1D Majorana Goldstinos and partial supersymmetry breaking in quantum wires

Abstract

One-dimensional Majorana modes can be obtained as boundary excitations of topologically nontrivial twodimensional topological superconductors. Here, we propose instead the bottom-up creation of one-dimensional, counterpropagating, and dispersive Majorana modes as bulk excitations of a periodic chain of partiallyoverlapping, zero-dimensional Majorana modes in proximitized quantum nanowires via periodically-modulated magnetic fields. These dispersive one-dimensional Majorana modes can be either massive or massless. Massless Majorana modes are pseudohelical, having opposite Majorana pseudospin, and realize emergent quantum mechanical supersymmetry. The experimental fingerprint of massless Majorana modes and supersymmetry is the presence of a finite zero-bias peak, which is generally not expected for Majorana modes with a finite overlap and localized at a finite distance. Moreover, slowly varying magnetic fields can induce adiabatic pumping of Majorana modes, which can be used as a dynamically probe of topological superconductivity.

Majorana/Andreev crossover and the fate of the topological phase transition in inhomogeneous nanowires

“…Following references [127,128] we define the Majorana pseudospin operator T = τ /2 as the analogous of the spin operator S = σ/2. The expectation values of the Majorana pseudospin are given by T(x) = ψ(x)|T|ψ(x) with Cartesian components given by…”