Holographic Hydrodynamics of {\it Tilted} Dirac Materials

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.Comment: 7 two-column page

Electron Currents from Gradual Heating in Tilted Dirac Cone Materials

Materials hosting tilted Dirac/Weyl fermions upgrade the solid-state phenomena into a new spacetime structure. They admit a geometric description in terms of an effective spacetime metric. Using this metric that is rooted in the long-distance behavior of the underlying lattice, we formulate the hydrodynamics theory for tilted Dirac/Weyl materials in $2+1$ spacetime dimensions. We find that the mingling of space and time through the off-diagonal components of the metric gives rise to: (i) heat and electric currents proportional to the "temporal" gradient of temperature, $\partial_t T$ and (ii) a non-zero Hall conductance $\sigma^{ij}\propto \zeta^i\zeta^j$ where $\zeta^j$ parametrizes the tilt in $j$'th space direction. The finding (i) above that can be demonstrated in the laboratory, suggests that thanks to the non-trivial spacetime geometry in these materials, naturally available sources of $\partial_t T$ in hot deserts offer a new concept for the conversion of sunlight heating into electric energy. We further find a tilt-induced non-Drude contribution to conductivity which can be experimentally disentangled from the usual Drude pole

Holographic hydrodynamics of tilted Dirac materials

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 (e.g. organic α-(BEDT-TTF)2I3 and 8Pmmn borophene) with tilted Dirac cone

Kinetic theory of tilted Dirac cone materials

We formulate the Boltzmann kinetic equations for interacting tilted Dirac fermions in two space dimensions characterized by a tilt parameter $0\le\zeta<1$. Solving the linearized Boltzmann equation, we find that the broadening of the Drude pole is enhanced by $\kappa(\zeta)\times(1-\zeta^2)^{-1/2}$, where the $\kappa$ is interaction-induced enhancement factor. The intensity of the Drude pole is also anisotropically enhanced by $(1-\zeta^2)^{-1}$. The ubiquitous "redshift" factors $(1-\zeta^2)^{1/2}$ can be regarded as a manifestation of an underlying spacetime structure in such solids. The additional broadening $\kappa$ indicates that interaction effects are more pronounced for electrons in a $\zeta$-deformed Minkowski spacetime of tilted Dirac fermions