Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session V45: Quantum Hall Effect and SuperconductivityFocus

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Sponsoring Units: DMP Room: 392 
Thursday, March 16, 2017 2:30PM  3:06PM 
V45.00001: Inducing Superconducting Correlation in Quantum Hall Edge States Invited Speaker: Amir Yacoby The quantum Hall (QH) effect supports a set of chiral edge states at the boundary of a 2dimensional electron gas (2DEG) system. A superconductor (SC) contacting these states induces correlation of the quasiparticles in the dissipationless 1D chiral QH edge states. If the superconducting electrode is narrower than the superconducting coherence length, the incoming electron are correlated to outgoing hole along the chiral edge state by the Andreev process. In order to realize this crossed Andreev conversion (CAC), it is necessary to fabricate highly transparent and nanometerscale superconducting junctions to QH system. Here we report the observation of CAC in a graphene QH system contacted with a nanostructured NbN superconducting electrode. The chemical potential of the edge states across the superconducting electrode exhibits a sign reversal, providing direct evidence of CAC. This hybrid SC/QH system is a novel route to create isolated nonAbelian anyonic zero modes, in resonance with the chiral QH edge. [Preview Abstract] 
Thursday, March 16, 2017 3:06PM  3:18PM 
V45.00002: The transport mechanism of supercurrents in the quantum Hall regime MingTso Wei, Chung Ting Ke, Anne Draelos, Andrew Seredinski, Ivan Borzenets, Kenji Watanabe, Takashi Taniguchi, Russell Deacon, Michihisa Yamamoto, Yuriy Bomze, Seigo Tarucha, Francois Amet, Gleb Finkelstein Supercurrent through quantum Hall (QH) edge states has been observed in ballistic graphene Josephson junctions at fields up to 2 Tesla. This provides a novel platform to study exotic topological states such as Majorana fermions and parafermions. However, the transport mechanism of supercurrents in the QH regime is not yet fully understood. Here, we report the studies of supercurrents in the QH regime with different sample geometries. The radius of cyclotron orbits altered by magnetic field and junction channel length determine the number of carrier bounces at the sample edges. In addition, the propagation of electronhole hybrid modes near the graphenesuperconductor interface may also be related to the width of the device. It is important to understand the geometric effects in order to optimize the supercurrent through the QH edge states. These studies would help us design better devices for ultimately detecting supercurrents through symmetrybreaking states. [Preview Abstract] 
Thursday, March 16, 2017 3:18PM  3:30PM 
V45.00003: Chiral Majorana fermion edge state in a quantum anomalous Hall insulatorsuperconductor structure Qing Lin He, Lei Pan, Gen Yin, Xufeng Kou, Kang L Wang Majorana fermion is a hypothetical fermionic particle which is its own antiparticle. Intense research efforts focus on its experimental observation as a fundamental particle in high energy physics and as a quasiparticle in condensed matter systems. Here we experimentally demonstrate the transport measurement to ascertain the onedimensional chiral Majorana fermion in a quantum anomalous Hall thin film coupled with a conventional superconductor, Crx(Bi,Sb)2xTe3  Nb. A collection of Majorana fermions living in a onedimensional transport channel at the boundary of such a hybrid system is experimentally realized. Topological phase transitions are controlled by the reversal of the magnetization under a scan of perpendicular magnetic field, where the halfinteger quantized conductance plateau (0.5e2/h) is observed as a compelling signature of the Majorana fermion as theoretically predicted. This transport signature can be repeated in many magnetic reversal sweeps, and can be tracked at different temperatures, providing direct evidence of the chiral Majorana edge modes in the system. [Preview Abstract] 
Thursday, March 16, 2017 3:30PM  3:42PM 
V45.00004: Effects of Domain Walls in Quantum Anomalous Hall Insulator/Superconductor Heterostructures ChuiZhen Chen, James Jun He, DongHui Xu, K. T. Law In a recent experiment, halfquantized longitudinal conductance plateaus (HQCPs) of height $\frac{e^2}{2h}$ have been observed in quantum anomalous Hall (QAH) insulator/superconductor heterostructure transport measurements. It was predicted that these HQCPs are signatures of chiral Majorana edge states. The HQCPs are supposed to appear in the regimes where the Hall conductance $\sigma_{xy}$ is quantized. However, experimentally, a pair of the HQCPs appear when the Hall conductance $\sigma_{xy}$ is only 80\% of the quantized value when dissipative channels appear in the bulk. The dissipative channels in the bulk are expected to induce Andreev reflections and ruin the HQCPs. In this work, we explain how domain walls can cause $\sigma_{xy}$ to deviate from its quantized value and at the same time maintain the quantization of HQCPs. Our work supports the claim that the experimentally observed HQCPs are indeed caused by chiral Majorana modes in the QAH insulator/superconductor heterostructure. [Preview Abstract] 
Thursday, March 16, 2017 3:42PM  3:54PM 
V45.00005: $\mathbb{Z}_3$ parafermions without superconducting backscattering from the $2/3$ fractional quantum Hall state Yahya Alavirad, David Clarke, Amit Nag, Jay Sau Parafermions, which are a generalization of Majorana modes, are a novel set of excitations that are predicted to occur from the combination of the fractional quantum Hall effect and superconductivity. Such parafermions have a nonAbelian statistics that are somewhat richer than Majorana modes. Despite substantial experimental progress, we argue that backscattering between fractional quantum Hall edges through a superconductor is a challenging milestone to reach. We propose a superconducting quantum dot array structure on a fractional quantum Hall edge that can lead to parafermions from coherent superconducting forward scattering on a quantum Hall edge. Such coherent forward scattering has already been demostrated in recent experiments. We show that even for proximity from a spinsinglet superconductor on a $2/3$ fractional quantum edge with an appropriately tuned array of gates of size of the order of ten should allow one to systematically tune into a parafermion degeneracy. [Preview Abstract] 
Thursday, March 16, 2017 3:54PM  4:06PM 
V45.00006: Topological phases of parafermions: a model with exactlysolvable ground states Christophe Mora, Fernando Iemini, Leonardo Mazza Parafermions are the simplest generalization of Majorana fermions: they show nonAbelian fractional statistics and can realize topological order. We present a nontrivial and quasiexactlysolvable model for a chain of parafermions in a symmetryprotected topological phase. We characterize analytically the groundstate wavefunctions, which are matrixproduct states and have a particularly elegant interpretation in terms of Fock parafermions, reflecting the factorized nature of the ground states. Using these wavefunctions, we demonstrate analytically several signatures of topological order such as nonlocal edgeedge correlations, the presence of edge zero modes and the threefold degeneracy of the entanglement spectrum. Our model also provides a typical example of weak edge modes which are not commuting with the full Hamiltonian. [Preview Abstract] 
Thursday, March 16, 2017 4:06PM  4:18PM 
V45.00007: Parafermionic wires at the interface of chiral topological states Luiz Santos, Taylor Hughes We discuss a scenario where local interactions form onedimensional gapped interfaces between a pair of distinct chiral twodimensional topological states such that each gapped region terminates at a domain wall separating the chiral gapless edge states of these phases. We show that this type of Tjunction supports pointlike fractionalized excitations obeying parafermion statistics, thus implying that the onedimensional gapped interface forms an effective topological parafermionic wire possessing a nontrivial ground state degeneracy. The physical properties of the anyon condensate that gives rise to the gapped interface are investigated. Remarkably, this condensate causes the gapped interface to behave as a type of anyon ``Andreev reflector" in the bulk, whereby anyons from one phase, upon hitting the interface, can be transformed into a combination of reflected anyons and outgoing anyons from the other phase. Thus, we conclude that while different topological orders can be connected via gapped interfaces, the interfaces are themselves topological. [Preview Abstract] 
Thursday, March 16, 2017 4:18PM  4:30PM 
V45.00008: Pairing in Luttinger Liquids and Quantum Hall States Ady Stern We study the effect of a twobody attractive interaction on spinless electrons in a quantum wire of a single mode, and the quantum Hall states (QHS) that may be constructed by an array of such wires. For a single wire we find a Luttinger liquid phase and a strongly paired phase. In contrast to a wire that is proximitycoupled to an external superconductor, for an isolated wire the phase of a topological, weakly paired, superconductor is adiabatically connected to the Luttinger liquid phase. The QHS formed by an array of singlechannel wires depend on the Landau level filling factors. For odddenominator fillings $\nu=1/(2n+1)$, wires at the Luttinger phase form Laughlin states while wires in the strongly paired states form bosonic fractional QHS of pairs at a filling of $1/(8n+4)$. The transition between the two is of the universality class of Ising transitions in three dimensions. For even denominator fractions $\nu=1/2n$ the two singlewire phases translate into four quantum Hall states. Two of those are bosonic fractional QHS of weakly and strongly bound pairs of electrons. The other two are nonabelian QHS, which originate from coupling wires close to their critical point. One of these nonabelian states is the MooreRead state. Work done with CL Kane and BI Halperin. [Preview Abstract] 
Thursday, March 16, 2017 4:30PM  4:42PM 
V45.00009: Topological superconducting phases from inversion symmetry breaking order Yuxuan Wang, Gil Young Cho, Taylor Hughes, Eduardo Fradkin We analyze the superconducting instabilities in the vicinity of the quantumcritical point of an inversion symmetry breaking order. We first show that the fluctuations of the inversion symmetry breaking order lead to two degenerate superconducting (SC) instabilities, one in the swave channel, and the other in a timereversal invariant oddparity pairing channel (the simplest case being the same as the of 3HeB phase). Remarkably, we find that unlike many wellknown examples, the selection of the pairing symmetry of the condensate is independent of the momentumspace structure of the collective mode that mediates the pairing interaction. We found that this degeneracy is a result of the existence of a conserved fermionic helicity, $\chi$, and the two degenerate channels correspond to even and odd combinations of SC order parameters with $\chi = \pm1$. As a result, the system has an enlarged symmetry $U(1) \times U(1)$, with each $U(1)$ corresponding to one value of the helicity $\chi$. We discuss how the enlarged symmetry can be lifted by small perturbations, such as the Coulomb interaction or Fermi surface splitting in the presence of broken inversion symmetry, and we show that the resulting superconducting state can be topological or trivial depending on parameters. [Preview Abstract] 
Thursday, March 16, 2017 4:42PM  4:54PM 
V45.00010: Topological order, symmetry, and Hall response of twodimensional spinsinglet superconductors Sergej Moroz, Abhinav Prem, Victor Gurarie, Leo Radzihovsky Fully gapped twodimensional superconductors coupled to dynamical electromagnetism are known to exhibit topological order. In this work, we develop a unified lowenergy description for spinsinglet paired states by deriving topological ChernSimons field theories for $s$wave, $d+id$, and chiral higher evenwave superconductors. These theories capture the quantum statistics and fusion rules of Bogoliubov quasiparticles and vortices and incorporate global continuous symmetries  specifically, spin rotation and conservation of magnetic flux  present in all singlet superconductors. For all such systems, we compute the Hall response for these symmetries and investigate the physics at the edge. In particular, the weaklycoupled phase of a chiral $d+id$ chiral state has a spin Hall coefficient $\nu_s=2$ and a vanishing Hall response for the magnetic flux symmetry. We argue that the latter is a generic result for twodimensional superconductors with gapped photons, thereby demonstrating the absence of a spontaneous magnetic field in the ground state of chiral superconductors. It is also shown that the ChernSimons theories of chiral spinsinglet superconductors derived here fall into Kitaev's 16fold classification of topological superconductors. [Preview Abstract] 
Thursday, March 16, 2017 4:54PM  5:06PM 
V45.00011: Pairing Instability and Quasiparticle Properties of an Unconventional Superconductor with a Skyrmion Texture of Localized Spins JianXin Zhu, YuanYen Tai Majorana fermions are believed to perform better than regular fermions in keeping quantum coherence, which is an important factor for quantum computation. Recently there has been intensive interest in their realization in solidstate systems. Zeroenergy quasiparticle modes in a superconductor serve as a promising candidate. We present a theoretical study on the influence of a twodimensional (2D) skyrmion texture of localized spins on the pairing instability and quasiparticle properties in an unconventional superconductor. By solving the Bogoliubovde Gennes equations for an effective BCS model Hamiltonian with nearestneighbor pairing interaction on a 2D square lattice, we analyze the spatial dependence of superconducting order parameter for varying strength of spinexchange interaction. The quasiparticle properties are studied by calculating local density of states and its spatial dependence. [Preview Abstract] 
Thursday, March 16, 2017 5:06PM  5:18PM 
V45.00012: Topological spin ordering and ChernSimons superconductivity Tigran Sedrakyan, Victor Galitski, Alex Kamenev We will discuss how the ChernSimons (CS) fermion representation of s =1/2 spin operators paves the way to construction of topological, longrange magnetically ordered states of interacting twodimensional (2D) quantum spin models. It will be shown that the fermionfermion interactions mediated by the dynamic CS flux attachment may give rise to Cooper pairing of the fermions. Specifically, in an XY model on the honeycomb lattice, this construction leads to a "CS superconductor," which belongs to a topologically nontrivial in 2D symmetry class DIII, with particlehole and timereversal symmetries. It is shown that in the original spin language, this state corresponds to a symmetry protected topological state, which coexists with a magnetic longrange order. We discuss physical manifestations of the topological character of the corresponding state. [Preview Abstract] 
Thursday, March 16, 2017 5:18PM  5:30PM 
V45.00013: Dynamic response functions, helical gaps, and fractional charges in quantum wires Tobias Meng, Christopher J. Pedder, Rakesh P. Tiwari, Thomas L. Schmidt We show how experimentally accessible dynamic response functions can discriminate between helical gaps due to magnetic field, and helical gaps driven by electronelectron interactions (``umklapp gaps’’). The latter are interesting since they feature gapped quasiparticles of fractional charge $e/2$, and  when coupled to a standard superconductor  an 8$\pi$Josephson effect and topological zero energy states bound to interfaces. [Preview Abstract] 
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