Majorana Modes in Time-Reversal Invariant<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>s</mml:mi></mml:math>-Wave Topological Superconductors

Deng, Shusa; Viola, Lorenza; Ortíz, Gerardo

doi:10.1103/physrevlett.108.036803

Cited by 117 publications

(149 citation statements)

References 34 publications

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“…According to this classification, the experimentally investigated semiconductorsuperconductor heterostructures [11][12][13][14][15][16][17][18][19][20][21] belong to the topological class D in which MBS are protected by the superconducting particle-hole (PH) symmetry. Additionally, one-dimensional topological superconductors belonging to the time reversal class DIII [27][28][29][30][31][32][33][34][35][36] and BDI [37][38][39][40][41][42] have recently been proposed. DIII topological superconductivity is indexed by a Z 2 topological invariant indicating the presence or absence of a Majorana Kramers pair, while in BDI topological superconductivity, for instance as recently proposed 43 in the context of putative spin-triplet ferromagnetic superconductors such as the organic superconductors and lithium purple bronze (Li 0.9 Mo 6 O 17 ), a Z invariant counts the number of MBS.…”

Section: Introductionmentioning

confidence: 99%

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Majorana fermions in chiral topological ferromagnetic nanowires

et al. 2015

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Motivated by a recent experiment in which zero-bias peaks have been observed in scanning tunneling microscopy (STM) experiments performed on chains of magnetic atoms on a superconductor, we show, by generalizing earlier work, that a multichannel ferromagnetic wire deposited on a spin-orbit coupled superconducting substrate can realize a non-trivial chiral topological superconducting state with Majorana bound states localized at the wire ends. The non-trivial topological state occurs for generic parameters requiring no fine tuning, at least for very large exchange spin splitting in the wire. We theoretically obtain the signatures which appear in the presence of an arbitrary number of Majorana modes in multi-wire systems incorporating the role of finite temperature, finite potential barrier at the STM tip, and finite wire length. These signatures are presented in terms of spatial profiles of STM differential conductance which clearly reveal zero energy Majorana end modes and the prediction of a multiple Majorana based fractional Josephson effect. A substantial part of this work is devoted to a detailed critical comparison between our theory and the recent STM experiment claiming the observation of Majorana fermions in ferromagnetic atomic chains on a superconductor. The conclusion of this detailed comparison is that although the experimental observations are not manifestly inconsistent with our theoretical findings, the very small topological superconducting gap and the very high temperature of the experiment make it impossible to decisively verify the existence of a localized Majorana zero mode, as the spectral weight of the Majorana mode is necessarily spread over a very broad energy regime exceeding the size of the gap. Such an extremely broad (and extremely weak) conductance peak could easily arise from any sub-gap states existing in the rather complex system studied experimentally and may or may not have anything to do with a putative Majorana zero mode as discussed in the first half of our paper. Thus, although the experimental findings are indeed consistent with a highly broadened and weakened Majorana zero bias peak, much lower experimental temperatures (and/or much larger experimental topological superconducting gaps) are necessary for any definitive conclusion.

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Section: Introductionmentioning

confidence: 99%

“…51. Nontrivial zero-bias phenomena appear across a broad range of parameters in contrast to the fine tuning necessary for a nontrivial topological phase in class D [11][12][13][14][15] or DIII systems [27][28][29][30][31][32][33][34][35][36] . Within this framework, manipulating the system width (i.e.…”

Section: Introductionmentioning

confidence: 99%

Majorana fermions in chiral topological ferromagnetic nanowires

et al. 2015

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“…17,18 In essence, most of these proposals rely on having two pairs of time-reversed Fermi surfaces of which the effective pairing potentials have opposite sign.…”

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confidence: 99%

Interaction effects on proximity-induced superconductivity in semiconducting nanowires

Danon

Flensberg

2015

Phys. Rev. B

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We investigate the effect of electron-electron interactions on proximity-induced s-wave superconductivity in one-dimensional nanowires. We treat the interactions on a self-consistent mean-field level, and find an analytic expression for the effective pairing potential in the presence of interactions, valid for a weakly tunnel coupled wire. We show that for a set of two nanowires placed in parallel on a superconducting substrate, the interaction-induced reduction of the pairing energy could result in the effective interwire pairing potential exceeding the intrawire potential, which is one of the requirements for creating a time-reversal symmetric topological superconducting state in such a two-wire system.

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“…The MBSs are of particular interest due to their potential application in topological quantum computation 5 . While the existence of these fractional excitations has been proposed theoretically in many systems [6][7][8][9][10][11][12][13][14][15][16][17][18] , the experimental effort for their realization and detection is still the subject of vigorous current research. Recently, a number of groups have reported observing signatures of MBSs [19][20][21][22][23] .…”

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confidence: 99%

Non-Abelian fermion parity interferometry of Majorana bound states in a Fermi sea

Dahan¹,

Ahari²,

Ortíz³

et al. 2017

Phys. Rev. B

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We study the quantum dynamics of Majorana and regular fermion bound states coupled to a quasi-one-dimensional metallic lead. The dynamics following the quench in the coupling to the lead exhibits a series of dynamical revivals as the bound state propagates in the lead and reflects from the boundaries. We show that the nature of revivals for a single Majorana bound state depends uniquely on the presence of a resonant level in the lead. When two spatially separated Majorana modes are coupled to the lead, the revivals depend only on the phase difference between their host superconductors. Remarkably, the quench in this case effectively performs a fermion-parity interferometry between Majorana bound states, revealing their unique non-Abelian braiding. Using both analytical and numerical techniques, we find the pattern of fermion parity transfers following the quench, study its evolution in the presence of disorder and interactions, and thus, ascertain the fate of Majorana in a rough Fermi sea.

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Majorana Modes in Time-Reversal Invariants-Wave Topological Superconductors

Cited by 117 publications

References 34 publications

Majorana fermions in chiral topological ferromagnetic nanowires

Majorana fermions in chiral topological ferromagnetic nanowires

Interaction effects on proximity-induced superconductivity in semiconducting nanowires

Non-Abelian fermion parity interferometry of Majorana bound states in a Fermi sea

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