$(1+3)$D topological superconductors: screening and confinement in presence of external fields

TL;DR

This paper investigates the interaction energy in $(1+3)$D topological superconductors under external fields, revealing screening and confinement phases depending on electric or magnetic field conditions.

Contribution

It introduces a gauge-invariant formalism to analyze topological superconductors, showing how external fields influence screening and confinement phenomena.

Findings

Electric fields induce a Yukawa screening potential.

Magnetic fields lead to confinement with a linear potential.

Small Josephson coupling enhances confinement effects.

Abstract

Adopting the gauge-invariant and path-dependent variables formalism, we compute the interaction energy for a topological field theory describing $(1+3)$D topological superconductors in presence of external fields. As a result, in the case of a constant electric field- strength expectation value, we show that the interaction energy describes a purely screening phase, encoded in a Yukawa potential. On the other hand, in the case of a constant magnetic field-strength and for a very small Josephson coupling constant, the particle-antiparticle binding potential displays a linear term leading to the confinement of static charge probes along with a screening contribution.