Striped phases in the holographic insulator/superconductor transition

TL;DR

This paper investigates how spatially modulated chemical potentials influence the insulator/superconductor transition in holographic models, revealing conditions under which striped phases emerge and are energetically favored.

Contribution

It introduces a detailed analysis of striped phases in holographic transitions with spatially modulated chemical potentials, including analytical explanations for observed discontinuities.

Findings

Striped phases develop above a critical chemical potential.

Discontinuity in charge density occurs at large wave vectors when the leading chemical potential term is zero.

Spatial modulation increases the critical chemical potential, disfavoring the phase transition.

Abstract

We study striped phases in holographic insulator/superconductor transition by considering a spatially modulated chemical potential in AdS soliton background. Generally striped phases can develop above a critical chemical potential. When the constant leading term in the chemical potential is set to zero, a discontinuity in the plot of charge density versus chemical potential is observed in the limit of large wave vector. We explain this discontinuity using an analytical approach. When the constant leading term in the chemical potential is present, the critical chemical potential is larger than in the case of a homogeneous chemical potential, which indicates that the spatially modulated chemical potential disfavors the phase transition. This behavior is also confirmed qualitatively by analytical calculations. We also calculate the grand canonical potential and find that the striped phase is favored.