The entropy of a tilted Dirac cone material, integrated across a spatially varying tilt, grows linearly with temperature behind the analogue horizon and can be mapped to BTZ black hole entropy.
Holographic Hydrodynamics of {\it Tilted} Dirac Materials
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abstract
We present a gravity dual to a quantum material with tilted Dirac cone in 2+1 dimensional spacetime. In this many-body system the electronics degrees of freedom are strongly-coupled, constitute a Dirac fluid and admit an effective hydrodynamic description. The holographic techniques are applied to compute the thermodynamic variables and hydrodynamic transports of a fluid on the boundary of an asymptotically anti de Sitter spacetime with a boosted black hole in the bulk. We find that these materials exhibit deviations from the normal Dirac fluid which rely on the tilt of the Dirac cone. In particular, the shear viscosity to entropy density ratio is reduced and the KSS bound is violated in this system. This prediction can be experimentally verified in two-dimensional quantum materials ({\it e.g.} organic $\alpha$-({BEDT}-{TTF})$_2$I$_3$ and $8Pmmn$ borophene) with tilted Dirac cone.
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Smart Holes: Analogue black holes with the right temperature and entropy
The entropy of a tilted Dirac cone material, integrated across a spatially varying tilt, grows linearly with temperature behind the analogue horizon and can be mapped to BTZ black hole entropy.