Magneto-shear modes and a.c. dissipation in a two-dimensional Wigner crystal

TL;DR

This paper analyzes the ac response of a 2D Wigner crystal under magnetic fields, revealing coupled magneto-shear modes and how they influence measurable properties like conductivity and shear modulus.

Contribution

It introduces a theoretical framework for magneto-shear modes in a 2D Wigner crystal and predicts their effects on ac response and magnetoconductivity measurements.

Findings

Identification of diffusive longitudinal and shear modes in zero magnetic field.

Coupling of modes to form magneto-shear modes under magnetic field.

Potential to measure shear modulus and magnetoconductivity simultaneously.

Abstract

The a.c. response of an unpinned and finite 2D Wigner crystal to electric fields at an angular frequency $\omega$ has been calculated in the dissipative limit, $\omega \tau \ll 1$, where $\tau ^{-1}$ is the scattering rate. For electrons screened by parallel electrodes, in zero magnetic field the long-wavelength excitations are a diffusive longitudinal transmission line mode and a diffusive shear mode. A magnetic field couples these modes together to form two new magneto-shear modes. The dimensionless coupling parameter $\beta =2(c_{t}/c_{l})|\sigma_{xy}/\sigma_{xx}|$ where $c_{t}$ and $c_{l}$ are the speeds of transverse and longitudinal sound in the collisionless limit and $\sigma_{xy}$ and $\sigma_{xx}$ are the tensor components of the magnetoconductivity. For $\beta \geqslant 1$, both the coupled modes contribute to the response of 2D electrons in a Corbino disk measurement of magnetoconductivity. For $\beta \gg 1$, the electron crystal rotates rigidly in a magnetic field. In general, both the amplitude and phase of the measured a.c. currents are changed by the shear modulus. In principle, both the magnetoconductivity and the shear modulus can be measured simultaneously.