Holographic charge density waves
Aristomenis Donos, Jerome P. Gauntlett
TL;DR
This work shows that strongly coupled holographic matter at finite density can host charge density waves (CDWs) that spontaneously break translation symmetry while preserving parity and time-reversal invariance. By analyzing two broad holographic frameworks—Einstein–Maxwell–dilaton models and Einstein–Maxwell–dilaton–vector models—the authors identify spatially modulated instabilities arising from BF-bound violations in an infrared $AdS_2\times \mathbb{R}^{D-2}$ region, controlled by model parameters such as $\tau_1$ and $\tau_2+v_2$. They derive and diagonalize the AdS$_2$ mass matrices, showing conditions for $m_i^2<-1/4$ and highlighting cases where the minimum occurs at nonzero momentum $k$, implying CDWs with preserved $P$ and $T$, including explicit results for $D=4$ and a concrete dilaton potential. For models with two vector fields, they also relate these instabilities to finite-temperature AdS–RN black brane instabilities by computing the critical temperature $T_c(k)$, finding a preferred wave number $k_c$ and a modulated charge density below $T_c$, suggesting rich spatially modulated ground states and possible holographic Mott-like behavior.
Abstract
We show that strongly coupled holographic matter at finite charge density can exhibit charge density wave phases which spontaneously break translation invariance while preserving time-reversal and parity invariance. We show that such phases are possible within Einstein-Maxwell-dilaton theory in general spacetime dimensions. We also discuss related spatially modulated phases when there is an additional coupling to a second vector field, possibly with non-zero mass. We discuss how these constructions, and others, should be associated with novel spatially modulated ground states.