# Analytical study of the holographic superconductor from higher derivative theory

## TL;DR

This paper analytically investigates holographic superconductors with higher derivative couplings, confirming the second order phase transition and analyzing conductivity and energy gap behaviors, aligning well with numerical results.

## Contribution

It introduces an analytical approach using Sturm-Liouville methods to study higher derivative holographic superconductors, validating perturbative calculations against numerical data.

## Key findings

- Critical temperature calculated analytically matches numerical results.
- Phase transition is second order with mean field behavior.
- Superconducting energy gap correlates with the condensation and HD coupling parameters.

## Abstract

In this paper, we analytically study the holographic superconductor models with the high derivative (HD) coupling terms. Using the Sturm-Liouville (SL) eigenvalue method, we perturbatively calculate the critical temperature. The analytical results are in good agreement with the numerical results. It confirms that the perturbative method in terms of the HD coupling parameters is available. Along the same line, we analytically calculate the value of the condensation near the critical temperature. We find that the phase transition is second order with mean field behavior, which is independent of the HD coupling parameters. Then in the low temperature limit, we also calculate the conductivity, which is qualitatively consistent with the numerical one. We find that the superconducting energy gap is proportional to the value of the condensation. But we note that since the condensation changes with the HD coupling parameters, as the function of the HD coupling parameters, the superconducting energy gap follows the same change trend as that of the condensation.

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Source: https://tomesphere.com/paper/1902.07125