Higgs Boson in Superconductors

TL;DR

This paper explores the theoretical and experimental evidence that superconductors exhibit both the massless Bogolubov mode and a finite energy Higgs mode, due to their approximate particle-hole symmetry, drawing parallels with Lorentz-invariant theories.

Contribution

It provides a detailed analysis of the Higgs mode in superconductors, highlighting its similarity to Lorentz-invariant theories and its distinction from superfluid helium.

Findings

Superconductors exhibit both Bogolubov and Higgs modes.

The Higgs mode has a finite energy at long wavelengths.

Particle-hole symmetry in superconductors enables the Higgs mode presence.

Abstract

Superfluid helium, describable by a two-component order parameter, exhibits only the Bogolubov mode with energy $\to 0$ at long wavelengths, while a Lorentz-invariant theory with a two-component order parameter exhibits a finite energy mode at long wavelengths (the Higgs Boson), besides the above mass-less mode. The mass-less mode moves to high energies if it couples to electromagnetic fields (the Anderson-Higgs mechanism). Superconductors, on the other hand have been theoretically and experimentally shown to exhibit both modes. This occurs because the excitations in superconductors have an (approximate) particle-hole symmetry and therefore show a similarity to Lorentz-invariant theories.