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]
Summary
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
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