Strong-coupling topological Josephson effect in quantum wires

Nogueira, Flavio S.; Eremin, I.

doi:10.1088/0953-8984/24/32/325701

Cited by 14 publications

(12 citation statements)

References 27 publications

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“…For recent work on the fractional Josephson effect in the limits of strong tunneling and long junctions, see Refs. [115] and [116]. Experimental evidence of fractional AC Josephson effect in the form of doubled Shapiro steps has been reported in semiconductor Majorana wires [79].…”

Section: Fig 4 (Color Online)mentioning

confidence: 96%

Majorana fermions in semiconductor nanowires: fundamentals, modeling, and experiment

Stãnescu¹,

Tewari²

2013

J. Phys.: Condens. Matter

490

509

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After a recent series of rapid and exciting developments, the long search for the Majorana fermion -the elusive quantum entity at the border between particles and antiparticles -has produced the first positive experimental results, but is not over yet. Originally proposed by E. Majorana in the context of particle physics, Majorana fermions have a condensed matter analog in the zero-energy bound states emerging in topological superconductors. A promising route to engineering topological superconductors capable of hosting Majorana zero modes consists of proximity coupling semiconductor thin films or nanowires with strong spin-orbit interaction to conventional s-wave superconductors in the presence of an external Zeeman field. The Majorana zero mode is predicted to emerge above a certain critical Zeeman field as a zero-energy state localized near the order parameter defects, viz., vortices for thin films and wire-ends for the nanowire. These Majorana bound states are expected to manifest non-Abelian quantum statistics, which makes them ideal building blocks for fault-tolerant topological quantum computation. This review provides an update on current status of the search for Majorana fermions in semiconductor nanowires by focusing on the recent developments, in particular the period following the first reports of experimental signatures consistent with the realization of Majorana bound states in semiconductor nanowire-superconductor hybrid structures. We start with a discussion of the fundamental aspects of the subject, followed by considerations on the realistic modeling which is a critical bridge between theoretical predictions based on idealized conditions and the real world, as probed experimentally. The last part is dedicated to a few intriguing issues that were brought to the fore by the recent encouraging experimental advances. CONTENTS

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Section: Fig 4 (Color Online)mentioning

confidence: 96%

Majorana fermions in semiconductor nanowires: fundamentals, modeling, and experiment

Stãnescu¹,

Tewari²

2013

J. Phys.: Condens. Matter

490

509

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“…where the wave vector k = {k x , k y }. In a finite system, the one-particle spectrum of the Hamiltonian H (1), (2), is also symmetric edge states including. The corresponding edge states are determined by the particle-hole states of Majorana fermions.…”

Section: Model Hamiltonian Edge Modesmentioning

confidence: 99%

Persistent current in 2D topological superconductors

Karnaukhov

2017

Sci Rep

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A junction between two boundaries of a topological superconductor (TSC), mediated by localized edge modes of Majorana fermions, is investigated. The tunneling of fermions across the junction depends on the magnetic flux. It breaks the time-reversal symmetry at the boundary of the sample. The persistent current is determined by the emergence of Majorana edge modes. The structure of the edge modes depends on the magnitude of the tunneling amplitude across the junction. It is shown that there are two different regimes, which correspond to strong and weak tunneling of Majorana fermions, distinctive in the persistent current behavior. In a strong tunneling regime, the fermion parity of edge modes is not conserved and the persistent current is a 2π-periodic function of the magnetic flux. When the tunneling is weak the chiral Majorana states, which are propagating along the edges have the same fermion parity. They form a 4π-phase periodic persistent current along the boundaries. The regions in the space of parameters, which correspond to the emergence of 2π- and of 4π-harmonics, are numerically determined. The peculiarities in the persistent current behavior are studied.

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“…As a promising experimental proof for the existence of MZMs, previous theoretical studies have suggested a fractional Josephson effect in a topological Josephson junction, where the Josephson current has a 4𝜋, rather than a 2𝜋, periodicity as a function of the phase difference between the two topological superconductors [4,[16][17][18][19][20][21][22][23][24][25]. The first paper presenting this idea is Ref.…”

Section: Introductionmentioning

confidence: 99%

Superconductor/normal-metal/superconductor junction of topological superconductors revisited: Fractional Josephson current, fermion parity, and oscillating wavefunctions

Sumita,

Furusaki

2021

Preprint

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The fractional Josephson effect is known to be a characteristic phenomenon of topological Josephson junctions hosting Majorana zero modes (MZMs), where the Josephson current has a 4𝜋 (rather than a 2𝜋) periodicity in the phase difference between the two topological superconductors. We introduce a one-dimensional model of a topological superconductor/normal-metal/superconductor (SNS) junction with the normal-metal (N) region of finite length, which is intermediate regime between the short-and long-junction limits. Assuming weak tunneling at the SN interfaces, we investigate resonance and finite-size effects on the fractional Josephson effect due to the existence of several discrete energy levels in the N region in which wavefunctions have oscillating nodal structure. Through careful analysis of the sign change in the transmission amplitudes through the junction and the fermion parity of the two MZMs, we find that the fractional Josephson current is proportional to the parity of total fermion numbers including both filled normal levels and two MZMs. Furthermore, we elucidate drastic enhancement of the Josephson current due to the resonance between a discrete level in the N region and MZMs.

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Strong-coupling topological Josephson effect in quantum wires

Cited by 14 publications

References 27 publications

Majorana fermions in semiconductor nanowires: fundamentals, modeling, and experiment

Majorana fermions in semiconductor nanowires: fundamentals, modeling, and experiment

Persistent current in 2D topological superconductors

Superconductor/normal-metal/superconductor junction of topological superconductors revisited: Fractional Josephson current, fermion parity, and oscillating wavefunctions

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