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 $2+1$ 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.

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Cited by in corpus (2)

• Nonminimal planar electrodynamics modified by higher-derivative terms
• Holographic Hydrodynamics of {\it Tilted} Dirac Materials