Interior structure of the holographic s + p superconductor and chaotic-stable transition near the black hole singularity

TL;DR

This paper explores the complex interior structure of a holographic s+p superconductor, revealing how s-wave order influences singularity behavior and induces a chaotic-stable transition near the black hole singularity, linking holography and cosmological billiards.

Contribution

It introduces a detailed analysis of the interior singularity structure of a holographic multi-band superconductor with coexisting s-wave and p-wave orders, including new Kasner laws and a chaotic-stable transition.

Findings

Derivation of Kasner alternation laws for the model

Identification of a chaotic-stable transition near the singularity

Linking the transition to boundary secondary condensation

Abstract

In this work, we investigate the interior structure of a holographic multi-band superconductor with the coexistence of s-wave and p-wave order parameters. Especially, we investigate the singularity structure of this multi-band model. Different from the single p-wave case, the alternation rule is jointly determined by parameters involving both s-wave order and p-wave order. In the coexistence region, we derive the Kasner alternation laws from both analytical and numerical methods which fit each other nicely. Furthermore, we find that the occurrence of the s-wave order parameter will lead to a chaotic-stable transition for the near singularity structure which matches the expectation of cosmological billiard approach. This novel transition for the near singularity structure constitutes a holographic counterpart of the secondary condensation in boundary superconducting system, offering a complementary perspective for characterizing the properties of boundary condensed matter systems.