# Theory of the collective magnetophonon resonance and melting of the field-induced Wigner solid

## TL;DR

This paper develops a hydrodynamic theory for the magnetophonon resonance in electron Wigner solids under strong magnetic fields, explaining experimental observations of resonance behavior near melting transitions.

## Contribution

It introduces a theoretical framework for understanding the magnetophonon resonance and its evolution during melting, linking dissipation channels to resonance shape changes.

## Key findings

- Violation of the Fukuyama-Lee sum rule near melting
- Non-Lorentzian resonance shape due to dislocations and charge carriers
- Explanation of experimental resonance data in 2D electron systems

## Abstract

Electron solid phases of matter are revealed by characteristic vibrational resonances. Sufficiently large magnetic fields can overcome the effects of disorder, leading to a weakly pinned collective mode called the magnetophonon. Consequently, in this regime it is possible to develop a tightly constrained hydrodynamic theory of pinned magnetophonons. The behavior of the magnetophonon resonance across thermal and quantum melting transitions has been experimentally characterized in two-dimensional electron systems. Applying our theory to these transitions we explain several key features of the data: (i) violation of the Fukuyama-Lee sum rule as the transition is approached is directly tied to the non-Lorentzian form taken by the resonance and (ii) the non-Lorentzian shape is caused by characteristic dissipative channels that become especially important close to melting: proliferating dislocations and uncondensed charge carriers.