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 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 low-energy physics of quantum materials such as topological superconductors and Weyl semimetals. Here, by performing state-of-the-art sign-problem-free 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 dynamically-generated masses, a hallmark of emergent SUSY. We further discuss experimental signatures of such EQCP and the associated edge SUSY. Ref: Zi-Xiang Li, Yi-Fan Jiang, Hong Yao, arXiv:1610.04616. [Preview Abstract] |
Friday, March 17, 2017 11:51AM - 12:03PM |
Y45.00002: Three-Dimensional Majorana Fermions in Chiral Superconductors Vladyslav Kozii, Jorn Venderbos, Liang Fu Through a systematic symmetry and topology analysis we establish that three-dimensional chiral superconductors with strong spin-orbit coupling and odd-parity pairing generically host low-energy nodal quasiparticles that are spin-non-degenerate 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 energy-momentum relation and location on the Fermi surface. We show that the existence of bulk Majorana fermions in the vicinity of spin-selective point nodes is rooted in the non-unitary nature of chiral pairing in spin-orbit-coupled 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 spin-selective 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 Majorana-Dimer 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 Ising-like topological order yet possesses a fully gapped edge--a possibility that is unique to fermions and has no analogue in bosonic systems. Based on an analysis of fermion-parity defects and fermion-parity 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 eight-fold 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 frustration-free Majorana-Dimer 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 Majorana-dimer models—wherein bosonic dimers are decorated with pairs of Majorana modes. We show that it is possible to construct a gapped, frustration-free, and analytically tractable Majorana-dimer Hamiltonians on the triangular and Fisher lattices. By analyzing the low-energy 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 three-fold ground-state degeneracy. From these, we suggest that these Hamiltonians possess non-Abelian 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: Majorana-decorated domain wall construction of fermionic SPTs Nicolas Tarantino, Lukasz Fidkowski A decorated domain wall construction generates a symmetry-protected topological phase (SPT) by begin in a symmetry-broken phase with multiple domains, binding a non-trivial 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 two-dimensional fermionic symmetry-protected 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 non-compact 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 non-interacting 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 Majorana-like ground states in number-conserving 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 non-Abelian 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 number-conserving but nevertheless can be shown to host robust Majorana-like degenerate ground states and exhibit non-abelian 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: Non-Abelian Majorana modes protected by an emergent 4D topological invariant Cheung Chan, Xiong-Jun Liu The search for topological superconductors and non-Abelian 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 time-reversal 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 non-Abelian statistics, similar as the vortices in a $p+ip$ superconductor. This work opens a new avenue in search for new type Majorana modes and non-Abelian 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 Sachdev-Ye-Kitaev (SYK) model as realized on the surface of three-dimensional 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 2-Majorana and 4-Majorana 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: Spin-Pairing Correlations and Spin Polarization of Majorana Bound States in Quantum Spin Hall Systems. Kunhua Zhang, Zhenhua Qiao We demonstrate that zero-energy 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 spin-triplet pairing correlations, and an additional weak spin-singlet pairing correlation is generated in the presence of coupling between two Majorana bound states in FMI-SC-FMI junction. We show that the position-independent local spin polarization of zero-energy 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 anti-parallel to that of MBS in ferromagnetic insulator, equal-spin Andreev reflection gives the widest resonance peak. Conversely, equal-spin Andreev reflection results in the narrowest peak. These signatures can facilitate the experimental detection of spin-triplet 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 type-II Weyl semimetal, the spectral cone is heavily tilted such that it is crosses the Fermi energy. For a fundamental Weyl particle, this type-IIs 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 space-time behind a horizon, i.e. inside a black hole. This allows us to study the interface between type-I and type-II 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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