The Fate of the Photon in Topological Matter: Superconductivity, Confinement and the Vortex Quantum Hall Effect

TL;DR

This paper explores how photons behave in topological matter, revealing new mechanisms for photon mass acquisition and confinement in topological superconductors and confinement phases, with implications for quantum transport.

Contribution

It derives effective electromagnetic actions in topological phases, introducing topological mass mechanisms without symmetry breaking and describing vortex quantum Hall effects.

Findings

Photon acquires topological mass in superconductors via BF mechanism

Electric charge confinement leads to massive antisymmetric tensor photons

Vortex quantum Hall effect enables dissipationless information transport

Abstract

Topological matter is characterized by the presence of a topological BF term in its long-distance effective action. Topological defects due to the compactness of the U(1) gauge fields induce quantum phase transitions between topological insulators, topological superconductors and topological confinement. In conventional superconductivity, due to spontaneous symmetry breaking, the photon acquires a mass due to the Anderson-Higgs mechanism. In this paper we derive the corresponding effective actions for the electromagnetic field in topological superconductors and topological confinement phases. In topological superconductors magnetic flux is confined and the photon acquires a topological mass through the BF mechanism: no symmetry breaking is involved, the ground state has topological order and the transition is induced by quantum fluctuations. In topological confinement, instead, electric charge is linearly confined and the photon becomes a massive antisymmetric tensor via the St\"uckelberg mechanism. Oblique confinement phases arise when the string condensate carries both magnetic and electric flux (dyonic strings). Such phases are characterized by a vortex quantum Hall effect potentially relevant for the dissipationless transport of information stored on vortices.