Holographic Polarons, the Metal-Insulator Transition and Massive Gravity

Abstract

Massive gravity is holographically dual to `realistic' materials with momentum relaxation. The dual graviton potential encodes the phonon dynamics and it allows for a much broader diversity than considered so far. We construct a simple family of isotropic and homogeneous materials that exhibit an interaction-driven Metal-Insulator transition. The transition is triggered by the formation of polarons -- phonon-electron quasi-bound states that dominate the conductivities, shifting the spectral weight above a mass gap. We characterize the polaron gap, width and dispersion.

Figures (3)

• Figure 1: Development of polaron formation as temperature is decreased. $T=1,\,0.46 (T_2),\, 0.35,\,0.3 (T_1),\,0.27,\,0.22,\,0.17,\,0.04$. Inset: motion of the lightest quasi-normal-mode (QNM) for the same temperatures (corresponding colours) and some intermediate additional values (purple dots). At large $T$, the QNM separates from the real axis with decreasing $T$, until it collides with the next QNM (near $T_1$) and forms a pair of conjugated poles with positive and negative real parts -- the polaron particle/anti-particle poles. (Similar QNM collisions have been observed in Davison:2014lua.)
• Figure 2: (a) The polaron energy-gap $\omega_0$ as a function of $T$, extracted numerically as the peak-position in ${\rm Abs}[\sigma(\omega)]$. $\omega_0$ detaches from 0 at $T_1$. (b) DC conductivity $\sigma_{\text{DC}}(T)$ as a function of $T$. The continuous line is the analytic result \ref{['DC']} and the dots are the numerical computation. One observes two critical temperatures: the the maximum in $\sigma_{\text{DC}}(T)$ marking the metal/insulator transition ($T_2$), and the polaron formation $T_1$. We find $T_1<T_2$ generically.
• Figure 3: Motion of the polaron peak with wavenumber. $T=0.04$, $k=0,\,0.5,\,0.8,1.2,\,2$. Inset: the extracted dispersion relation.