# Electron Currents from Gradual Heating in Tilted Dirac Cone Materials

### Submission summary

 As Contributors: Seyed Akbar Jafari Preprint link: scipost_202110_00027v3 Date submitted: 2022-05-18 15:12 Submitted by: Jafari, Seyed Akbar Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Approach: Theoretical

### 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 proportional to the {\em temporal} gradient of temperature, $\partial_t T$ and (ii) a non-zero 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, implies that the non-trivial emergent spacetime geometry in these materials empowers them with a fascinating capability to harness naturally available sources of $\partial_t T$ 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.

###### Current status:
Editor-in-charge assigned

In this revision we have added two important new ingredients to address the concerns of the referees. The details are given in the attached PDF file.

### List of changes

1- We have added discussions after Eq. (54) to show that steady-state solutions are also possible. But in addition to steady- state solutions, there are also non-steady-state solutions that are of interest to us. Hopefully this will convince the referee 1 that our theory does not miss the steady-state solutions.
2- Around newly added equations (65)-(68) we have added estimates based on the measurements done on graphene samples to estimate that for tilted Dirac cone samples that are ∼ 1cm wide, currents of ∼ 4nA are attainable.
3- We have corrected typos here and there.