Electron Currents from Gradual Heating in Tilted Dirac Cone Materials

TL;DR

This paper develops a hydrodynamic theory for tilted Dirac/Weyl materials, revealing how their emergent spacetime geometry enables novel heat and electric current responses to temperature changes and introduces tilt-dependent conductivity effects.

Contribution

It formulates a hydrodynamic framework based on an effective spacetime metric for tilted Dirac/Weyl materials, uncovering new transport phenomena linked to the tilt and spacetime geometry.

Findings

Heat and electric currents respond to the temporal temperature gradient.

Tilt induces a non-zero symmetric Hall-like conductance.

Tilt-related conductivity contributions can be experimentally distinguished.

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 $2+1$ 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 in response to the $temporal$ gradient of temperature, $\partial_t T$ and (ii) a non-zero symmetric Hall-like conductance $\sigma^{ij}\propto \zeta^i\zeta^j$ where $\zeta^j$ parameterize the tilt in $j$'th space direction. The finding (i) above that can be demonstrated in the laboratory in state of the art cooling/heating rate settings, implies that the non-trivial emergent spacetime geometry in these materials empowers them with a fascinating capability to harvest the naturally available sources of $\partial_t T$ of hot deserts to produce electric energy. We further find a tilt-induced contribution to the conductivity which is an offspring of Drude pole and can be experimentally disentangled from the Drude pole itself.