From Majorana fermions to topological quantum computation in semiconductor/superconductor heterostructures

Abstract

We present a pedagogical review of topological superconductivity and its consequences in spin-orbit coupled semiconductor/superconductor heterostructures. We start by reviewing the historical origins of the notions of Dirac and Majorana fermions in particle physics and discuss how lower dimensional versions of these emerge in one dimensional superconductors. Ultimately, we focus on Majorana zero-modes, which emerge at defects in the Majorana equation. We then review the definition of the topological invariant, and how it allows the prediction of such Majorana modes from the bulk bandstructure of realistic superconductors, which do not have Lorentz invariance. Finally, we end with a discussion of protocols for how to detect such Majorana modes and use them for topological quantum computation.

A pedagogical review submitted as a book chapter

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Cited by in corpus (3)

• Non-perturbative constraints from symmetry and chirality on Majorana zero modes and defect quantum numbers in (2+1)D
• Topological Solitons in Su-Schrieffer-Heeger Chain with periodic hopping modulation, domain walls and disorder
• Edge state behavior in a Su-Schrieffer-Heeger like model with periodically modulated hopping