Interplay of Disorder and Interaction in Majorana Quantum Wires

Lobos, Alejandro M.; Lutchyn, Roman M.; Sarma, S. Das

doi:10.1103/physrevlett.109.146403

Cited by 151 publications

(157 citation statements)

References 40 publications

(103 reference statements)

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“…The effects of interactions between MM's in such setups is a relatively unexplored field [18,[20][21][22][23][24][25][26]. Interaction effects have also been studied [27,28] in the Kitaev model [11] in which two localized Majorana modes appear at the ends of a chain. The corresponding Hamiltonians are Hubbard-like (with Majorana fermions serving as Hermitian counterparts of electrons), but necessarily have interactions spanning at least four lattice sites, since the square of a Majorana operator is a constant.…”

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confidence: 99%

Majorana-Hubbard model on the square lattice

2017

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We study a tight-binding model of interacting Majorana (Hermitian) modes on a square lattice. The model may have an experimental realization in a superconducting-film-topological-insulator heterostructure in a magnetic field. We find a rich phase diagram, as a function of interaction strength, including an emergent superfluid phase with spontaneous breaking of an emergent U (1) symmetry, separated by a supersymmetric transition from a gapless normal phase.

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confidence: 99%

Majorana-Hubbard model on the square lattice

2017

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“…For example, considerable progress has been made towards developing number preserving theories of the Majorana modes, [15][16][17][18][19][20] as well as a growing body of work which examines how free-topological superconducting phases are affected by the addition of interacting electron-electron terms. [21][22][23][24][25][26][27][28][29][30][31][32][33] One aspect of this latter story is concerned with the stability and structure of the Majorana zero-modes themselves and how they are affected by the presence of density-density interaction terms that break the exactly solvable nature of the underlying model. The issue of stable zero-modes has also been addressed in the related context of 1-d parafermionic chains.…”

Section: Introductionmentioning

confidence: 99%

Multiparticle content of Majorana zero modes in the interactingp-wave wire

Kells

2015

Phys. Rev. B

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In the topological phase of p-wave superconductors, zero-energy Majorana quasi-particle excitations can be well-defined in the presence of local density-density interactions. Here we examine this phenomenon from the perspective of matrix representations of the commutator H = [H, •] ,with the aim of characterising the multiparticle content of the many-body Majorana mode. To do this we show that, for quadratic fermionic systems, H can always be decomposed into sub-blocks that act as multi-particle generalisations of the BdG/Majorana forms that encode single-particle excitations. In this picture, density-density like interactions will break this exact excitation-number symmetry, coupling different sub-blocks and lifting degeneracies so that the eigen-operators of the commutator H take the form of individual eigenstate transitions | n m |. However, the Majorana mode is special in that zero-energy transitions are not destroyed by local interactions and it becomes possible to define many-body Majoranas as the odd-parity zero-energy solutions of H that minimise their excitation number. This idea forms the basis for an algorithm which is used to characterise the multi-particle excitation content of the Majorana zero modes of the one-dimensional p-wave lattice model. We find that the multi-particle content of the Majorana zero-mode operators is significant even at modest interaction strengths. This has important consequences for the stability of Majorana based qubits when they are coupled to a heat bath. We will also discuss how these findings differ from previous work regarding the structure of the many-body-Majorana operators and point out that this should affect how certain experimental features are interpreted.

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“…Then the low-energy quasiparticles are described by an effective p-wave Hamiltonian as discussed in the literature [33][34][35][36][37][38][39][42][43][44][45]47,56]. For completeness, we discuss this limit in Appendix D.…”

Section: Topological Order In Disordered Multichannel Wiresmentioning

confidence: 99%

Disorder-induced topological transitions in multichannel Majorana wires

et al. 2017

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In this work, we investigate the effect of disorder on the topological properties of multichannel superconductor nanowires. While the standard expectation is that the spectral gap is closed and opened at transitions that change the topological index of the wire, we show that the closing and opening of a transport gap can also cause topological transitions, even in the presence of nonzero density of states across the transition. Such transport gaps induced by disorder can change the topological index, driving a topologically trivial wire into a nontrivial state or vice versa. We focus on the Rashba spin-orbit coupled semiconductor nanowires in proximity to a conventional superconductor, which is an experimentally relevant system, and we obtain analytical formulas for topological transitions in these wires, valid for generic realizations of disorder. Full tight-binding simulations show excellent agreement with our analytical results without any fitting parameters.

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Interplay of Disorder and Interaction in Majorana Quantum Wires

Cited by 151 publications

References 40 publications

Majorana-Hubbard model on the square lattice

Majorana-Hubbard model on the square lattice

Multiparticle content of Majorana zero modes in the interactingp-wave wire

Disorder-induced topological transitions in multichannel Majorana wires

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