Abstract

The chiral edge modes of a topological superconductor support two types of excitations: fermionic quasiparticles known as Majorana fermions and \bm\pi𝛑-phase domain walls known as edge vortices. Edge vortices are injected pairwise into counter-propagating edge modes by a flux bias or voltage bias applied to a Josephson junction. An unpaired edge mode carries zero electrical current on average, but there are time-dependent current fluctuations. We calculate the shot noise power produced by a sequence of edge vortices and find that it increases logarithmically with their spacing — even if the spacing is much larger than the core size so the vortices do not overlap. This nonlocality produces an anomalous \bm{V\ln V}𝐕ln𝐕 increase of the shot noise in a voltage-biased geometry, which serves as a distinguishing feature in comparison with the linear-in-\bm V𝐕 Majorana fermion shot noise.

Highlights

  • A chiral p-wave superconductor is the superconducting counterpart to a quantum Hall insulator [1]: Both are two-dimensional materials with a gapped bulk and gapless modes that circulate unidirectionally along the boundary

  • The resulting unit transmission probability for quasiparticles injected into an edge mode implies a quantized thermal conductance for both systems — half as large in the superconductor because the quasiparticles are Majorana fermions [2,3,4] rather than the Dirac fermions of an integer quantum Hall edge mode

  • The superconducting phase allows for an additional collective degree of freedom, a winding of the phase field forming a vortex, with non-Abelian rather than fermionic exchange statistics [3, 6]

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Summary

Introduction

A chiral p-wave superconductor is the superconducting counterpart to a quantum Hall insulator [1]: Both are two-dimensional materials with a gapped bulk and gapless modes that circulate unidirectionally (chirally) along the boundary. The 2π winding of the superconducting phase around a bulk vortex corresponds on the edge to a π-phase domain wall for Majorana fermions [7]. It is the purpose of this work to identify electrical signatures of edge vortices, and to distinguish these from the familiar electronic transport properties of Majorana fermions [8,9,10,11,12,13,14,15,16]. We propose a voltage-biased geometry in which the edge vortices produce a shot noise power that increases ∝ V ln V — in contrast to the linear voltage dependence of the Majorana fermion noise power

Trace formula for the variance of the transferred charge
Correspondence between charge variance and average particle number
Evaluation of the charge noise
Discussion
C Computation of the logarithmic asymptote of the charge noise
D Divergent charge noise for an unpaired edge vortex
E Charge noise in a double-Josephson junction geometry
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