Excited states of holographic superconductors with hyperscaling violation

TL;DR

This paper investigates how hyperscaling violation influences the properties of excited states in holographic superconductors, revealing effects on critical temperatures, chemical potentials, and conductivity spectra through numerical and analytical methods.

Contribution

It provides a detailed analysis of excited and ground states in holographic superconductors with hyperscaling violation, highlighting novel temperature and conductivity behaviors.

Findings

Excited states have lower critical temperatures than ground states.

Hyperscaling violation decreases the critical chemical potential difference between states.

Conductivity spectra exhibit multiple peaks corresponding to excited states.

Abstract

We employ the numerical and analytical methods to study the effects of the hyperscaling violation on the ground and excited states of holographic superconductors for $d=2,~z=2$. For both the holographic s-wave and p-wave models with the hyperscaling violation, we observe that the excited state has a lower critical temperature than the corresponding ground state, which is similar to the relativistic case, and the difference of the dimensionless critical chemical potential between the consecutive states decreases as the hyperscaling violation increases. Interestingly, as we amplify the hyperscaling violation in the s-wave model, the critical temperature of the ground state first decreases and then increases, but that of the excited states always decreases. In the p-wave model, regardless of the ground state or the excited states, the critical temperature always decreases with increasing the hyperscaling violation. In addition, we find that the hyperscaling violation affects the conductivity $\sigma$ which has $n$ peaks for the $n$-th excited state, and changes the relation in the gap frequency for the excited states in both s-wave and p-wave models.