Theory of a two-dimensional anharmonic piezoelectric crystal resonator

TL;DR

This paper develops a lattice dynamical theory for atomically-thin piezoelectric resonators, analyzing their electromechanical response, resonance behavior, and quantum effects, with applications to 2D materials like boron nitride and molybdenum disulfide.

Contribution

It introduces a comprehensive theoretical framework for 2D piezoelectric resonators, including quantum effects and size dependence, which was not previously established.

Findings

Resonance quality factor inversely proportional to temperature and size in classical regime.

Quantum zero-point fluctuations limit the quality factor independently of size.

Application to 2D materials demonstrates the theory's practical relevance.

Abstract

We developed a lattice dynamical theory of an atomically-thin compressional piezoelectric resonator. Acoustic and optical dynamic displacement response functions are derived and account for frequency-dependent electromechanical coupling. The dynamic susceptibilities for the direct and the converse piezoelectric effects are found equal. The mechanical resonant behavior of longitudinal in-plane displacement waves is investigated as a function of the lateral crystal size and of temperature in the classical and in the quantum regime. In the former case the quality factor of the resonator is inversely proportional to temperature and to crystal size. Below a cross-over temperature the quantum zero-point fluctuations become dominant and put an upper limit on the quality factor which is size independent. As experimentally relevant examples, the theory is applied on two-dimensional hexagonal boron nitride and molybdenum disulfide.