Pinned Bilayer Wigner Crystals with Pseudospin Magnetism

TL;DR

This paper investigates how interlayer coherence enhances pinning in bilayer Wigner crystals, revealing distinct behaviors for ferromagnetic and antiferromagnetic pseudospin configurations and predicting a transition-related drop in pinning mode frequency.

Contribution

It introduces a model showing that interlayer coherence increases pinning strength in bilayer Wigner crystals and predicts a transition-induced change in pinning mode frequency.

Findings

FMWC can be pinned more strongly due to interlayer coherence.

Pinning mode frequency decreases with layer separation in FMWC.

An abrupt drop in pinning mode frequency occurs at the FMWC to AFMWC transition.

Abstract

We study a model of \textit{pinned} bilayer Wigner crystals (WC) and focus on the effects of interlayer coherence (IC) on pinning. We consider both a pseudospin ferromagnetic WC (FMWC) with IC and a pseudospin antiferromagnetic WC (AFMWC) without IC. Our central finding is that a FMWC can be pinned more strongly due to the presence of IC. One specific mechanism is through the disorder induced interlayer tunneling, which effectively manifests as an extra pinning in a FMWC. We also construct a general "effective disorder" model and effective pinning Hamiltonian for the case of FMWC and AFMWC respectively. Under this framework, pinning in the presence of IC involves \textit{interlayer} spatial correlation of disorder in addition to intralayer correlation, leading to \textit{enhanced} pinning in the FMWC. The pinning mode frequency (\wpk) of a FMWC is found to decease with the effective layer separation, whereas for an AFMWC the opposite behavior is expected. An abrupt drop of \wpk is predicted at a transition from a FMWC to AFMWC. Possible effects of in-plane magnetic fields and finite temperatures are addressed. Finally we discuss some other possible ramifications of the FMWC as an electronic supersolid-like phase.