Criticality and Phase Structures of Excited Holographic Superconductors in Nonlinear Electrodynamics

TL;DR

This paper studies how nonlinear electrodynamics and black hole curvature influence the phase structure and energy gaps of excited holographic superconductors, revealing a curvature-controlled transition between gapped and gapless phases.

Contribution

It uncovers a novel mechanism where black hole curvature controls the emergence of gapless phases in excited states of holographic superconductors within nonlinear electrodynamics.

Findings

Excited states exhibit both gapped and gapless phases depending on pressure.

Higher pressure leads to gapped ground and first excited states, while second excited state becomes gapless.

Curvature effects, not numerical artifacts, drive the transition between gapped and gapless phases.

Abstract

We investigate the critical properties and phase structure of excited states in a holographic superconductor model within the framework of Varying Central Charge Thermodynamics, where the cosmological constant serves as a fundamental parameter controlling the number of degrees of freedom in the boundary conformal field theory. Employing Born-Infeld nonlinear electrodynamics, we explore how the nonlinear parameter $b$ affects the condensation of the ground state (GS) and the two lowest excited states (ES1, ES2) in the background of a spherically symmetric Schwarzschild-AdS black hole. A state is classified as possessing a \textbf{hard gap} if its optical conductivity exhibits $\mathrm{Re}\sigma(\omega) = 0$ for $\omega < \omega_g$, indicating a hard energy gap in the excitation spectrum and the Meissner effect. In contrast, a \textbf{gapless superconductor} possesses a non-zero order parameter but lacks a hard gap, with $\mathrm{Re}\sigma(\omega) \neq 0$ as $\omega \to 0$. Our central finding reveals that the emergence of gapless phases in the excited states represents a genuine physical phenomenon arising from the competition between Born-Infeld nonlinear screening effects and the spatial curvature of the black hole geometry, not from numerical artifacts. Specifically, when the pressure $P$ exceeds the critical pressure $P_c$, both GS and ES1 are gapped superconductors with hard energy gaps while ES2 is a gapless superconductor. However, when $P \leq P_c$, only GS remains gapped while both ES1 and ES2 condense into gapless phases. This curvature-controlled switching of superconducting properties provides a novel mechanism for engineering gapless superconductivity in strongly coupled systems through variation of the boundary CFT degrees of freedom, with potential implications for understanding unconventional high-temperature superconductors.