Electron Currents from Gradual Heating in Tilted Dirac Cone Materials

Abstract

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