Topological Invariants for Spin-Orbit Coupled Superconductor Nanowires

Tewari, Sumanta; Sau, Jay D.

doi:10.1103/physrevlett.109.150408

Cited by 259 publications

(316 citation statements)

References 43 publications

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“…Unwanted Majorana bilinears are suppressed by an approximate time-reversal symmetry [43] that, importantly, is preserved by the dominant sources of disorder expected in the dot. Interactions intrinsic to the dot instead generate the desired all-to-all four-Majorana couplings, thus approximating the SYK model up to corrections that we quantify (and which appear generic for any physical realization).…”

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confidence: 99%

“…Together these ingredients allow the formation of Majorana zero modes γ,γ at the wire ends over a chemical potential window centered around μ = 0 [41,42]. Crucially, the terms explicitly displayed above respect a time-reversal transformation T that sends ψ → ψ, i → −i and thus satisfies T 2 = +1 [43]. Additional couplings denoted by the ellipsis can in general violate T since it is not a true microscopic symmetry.…”

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confidence: 99%

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Approximating the Sachdev-Ye-Kitaev model with Majorana wires

2017

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The Sachdev-Ye-Kitaev (SYK) model describes a collection of randomly interacting Majorana fermions that exhibits profound connections to quantum chaos and black holes. We propose a solid-state implementation based on a quantum dot coupled to an array of topological superconducting wires hosting Majorana zero modes. Interactions and disorder intrinsic to the dot mediate the desired random Majorana couplings, while an approximate symmetry suppresses additional unwanted terms. We use random-matrix theory and numerics to show that our setup emulates the SYK model (up to corrections that we quantify) and discuss experimental signatures. DOI: 10.1103/PhysRevB.96.121119 Introduction. Majorana fermions provide building blocks for many novel phenomena. As one notable example, Majorana-fermion zero modes [1,2] capture the essence of non-Abelian statistics and topological quantum computation [3,4], and correspondingly now form the centerpiece of a vibrant experimental effort [5][6][7][8][9][10][11][12][13][14][15][16]. More recently, randomly interacting Majorana fermions governed by the "Sachdev-YeKitaev (SYK) model" [17][18][19] were shown to exhibit sharp connections to chaos, quantum-information scrambling, and black holes-naturally igniting broad interdisciplinary activity (see, e.g., [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]). The goal of this Rapid Communication is to exploit hardware components of a Majorana-based topological quantum computer for a tabletop implementation of the SYK model, thus uniting these very different topics.The SYK Hamiltonian reads

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confidence: 99%

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confidence: 99%

Approximating the Sachdev-Ye-Kitaev model with Majorana wires

2017

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“…For thin wires W ξ, with the superconducting coherence length ξ = /m∆ x , the term ∆ y p y σ y only has a small effect on the wavefunctions and the spectrum and can be treated in perturbation theory. Without it, H obeys the chiral symmetry σ y Hσ y = −H [35,36]. In the Cartan classification this corresponds to symmetry class "BDI".…”

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confidence: 99%

Density of states at disorder-induced phase transitions in a multichannel Majorana wire

Rieder

Brouwer

2014

Phys. Rev. B

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An N-channel spinless p-wave superconducting wire is known to go through a series of N topological phase transitions upon increasing the disorder strength. Here, we show that at each of those transitions the density of states shows a Dyson singularity ν(ε) ∝ ε −1 | ln ε| −3 , whereas ν(ε) ∝ ε |α|−1 has a power-law singularity for small energies ε away from the critical points. Using the concept of "superuniversality" [Gruzberg, Read, and Vishveshwara, Phys. Rev. B 71, 245124 (2005)], we are able to relate the exponent α to the wire's transport properties at zero energy and, hence, to the mean free path l and the superconducting coherence length ξ.

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“…We observe that the number of singularities in the phase of the determinant is a topological invariant [35] because it is not related to any symmetry breaking and it cannot change without the amplitude going to zero, thus implying a gap closing and a topological phase transition. The integer W counts the number of MFs at the edges of 1d-PSC.…”

Section: Model and Methodologymentioning

confidence: 96%

“…We show that the Cooper pair spin-configuration of a 1d PSC with an easy arXiv:1710.05567v1 [cond-mat.supr-con] 16 Oct 2017 spin-plane, chiral symmetry [33,[35][36][37][38][39] and long-range hoppings can have a fundamental role to set topological phases with an enhanced number of Majorana fermions per edge (e.g. ranging from N = 0 to 4).…”

Section: Introductionmentioning

confidence: 99%

Magnetic manipulation of topological states in p-wave superconductors

Mercaldo

Cuoco

Kotetes

2018

Physica B: Condensed Matter

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Substantial experimental investigation has provided evidence for spin-triplet pairing in diverse classes of materials and in a variety of artificial heterostructures. A fundamental challenge in actual experiments is how to manipulate the topological behavior of p-wave superconductors (PSCs) that could open perspectives for applications. Such a control knob is naturally provided by the spintriplet character of the PSC order parameter, described by the spin d-vector. Therefore, in this work we investigate the magnetic field response of one-dimensional (1d) PSCs and demonstrate that the structure of the Cooper pair spin-configuration is crucial to set topological phases with an enhanced number of Majorana fermions per edge, N , ranging from N = 0 to 4. The topological phase diagram, consisting of phases with Majorana modes at the edge, becomes significantly modified when one tunes the strength of the applied field and allows for long range hopping amplitudes in the 1d PSC. We find transitions between phases with different number of Majorana fermions per edge that can be both induced by a variation of the hopping strength and a spin rotation of d. Hence, the interplay of the applied magnetic field and the internal spin degree of freedom of the PSC opens a new promising route for engineering topological phases with large number of Majorana modes.

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Topological Invariants for Spin-Orbit Coupled Superconductor Nanowires

Cited by 259 publications

References 43 publications

Approximating the Sachdev-Ye-Kitaev model with Majorana wires

Approximating the Sachdev-Ye-Kitaev model with Majorana wires

Density of states at disorder-induced phase transitions in a multichannel Majorana wire

Magnetic manipulation of topological states in p-wave superconductors

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