Theory of anharmonic phonons in 2D crystals

TL;DR

This paper investigates anharmonic phonon effects in 2D honeycomb crystals like graphene, analyzing thermal properties, phonon renormalization, and decay processes through analytical and numerical methods, highlighting size and temperature dependencies.

Contribution

It provides a comprehensive analytical and numerical study of anharmonic phonons in 2D crystals, including temperature and size effects on phonon behavior and thermal expansion.

Findings

Transition temperature for thermal expansion shifts with system size.

Flexural mode frequency renormalization affects thermal properties.

Normal and Umklapp processes' roles are quantitatively analyzed.

Abstract

Anharmonic effects in an atomic monolayer thin crystal with honeycomb lattice structure are investigated by analytical and numerical lattice dynamical methods. Starting from a semi-empirical model for anharmonic couplings of third and fourth order, we study the in-plane and out-of-plane (flexural) mode components of the generalized wave vector dependent Gr\"uneisen parameters, the thermal tension and the thermal expansion coefficients as function of temperature and crystal size. From the resonances of the displacement-displacement correlation functions we obtain the renormalization and decay rate of in-plane and flexural phonons as function of temperature, wave vector and crystal size in the classical and in the quantum regime. Quantitative results are presented for graphene. There we find that the transition temperature from negative to positive thermal expansion is lowered with smaller system size and by renormalization of the flexural mode frequency. Extensive numerical analysis throughout the Brillouin zone explores various decay and scattering channels. The relative importance of Normal and Umklapp processes is investigated. The work is complementary to crystalline membrane theory and computational studies of anharmonic effects in two-dimensional crystals.