachdevYeKitaev (SYK) model as realized on the surface of threedimensional topological insulator. I will discuss the possible paths to realizations of the model in a vortex lattice or Corbino disk geometry. I will comment on the randomness in 2Majorana and 4Majorana versions of the model, and the crossover between the two limiting case. I will finish with discussing measurable signatures of the model. [Preview Abstract] 
Friday, March 17, 2017 1:39PM  1:51PM 
Y45.00011: SpinPairing Correlations and Spin Polarization of Majorana Bound States in Quantum Spin Hall Systems. Kunhua Zhang, Zhenhua Qiao We demonstrate that zeroenergy Majorana bound state in ferromagnetic insulator (FMI)superconductor (SC) junction formed on the edge states of a quantum spin Hall insulator exhibits three types of spintriplet pairing correlations, and an additional weak spinsinglet pairing correlation is generated in the presence of coupling between two Majorana bound states in FMISCFMI junction. We show that the positionindependent local spin polarization of zeroenergy Majorana bound state in ferromagnetic insulator possesses opposite directions in two ferromagnetic insulators when the coupling between the corresponding Majorana bound states is considered. When spin directions of the incident electron and the reflected hole are identical, which two are antiparallel to that of MBS in ferromagnetic insulator, equalspin Andreev reflection gives the widest resonance peak. Conversely, equalspin Andreev reflection results in the narrowest peak. These signatures can facilitate the experimental detection of spintriplet correlations and spin polarization of Majorana bound states. [Preview Abstract] 
Friday, March 17, 2017 1:51PM  2:03PM 
Y45.00012: Gravitational phenomena Weyl semimetal interfaces Yaron Kedem, Emil Bergholtz After the discovery of TaAs as a Weyl semimetal, a different type of Weyl fermions was predicted and shortly after found in several materials (including MoTe2, LaAlGe, and WTe2). In this so called typeII Weyl semimetal, the spectral cone is heavily tilted such that it is crosses the Fermi energy. For a fundamental Weyl particle, this typeIIs tilting is prohibited by Lorentz symmetry, which is absent in condensed matter systems, but introducing a gravitational background would break the symmetry and allow tilting. The metric that is needed in order to over tilt the cone is analogues to the one describing the spacetime behind a horizon, i.e. inside a black hole. This allows us to study the interface between typeI and typeII Weyl semimetals using an equivalent system described by the Dirac equation on a gravitational background, in the vicinity of a horizon. The Hawking temperature, associated with the gravitational system, is connected to a change in the effective chemical potential due to the effect of the spin connection, coming from the covariant derivative. We discuss several phenomena of general relativity that can be simulated in this context. [Preview Abstract] 
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