Suppression of anharmonicities in crystalline membranes by external strain

TL;DR

Applying external tension to stiff two-dimensional membranes like graphene significantly suppresses anharmonic effects, with less than 1% strain sufficient to restore harmonic behavior, as shown through theoretical and simulation methods.

Contribution

This study demonstrates that external tension effectively suppresses anharmonicities in stiff membranes, combining theoretical analysis with atomistic simulations.

Findings

Less than 1% strain suppresses anharmonic effects in graphene.

Anharmonic effects are more resistant to suppression in soft membranes.

Theoretical predictions align with Monte Carlo simulation results.

Abstract

In practice, physical membranes are exposed to a certain amount of external strain (tension or compression), due to the environment where they are placed. As a result, the behavior of the phonon modes of the membrane is modified. We show that anharmonic effects in stiff two-dimensional membranes are highly suppressed under the application of tension. For this, we consider the anharmonic coupling between bending and stretching modes in the self-consistent screening approximation (SCSA), and compare the obtained height-height correlation function in the SCSA to the corresponding harmonic propagator. The elasticity theory results are compared to atomistic Monte Carlo simulations for a graphene membrane under tension. We find that, while rather high values of strain are needed to avoid anharmonicity in soft membranes, strain fields less than 1% are enough to suppress all the anharmonic effects in stiff membranes, as graphene.