Holographic Pair and Charge Density Waves

TL;DR

This paper presents a holographic model demonstrating spontaneous breaking of U(1) symmetry and translational invariance, resulting in pair-density wave order with spatially modulated superconductivity and charge density oscillations, including coexistence phases.

Contribution

It introduces a novel holographic framework capturing pair-density wave phenomena and co-existing orders, expanding understanding of spatially modulated superconducting states.

Findings

Demonstrates a holographic model with pair-density wave order.

Shows coexistence of superconducting and charge density wave orders.

Reveals charge density oscillates at twice the scalar condensate frequency.

Abstract

We examine a holographic model in which a U(1) symmetry and translational invariance are broken spontaneously at the same time. Our construction provides an example of a system with pair-density wave order, in which the superconducting order parameter is spatially modulated but has a zero average. In addition, the charge density oscillates at twice the frequency of the scalar condensate. Depending on the choice of parameters, the model also admits a state with co-existing superconducting and charge density wave orders, in which the scalar condensate has a uniform component.