Flexural phonons in free-standing graphene

TL;DR

This paper studies flexural phonons in free-standing graphene, revealing their quadratic dispersion and dominant role in electrical resistivity at low temperatures, with an anomalous temperature dependence influenced by membrane coupling effects.

Contribution

It provides a theoretical analysis of flexural phonons' dispersion and their impact on graphene's resistivity, including the derivation of an unusual temperature dependence.

Findings

Flexural phonons have quadratic dispersion due to symmetry constraints.

Flexural phonons dominate resistivity below a certain temperature.

Resistivity exhibits an anomalous T^{5/2} log T dependence.

Abstract

Rotation and reflection symmetries impose that out-of-plane (flexural) phonons of free-standing graphene membranes have a quadratic dispersion at long wavelength and can be excited by charge carriers in pairs only. As a result, we find that flexural phonons dominate the phonon contribution to the resistivity $\rho$ below a crossover temperature T_x where we obtain an anomalous temperature dependence $\rho\propto T^{5/2}_{}\ln T$. The logarithmic factor arises from renormalizations of the flexural phonon dispersion due to coupling between bending and stretching degrees of freedom of the membrane.