Deformation of graphene sheet: Interaction of fermions with phonons

TL;DR

This paper develops a low-energy Hamiltonian for fermions on a deformed graphene lattice, incorporating lattice defects and phonon interactions, revealing a response linked to a Z_2 anomaly that can be experimentally observed.

Contribution

It introduces a novel effective Hamiltonian describing fermion-phonon interactions in deformed graphene with topological defects, incorporating 2D gravity and gauge invariance.

Findings

Fermion currents respond to lattice deformations via a Z_2 anomaly.

The model links lattice deformations to a 2D gravity framework.

Potential for experimental detection of fermion response to phonons.

Abstract

We construct an effective low energy Hamiltonian which describes fermions dwelling on a deformed honeycomb lattice with dislocations and disclinations, and with an arbitrary hopping parameters of the corresponding tight binding model. It describes the interaction of fermions with a 2d gravity and has also a local SU(2) gauge invariance of the group of rotations. We reformulate the model as interaction of fermions with the deformation of the lattice, which forms a phonon field. We calculate the response of fermion currents to the external deformation or phonon field, which is a result of a Z_2 anomaly. This can be detected experimentally.