On holographic disorder-driven metal-insulator transitions

TL;DR

The paper addresses disorder-driven metal-insulator transitions in strongly coupled systems using holography. It builds a minimal Massive Gravity–Maxwell model with a direct $Y(X)F_{}F^{}$ coupling to encode charged disorder and uses homogeneous translation-breaking deformations to describe momentum relaxation. It finds that the DC conductivity can be driven to arbitrarily small values, enabling a disorder-driven MIT and showing that there is no universal lower bound on $\sigma_{DC}$ in these holographic disordered systems; finite-temperature crossovers and potential gradient instabilities toward modulated phases are discussed. The work suggests a controlled EFT-like framework for disorder effects in strongly correlated materials and motivates further study of gap formation, striped phases, and viscoelastic responses within holographic models.

Abstract

We give a minimal holographic model of a disorder-driven metal-insulator transition. It consists in a CFT with a charge sector and a translation-breaking sector that interact in the most generic way allowed by the symmetries and by dynamical consistency. In the gravity dual, it reduces to a Massive Gravity-Maxwell model with new direct couplings between the Maxwell and metric that are allowed when gravity is massive. We show that, generically, the effect of disorder is to decrease the DC electrical conductivity. This happens to such an extent that the conductivity does not obey any lower bound and can be very small in the insulating phase. In some cases, the large disorder limit produces gradient instabilities that hint at the formation of modulated phases.

Figures (6)

• Figure 1: Electric DC conductivity at zero temperature and charge density $\rho=1$ for the model \ref{['themodel']} dialing the disorder strength $\alpha$ (i.e the graviton mass); Left:$\kappa=0$ (i.e. previous literature); Right: with the new coupling $\kappa=0.5$ (safe region) .
• Figure 2: Temperature features of the DC conductivity at different disorder strengths $\alpha$ (i.e. graviton mass) for the model considered in \ref{['themodel']} with unitary charge density $\rho=1$; Left: metal-incoherent metal transition for $\kappa=0$ (i.e. previous literature); Right: metal-insulator transition for $\kappa=0.5$ (safe region).
• Figure 3: Phase diagrams for the model \ref{['model']} with unitary charge density $\rho=1$. Dashed lines correspond to $\sigma_{DC}=0.1,\,0.8\,,1.2$ and they divide the four regions: a) good metal, b) incoherent metal, c) bad insulator and d) good insulator . Top Left: Temperature-disorder plane with $\kappa=0$. Top Right: Temperature-disorder plane with graviton mass $\kappa=0.5$. Bottom: For every region (a,b,c,d) in the phase diagrams one representative example of $\mathrm{Re}\,(\sigma)$ is shown. The parameters for each one of the AC plots are pinpointed in the $T-\alpha$ phase diagram (top right) and they correspond to: $\left[\,\bullet:(\alpha=0.5,T=0.5),\,\blacksquare:(\alpha=1,T=1.2),\,\bigstar:(\alpha=6,T=1),\,\blacktriangle:(\alpha=10,T=0.2)\,\right]$ .
• Figure 4: Gradient instability for the scalar perturbations at $u=u_!$ for $\kappa=1,\rho=1,\alpha=10$ regarding the model considered in \ref{['themodel']}.
• Figure 5: No gradient instability for $\kappa=0.5,\rho=1$ upon varying the strength of disorder (i.e. graviton mass) for the model considered in \ref{['themodel']}.