Holographic Charge Density Waves

Abstract

We discuss a gravity dual of a charge density wave consisting of a U(1) gauge field and two scalar fields in the background of an AdS$_4$ Schwarzschild black hole together with an antisymmetric field (probe limit). Interactions drive the system to a phase transition below a critical temperature. We numerically compute the ground states characterized by modulated solutions for the gauge potential corresponding to a dynamically generated unidirectional charge density wave in the conformal field theory. Signatures of the holographic density waves are retrieved by studying the dynamical response to an external electric field. We find that this novel holographic state shares many common features with the standard condensed matter version of charge density wave systems.

Figures (2)

• Figure 1: Temperature dependence of the condensate (solid line). The dashed line is the BCS fit to the numerical values near $T_c$. We find $\langle {\cal O}_1\rangle\approx 8.5T_c\left(1-T/T_c\right)^{1/2}$ near $T\rightarrow T_c$.
• Figure 2: The numerically calculated real part of the conductivity $Re[\sigma(\omega)]$, versus normalized frequency with the condensate $\omega/\langle {\cal O}_1 \rangle$ (left) and temperature $\omega/T$ (right). In both plots, we clearly observe a 'dip' that arises from the CDW formation and softens with $T\rightarrow T_c$ since $\langle {\cal O}_1 \rangle\rightarrow 0$. At $T=T_c$ we retrieve the normal state conductivity $Re[\sigma(\omega)]=1$.