Majorana Edge States in Interacting One-Dimensional Systems

Gangadharaiah, Suhas; Braunecker, Bernd; Simon, Pascal; Loss, Daniel

doi:10.1103/physrevlett.107.036801

Cited by 255 publications

(315 citation statements)

References 33 publications

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“…The interactions involved in Majorana zero-energy pinning are not intrinsic to the wire, 18,[21][22][23][24][25][26][27][28] but rather extrinsic, between electrons that enter the wire and bound charges in the dielectric environment that arise in response. Our results suggest that such electronic interactions provide a powerful mechanism to stabilize Majorana-based qubits in realistic nanowires, and may account for the hitherto unexplained experimental features.…”

Section: Introductionmentioning

confidence: 99%

Zero-energy pinning from interactions in Majorana nanowires

et al. 2017

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Majorana zero modes at the boundaries of topological superconductors are charge-neutral, an equal superposition of electrons and holes. This ideal situation is, however, hard to achieve in physical implementations, such as proximitized semiconducting nanowires of realistic length. In such systems Majorana overlaps are unavoidable and lead to their hybridization into charged Bogoliubov quasiparticles of finite energy, which, unlike true zero modes, are affected by electronic interactions. We here demonstrate that these interactions, particularly with bound charges in the dielectric surroundings, drastically change the non-interacting paradigm. Remarkably, interactions may completely suppress Majorana hybridization around parity crossings, where the total charge in the nanowire changes. This effect, dubbed zero-energy pinning, stabilizes Majoranas back to zero energy and charge, and leads to electronically incompressible parameter regions wherein Majoranas remain insensitive to local perturbations, despite their overlap.

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Section: Introductionmentioning

confidence: 99%

Zero-energy pinning from interactions in Majorana nanowires

et al. 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%

“…In Ref. 23 it was shown that, when the p-wave system can be bosonized, a refermionization argument indicates the continued stability of the modes in interacting regions of the topological phase. Importantly, this argument does not require the restriction to an odd number of Majorana modes.…”

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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“…Majorana fermions 1 (MFs), being their own antiparticles, have attracted much attention in recent years in condensed matter physics [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] . Besides being of fundamental interest, these exotic quantum particles have the potential for being used in topological quantum computing due to their non-Abelian statistics [20][21][22][23][24][25][26] .…”

Section: Introductionmentioning

confidence: 99%

Composite Majorana fermion wave functions in nanowires

2012

Self Cite

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We consider Majorana fermions (MFs) in quasi-one-dimensional nanowire systems containing normal and superconducting sections where the topological phase based on Rashba spin orbit interaction can be tuned by magnetic fields. We derive explicit analytic solutions of the MF wavefunction in the weak and strong spin orbit interaction regimes. We find that the wavefunction for one single MF is a composite object formed by superpositions of different MF wavefunctions which have nearly disjoint supports in momentum space. These contributions are coming from the extrema of the spectrum, one centered around zero momentum and the other around the two Fermi points. As a result, the various MF wavefunctions have different localization lengths in real space and interference among them leads to pronounced oscillations of the MF probability density. For a transparent normal-superconducting junction we find that in the topological phase the MF leaks out from the superconducting into the normal section of the wire and is delocalized over the entire normal section, in agreement with recent numerical results by Chevallier et al..

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Majorana Edge States in Interacting One-Dimensional Systems

Cited by 255 publications

References 33 publications

Zero-energy pinning from interactions in Majorana nanowires

Zero-energy pinning from interactions in Majorana nanowires

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

Composite Majorana fermion wave functions in nanowires

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