Fermionic Hopf solitons and Berry's phase in topological surface superconductors

TL;DR

This paper demonstrates that Hopf textures in topological superconductor surfaces behave as fermions, revealing emergent fermionic properties in bosonic field configurations and predicting observable effects in tunneling experiments.

Contribution

It introduces a topological Berry phase term to the Landau-Ginzburg theory to describe fermionic Hopf textures in topological surface superconductors, a novel theoretical insight.

Findings

Hopf textures act as fermions in topological superconductors

Berry phase term modifies superconductivity theory to include topological effects

Predicted observable consequences in tunneling experiments

Abstract

A central theme in many body physics is emergence - new properties arise when several particles are brought together. Particularly fascinating is the idea that the quantum statistics may be an emergent property. This was first noted in the Skyrme model of nuclear matter, where a theory formulated entirely in terms of a bosonic order parameter field contains fermionic excitations. These excitations are smooth field textures, and believed to describe neutrons and protons. We argue that a similar phenomenon occurs in topological insulators when superconductivity gaps out their surface states. Here, a smooth texture is naturally described by a three component real vector. Two components describe superconductivity, while the third captures the band topology. Such a vector field can assume a 'knotted' configuration in three dimensional space - the Hopf texture - that cannot smoothly be unwound. Here we show that the Hopf texture is a fermion. To describe the resulting state, the regular Landau-Ginzburg theory of superconductivity must be augmented by a topological Berry phase term. When the Hopf texture is the cheapest fermionic excitation, striking consequences for tunneling experiments are predicted.