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Finite-frequency anomaly-induced electromechanical response of Dirac fermions in deformed graphene

Ara Sedrakyan

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Phys. Rev. B 114, 175103 – Published 2 September, 2026

DOI: https://doi.org/10.1103/lxn4-s9j4

Abstract

A deformation of a graphene sheet changes more than the positions of the atoms. In the low-energy Dirac theory it also produces geometric electron-phonon vertices. One of these vertices acts as an emergent phonon gauge field Aμ, which couples to the same Dirac current as the electromagnetic vector potential. This shared current vertex gives a direct route from mechanics to electronics: a moving deformation can generate a transverse electric current, and a deformation pattern with emergent phonon flux can bind electric charge. We show that the coefficient of this mixed electromechanical response is the parity-odd current-current correlator of a massive Dirac cone. For an insulating cone the coefficient is the one-cone Chern-Simons value, while for a doped cone in the local regime it is reduced by the Berry curvature factor m/|μ|. We apply the response to explicit deformations. A traveling flexural wave generates a transverse second-harmonic current; a static ripple mixed with a dynamic phonon generates a transverse current at the drive frequency; and two noncollinear modes can generate charge modulation through the emergent phonon flux. We keep the spin and valley sum explicit, so the paper shows when the one-cone anomaly becomes a charge current in graphene and when it instead appears in a valley, spin, or spin-valley channel. For sublattice-gapped graphene with a valley-odd deformation gauge coupling, the two valleys add rather than cancel. The experimentally sharp signature is a transverse electrical signal at twice the flexural-wave frequency, with a phase fixed by the sign of the sublattice gap and a gate dependence that crosses over from a gap plateau to a 1/|μ| decay. These direction, phase, frequency, and gate-voltage selection rules give clean tests of the anomaly-induced electromechanical channel in deformed graphene.

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Phys. Rev. B 114, 175103– Published 2 September, 2026
  • Received 21 May 2026
  • Revised 10 August 2026
  • Accepted 17 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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