Bimodal conductance distribution of Kitaev edge modes in topological superconductors

Diez, M.; Fulga, Ion Cosma; Pikulin, Dmitry I.; Tworzydło, J.; Beenakker, C. W. J.

doi:10.1088/1367-2630/16/6/063049

Cited by 31 publications

(44 citation statements)

References 38 publications

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“…The presence of this term is what distinguishes the Kitaev chain (a 1D array) from the Kitaev edge (the 1D edge of a 2D array) [42]. The fact that all two-and four-Majorana terms appear on equal footing, that is, there is no statistical distinction between α 2j −1 ,κ 2j −1 and α 2j ,κ 2j determines that the edge Hamiltonian is exactly self-dual in the sense of quantum statistical mechanics [45].…”

Section: Interacting Kitaev Edgementioning

confidence: 99%

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Statistical translation invariance protects a topological insulator from interactions

et al. 2015

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We investigate the effect of interactions on the stability of a disordered, two-dimensional topological insulator realized as an array of nanowires or chains of magnetic atoms on a superconducting substrate. The Majorana zero-energy modes present at the ends of the wires overlap, forming a dispersive edge mode with thermal conductance determined by the central charge c of the low-energy effective field theory of the edge. We show numerically that, in the presence of disorder, the c = 1/2 Majorana edge mode remains delocalized up to extremely strong attractive interactions, while repulsive interactions drive a transition to a c = 3/2 edge phase localized by disorder. The absence of localization for strong attractive interactions is explained by a self-duality symmetry of the statistical ensemble of disorder configurations and of the edge interactions, originating from translation invariance on the length scale of the underlying mesoscopic array.

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Section: Interacting Kitaev Edgementioning

confidence: 99%

“…These zero modes overlap to form a dispersive one-dimensional (1D) edge mode of Majorana fermions [38][39][40]. Backscattering by disorder is not forbidden, yet this "Kitaev edge mode" does not localize [41,42].…”

Section: Introductionmentioning

confidence: 99%

Statistical translation invariance protects a topological insulator from interactions

et al. 2015

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“…[28], where it was shown that with increasing disorder a topological state transits to a metal. The effect of disorder in Kitaev chains has also been studied [29]. Other pertinent studies include, how an onsite disorder can induce [30] a topological phase in a trivial system (which has the necessary ingredients to produce topological phases), and an interesting concept of "statistical topological insulators" which requires another statistical symmetry apart from the symmetry protecting the topological phase [31].…”

Section: Introductionmentioning

confidence: 99%

Topological Insulators in Amorphous Systems

2017

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Our understanding of topological insulators is based on an underlying crystalline lattice where the local electronic degrees of freedom at different sites hybridize with each other in ways that produce nontrivial band topology, and the search for material systems to realize such phases have been strongly influenced by this. Here we theoretically demonstrate topological insulators in systems with a random distribution of sites in space, i. e., a random lattice. This is achieved by constructing hopping models on random lattices whose ground states possess nontrivial topological nature (characterized e. g., by Bott indices) that manifests as quantized conductances in systems with a boundary. By tuning parameters such as the density of sites (for a given range of fermion hopping), we can achieve transitions from trivial to topological phases. We discuss interesting features of these transitions. In two spatial dimensions, we show this for all five symmetry classes (A, AII, D, DIII and C) that are known to host nontrivial topology in crystalline systems. We expect similar physics to be realizable in any dimension and provide an explicit example of a Z2 topological insulator on a random lattice in three spatial dimensions. Our study not only provides a deeper understanding of the topological phases of non-interacting fermions, but also suggests new directions in the pursuit of the laboratory realization of topological quantum matter. Introduction:The band insulating state of many fermions has received renewed attention in recent times [1][2][3]. Clues that the band insulating state may support additional nontrivial physics -attributed to topology -was provided by the discovery of the integer quantum Hall effect[4] and the theoretical work that followed [5][6][7]. These ideas saw a resurgence with the discovery of the two dimensional spin Hall insulator[8-13], soon followed [14][15][16][17] by the three dimensional topological insulator (see [1][2][3]).A complete classification of gapped phases of noninteracting fermions soon appeared [18][19][20][21]. This classification hinges on the ten symmetry classes of Altland and Zirnbauer [22]. In any given spatial dimension d only five symmetry classes of the ten host topologically nontrivial phases (see e.g Kitaev [21]). Two gapped systems are considered to be topologically equivalent if the ground state of one can be reached starting from the ground state of the other by a symmetry preserving adiabatic deformation of the Hamiltonian which does not close the gap during the deformation process. The ground state of a gapped crystalline system is characterized by a set of filled bands. For each point in the Brillouin zone (BZ), this amounts to a Slater determinant state made of Bloch wavefunctions (whose character is determined by the symmetry class) of the filled bands. In d-dimensions this turns out to be a map from the BZ (d-dimensional torus) to points on a symmetric space whose character is determined by the total number of bands and the symmetry of the system [21]. Whethe...

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“…Among the peculiar properties of topologically conserved surface states one can be addressed: i) theoretically proposed by Fu and Kane [4], and experimentally observed [5,6] -wave-like superconducting correlations emerged via proximity coupling 3DTI to a conventional -type superconductor ii) the emergence of chiral Majorana mode [7] at the ferromagnet/superconductor (F/S) interface, which is of experimentally importance to detect the Majorana fermions [8,9]. However, chiral Majorana mode, which corresponds to the zero-energy bound state has a significant impact on the low-energy electron-hole excitations, leading to modifying Andreev reflection (AR) at the F/S interface [10] and thermal transport [11,12]. On the other hand, anisotropic -wave asymmetry pairing due to including nodal points in its superconducting gap can give rise to potentially forming the zero-energy Andreev bound state and, of course, zero-bias conductance [13,14].…”

Section: Introductionmentioning

confidence: 99%

Asymmetric d -wave superconducting topological insulator in proximity with a magnetic order

2018

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In the framework of the Dirac-Bogoliubov-de Gennes formalism, we investigate the transport properties in the surface of a 3-dimensional topological insulator-based hybrid structure, where the ferromagnetic and superconducting orders are simultaneously induced to the surface states via the proximity effect. The superconductor gap is taken to be spin-singlet ¦ -wave symmetry. The asymmetric role of this gap respect to the electron-hole exchange, in one hand, affects the topological insulator superconducting binding excitations and, on the other hand, gives rise to forming distinct Majorana bound states at the ferromagnet/superconductor interface. We propose a topological insulator N/F/FS junction and proceed to clarify the role of ¦ -wave asymmetry pairing in the resulting subgap and overgap tunneling conductance. The perpendicular component of magnetizations in F and FS regions can be at the parallel and antiparallel configurations leading to capture the experimentally important magnetoresistance (MR) of junction. It is found that the zero-bias conductance is strongly sensitive to the magnitude of magnetization in FS region § © and orbital rotated angle of superconductor gap. The negative MR only occurs in zero orbital rotated angle. This result can pave the way to distinguish the unconventional superconducting state in the relating topological insulator hybrid structures.

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Bimodal conductance distribution of Kitaev edge modes in topological superconductors

Cited by 31 publications

References 38 publications

Statistical translation invariance protects a topological insulator from interactions

Statistical translation invariance protects a topological insulator from interactions

Topological Insulators in Amorphous Systems

Asymmetric d -wave superconducting topological insulator in proximity with a magnetic order

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