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arXiv · 2602.18924

Critical Temperatures of Excited Holographic Superconductors in Born--Infeld Electrodynamics on a Reissner--Nordstr\"om--AdS Background

Hoang Van Quyet
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Abstract

We study the ground state (GS) and the two lowest excited states (ES1, ES2) of a probe holographic superconductor with Born-Infeld (BI) electrodynamics on a charged Reissner-Nordstrom-AdS (RN-AdS) black hole background. Distinguishing these background geometries by their extended-thermodynamic pressure P=-Lambda/8pi requires the electric charge Q: the neutral Schwarzschild-AdS metric admits only one positive horizon for any M,L^2>0 and cannot support the SBH/LBH transition. Working on the correctly identified RN-AdS geometry, we set up the scalar/BI-gauge probe sector, formulate the linear eigenvalue problem for the onset of condensation, and solve it by a shooting method. We obtain T_c of GS, ES1, ES2 at three representative pressures (P>P_c, P=P_c, P<P_c) and five values of the BI parameter b in {0,1,2,3,5} Q^-1. T_c increases monotonically with P and is suppressed by b for all three states, more for the excited states (~2% for GS versus ~10-27% for ES1/ES2 at b=5 Q^-1). A finer scan in b shows the suppression follows a quadratic law T_c(b)/T_c(0)=1-alpha b^2, with alpha(GS)~7.4e-4, alpha(ES1)~4.1e-3, alpha(ES2)~1.1e-2, consistent with the radial profiles of the threshold modes: the ground-state mode is concentrated near the horizon, while the nodal excited-state modes extend further into the bulk. We present this as a nodal-sensitivity picture rather than a proven mechanism, and make it concrete with an explicit leading-order BI correction to the bulk gauge field: this differential coupling has not previously been isolated and quantified, independently of the back-reacted problem left to a companion study. These results clarify how BI nonlinearity interacts with the nodal structure of excited states, giving a sharper linear baseline for the back-reacted, finite-temperature holographic superconductor.

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Hoang Van Quyet. 2026-02-21. Critical Temperatures of Excited Holographic Superconductors in Born--Infeld Electrodynamics on a Reissner--Nordstr\"om--AdS Background. https://arxiv.org/abs/2602.18924

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