Anomalous thermal expansion in Ising-like puckered sheets

TL;DR

This paper investigates how buckled nanoscale sheets exhibit unusual thermal expansion behavior near phase transitions, driven by coupling between atomic-scale buckling and flexural vibrations, with implications for designing advanced materials.

Contribution

It introduces a model coupling Ising-like buckling states to flexural phonons, explaining anomalous thermal expansion in atomically thin membranes.

Findings

Divergence and sign change of thermal expansion coefficient near critical temperature.

Observation of phase transition in buckled nanosheets via molecular dynamics.

Coupling of flexural phonons to buckling states causes unusual thermal responses.

Abstract

Motivated by efforts to create thin nanoscale metamaterials and understand atomically thin binary monolayers, we study the finite temperature statistical mechanics of arrays of bistable buckled dilations embedded in free-standing two-dimensional crystalline membranes that are allowed to fluctuate in three dimensions. The buckled nodes behave like discrete, but highly compressible, Ising spins, leading to a phase transition at $T_c$ with singularities in the staggered "magnetization," susceptibility, and specific heat, studied via molecular dynamics simulations. Unlike conventional Ising models, we observe a striking divergence and sign change of the coefficient of thermal expansion near $T_c$ caused by the coupling of flexural phonons to the buckled spin texture. We argue that a phenomenological model coupling Ising degrees of freedom to the flexural phonons in a thin elastic sheet can explain this unusual response.