Multifaceted properties of Andreev bound states: Interplay of symmetry and topology

TL;DR

This paper reviews the complex properties of Andreev bound states in superfluids and superconductors, emphasizing their topological and symmetry-related features, especially in superfluid helium-3, and discusses future research directions.

Contribution

It provides a comprehensive overview of Andreev bound states, highlighting their multifaceted nature and the role of symmetry and topology, with a focus on superfluid helium-3.

Findings

Andreev bound states can host Majorana fermions and odd-frequency pairing.

The interplay of symmetry and topology enriches the physical characteristics of ABS.

Superfluid helium-3 serves as a platform for observing topological quantum phenomena.

Abstract

Andreev bound states ubiquitously emerge as a consequence of nontrivial topological structures of the order parameter of superfluids and superconductors and significantly contribute to thermodynamics and low-energy quantum transport phenomena. We here share the current status of our knowledge on their multifaceted properties as Majorana fermions and odd-frequency pairing. A unified concept behind Andreev bound states originates from a soliton state in the one-dimensional Dirac equation with mass domain wall, and the interplay of ABSs with symmetry and topology enriches their physical characteristics. We make an overview of Andreev bound states with a special focus on superfluid $^3$He. The quantum liquid confined to restricted geometries serves as a rich repository of noteworthy quantum phenomena, such as mass acquisition of Majorana fermions driven by spontaneous symmetry breaking, topological quantum criticality, Weyl superfluidity, and the anomalous magnetic response. The marriage of the superfluid $^3$He and nano-fabrication techniques will take one to a new horizon of topological quantum phenomena associated with Andreev bound states.