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Holographic helical superconductors

Aristomenis Donos, Jerome P. Gauntlett

TL;DR

The paper tackles the emergence of spatially modulated helical $p$-wave superconductors in $D=5$ charged AdS black branes by analyzing linearised perturbations in multiple consistent truncations, including $N=4\;SU(2)\times U(1)$ gauged supergravity and Romans' theory. By examining near-horizon $AdS_{2}$ BF bounds and constructing normalisable zero modes on full RN black branes, the authors identify regimes where helical $p$-wave order becomes unstable and determine critical temperatures $T_c(k)$ for these modulated phases, revealing both charged and neutral instabilities and distinct helical orders ($p_x$ and $(p_x+ip_y)$). In Romans' theory, they also uncover a high-temperature Gubser-Mitra instability, underscoring a rich phase structure with multiple competing branches; overall, the work demonstrates that helical superconducting states exist within string/M-theory embeddings and motivates constructing fully back-reacted, spatially modulated black-hole solutions in the AdS/CFT context.

Abstract

We show that D=5 electrically charged AdS black branes can have instabilities associated with spatially modulated p-wave superconductors with helical structure. We show that the instabilities are present within N=4 $SU(2)\times U(1)$ gauged supergravity and hence within D=10 and D=11 supergravity.

Holographic helical superconductors

TL;DR

The paper tackles the emergence of spatially modulated helical -wave superconductors in charged AdS black branes by analyzing linearised perturbations in multiple consistent truncations, including gauged supergravity and Romans' theory. By examining near-horizon BF bounds and constructing normalisable zero modes on full RN black branes, the authors identify regimes where helical -wave order becomes unstable and determine critical temperatures for these modulated phases, revealing both charged and neutral instabilities and distinct helical orders ( and ). In Romans' theory, they also uncover a high-temperature Gubser-Mitra instability, underscoring a rich phase structure with multiple competing branches; overall, the work demonstrates that helical superconducting states exist within string/M-theory embeddings and motivates constructing fully back-reacted, spatially modulated black-hole solutions in the AdS/CFT context.

Abstract

We show that D=5 electrically charged AdS black branes can have instabilities associated with spatially modulated p-wave superconductors with helical structure. We show that the instabilities are present within N=4 gauged supergravity and hence within D=10 and D=11 supergravity.

Paper Structure

This paper contains 14 sections, 46 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The charged two-form model
  3. Instabilities for $AdS_{2}\times \mathbb{R}^{3}$
  4. Zero modes for the AdS-RN black brane
  5. The character of the $p$-wave superconductors
  6. The $SU(2)\times U(1)$ model
  7. Instabilities for $AdS_{2}\times \mathbb{R}^{3}$
  8. Zero modes for the AdS-RN black brane
  9. Spatially modulated neutral instabilities
  10. Romans' Theory
  11. The Gubser-Mitra instability
  12. Final Comments
  13. Neutral instabilities for the $SU(2)\times U(1)$ model
  14. Instabilities of a line of $AdS_{2}\times \mathbb{R}^{3}$ solutions

Figures (3)

  • Figure 1: Plots of critical temperatures $T$ versus $k$ for the existence of normalisable static perturbations of the two-form about the AdS-RN black brane \ref{['eq:RN_sol']} for $m=1$ and, from top to bottom, $q=2$, $q=1.812$, $q=1.7$ and $q=1.5$. We have set $\mu=\sqrt{3}$.
  • Figure 2: Plot of critical temperatures $T$ versus $k$ for the existence of normalisable static perturbations of $A^1$, $A^2$ about the electrically charged black holes \ref{['eq:RN_solb2']}. The plot is for Romans' theory with $\gamma=g=1$ and also $\mu_{2}=\sqrt{2}$ and $\mu_{1}=1$.
  • Figure 3: The shaded region indicates values of $\left(\chi, \gamma\right)$ for which the $AdS_{2}\times \mathbb{R}^{3}$ solutions \ref{['eq:AdS2_limitb2']} have neutral instabilities of the form \ref{['neutansatz']} which break translational and rotational invariance.