Luca V. Delacrétaz, Blaise Goutéraux, Sean A. Hartnoll, Anna Karlsson
SciPost Phys. 3, 025 (2017) ·
published 29 September 2017

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Bad metals have a large resistivity without being strongly disordered. In
many bad metals the Drude peak moves away from zero frequency as the
resistivity becomes large at increasing temperatures. We catalogue the position
and width of the `displaced Drude peak' in the observed optical conductivity of
several families of bad metals, showing that $\omega_\text{peak} \sim \Delta
\omega \sim k_BT/\hbar$. This is the same quantum critical timescale that
underpins the $T$linear dc resistivity of many of these materials. We provide
a unified theoretical description of the optical and dc transport properties of
bad metals in terms of the hydrodynamics of short range quantum critical
fluctuations of incommensurate density wave order. Within hydrodynamics, pinned
translational order is essential to obtain the nonzero frequency peak.