Electron currents from gradual heating in tilted Dirac cone materials

Abstract

Materials hosting tilted Dirac/Weyl fermions provide an emergent spacetime structure for the solid state physics. 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 hydrodynamic theory for tilted Dirac/Weyl materials in 2+12+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∂tT and (ii) a non-zero Hall-like conductance \sigma^{ij}\propto \zeta^i\zeta^jσij∝ζiζj where \zeta^jζj parameterize the tilt in jj’th space direction. The finding (i) above that can be demonstrated in the laboratory, implies that the non-trivial emergent spacetime geometry in these materials empowers them with a fascinating capability to harness naturally available sources of \partial_t T∂tT of hot deserts to produce electric current. We further find a tilt-induced non-Drude contribution to conductivity which can be experimentally disentangled from the usual Drude pole.