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Electron Currents from Gradual Heating in Tilted Dirac Cone Materials

by Ahmadreza Moradpouri, Mahdi Torabian, Seyed Akbar Jafari

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


Author comments upon resubmission

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.

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