Collective dynamics and the Anderson-Higgs mechanism in a bona fide holographic superconductor

TL;DR

This paper investigates the collective excitations and the Anderson-Higgs mechanism in a genuine holographic superconductor model, revealing how the Higgs mode behaves and confirming theoretical predictions through holographic analysis.

Contribution

It constructs a bona fide holographic superconductor using mixed boundary conditions and analyzes its collective dynamics, demonstrating the Anderson-Higgs mechanism and validating Ginzburg-Landau theory predictions.

Findings

Second sound disappears in the spectrum.

The gauge field acquires a finite energy gap.

The Higgs mode becomes underdamped below T_c/2.

Abstract

The holographic superconductor is one of the most popular models in the context of applied holography. Despite what its name suggests, it does not describe a superconductor. On the contrary, the low temperature phase of its dual field theory is a superfluid with a spontaneously broken U(1) global symmetry. As already observed in the previous literature, a bona fide holographic superconductor can be constructed using mixed boundary conditions for the bulk gauge field. By exploiting this prescription, we study the near-equilibrium collective dynamics in the Higgs phase and reveal the characteristic features of the Anderson-Higgs mechanism. We show that second sound disappears from the spectrum and the gauge field acquires a finite energy gap of the order of the plasma frequency. We observe an overdamped to underdamped crossover for the Higgs mode which acquires a finite energy gap below $\approx T_c/2$, with $T_c$ the superconducting critical temperature. Interestingly, the energy gap of the Higgs mode at low temperature is significantly smaller than $2\Delta$, with $\Delta$ the superconducting energy gap. Finally, we interpret our results using Ginzburg-Landau theory and we confirm the validity of previously derived perturbative analytic expressions.