Phases of holographic d-wave superconductor

TL;DR

This paper explores various phases of a holographic d-wave superconductor model, discovering new spatially modulated and homogeneous phases, and analyzing their symmetries and thermodynamic preferences relevant to high-Tc cuprates.

Contribution

It introduces three novel solutions in the holographic d-wave superconductor model, including two spatially modulated phases and a homogeneous anapole phase, expanding understanding of possible phases.

Findings

Anapole phase is thermodynamically preferred in the simplest model.

Two spatially modulated phases correspond to charge density wave states.

Symmetry properties vary across different phases, with some breaking translation, parity, and time-reversal symmetries.

Abstract

We study different phases in the holographic model of d-wave superconductor. These are described by solutions to the classical equations of motion found in different ansatze. Apart from the known homogeneous d-wave superconducting phase we find three new solutions. Two of them represent two distinct families of the spatially modulated solutions, which realize the charge density wave phases in the dual theory. The third one is the new homogeneous phase with nonzero anapole moment. These phases are relevant to the physics of cuprate high-Tc superconductor in pseudogap region. While the d-wave phase preserves translation, parity and time reversal symmetry, the striped phases break translations spontaneously. Parity and time-reversal are preserved when combined with discrete half-periodic shift of the wave. In anapole phase translation symmetry is preserved, but parity and time reversal are spontaneously broken. All of the considered solutions brake the global $U(1)$. Thermodynamical treatment shows that in the simplest d-wave model the anapole phase is always preferred, while the stripe phases realize the continuous transition in solution space between the normal phase and two homogeneous condensed phases.