Non-hermitian topology as\xa0a unifying framework for the Andreev versus Majorana states controversy

J Avila,E Prada,F Peñaranda,R Aguado,P San-Jose

doi:10.1038/s42005-019-0231-8

Abstract

Zero-energy Andreev levels in hybrid semiconductor-superconductor nanowires mimic all expected Majorana phenomenology, including 2{e}^{2}/h conductance quantisation, even where band topology predicts trivial phases. This surprising fact has been used to challenge the interpretation of various transport experiments in terms of Majorana zero modes. Here we show that the Andreev versus Majorana controversy is clarified when framed in the language of non-Hermitian topology, the natural description for quantum systems open to the environment. This change of paradigm allows one to understand topological transitions and the emergence of zero modes in more general systems than can be described by band topology. This is achieved by studying exceptional point bifurcations in the complex spectrum of the system’s non-Hermitian Hamiltonian. Within this broader topological classification, Majoranas from both conventional band topology and a large subset of Andreev levels at zero energy are in fact topologically equivalent, which explains why they cannot be distinguished.

Highlights

Zero-energy Andreev levels in hybrid semiconductor-superconductor nanowires mimic all expected Majorana phenomenology, including 2e2=h conductance quantisation, even where band topology predicts trivial phases
As discussed first by Pikulin and Nazarov in the context of nanowires coupled to superconductors[23,24], the distribution of complex eigenvalues of Heff allows for a natural topological classification of open system phases
This framework provides a theoretical explanation of why Majoranas from conventional band topology and so-called trivial zero-energy Andreev levels[9,10,11,12,13,14] behave the same

Summary

Introduction

Zero-energy Andreev levels in hybrid semiconductor-superconductor nanowires mimic all expected Majorana phenomenology, including 2e2=h conductance quantisation, even where band topology predicts trivial phases. A hybrid semiconductor-superconductor nanowire can be tuned into a topological superconductor phase with Majorana zero modes (MZMs)[1] when an external Zeeman fitoepldoloBgiecxacleterdans saiticornit2i,c3.alSivnacleuethBe ceaarnlyd the system undergoes a measurements[4] following this remarkable theoretical prediction, there has been great progress in the field and the latest experiments report extremely robust zero-bias anomalies (ZBAs) in the differential conductance (dI=dV)[5,6]. Deviations include finite length, nonuniform chemical potentials, or coupling to an external environment through leads and gates In such systems the conventional band-topological picture cannot be invoked and the problem of discerning between ABS zero modes and MZMs is ill-defined, as the wavefunctions of both states are continuously connected, and topological transitions are mere crossovers. This classification matches band topological theory in the case of sufficiently long and uniform systems where the latter is applicable, while generalising it to a wider range of physically relevant scenarios where it is not

Methods

Results

Conclusion