Melting of quantum Hall Wigner and bubble crystals

TL;DR

This study combines experimental transport measurements with theoretical models to accurately predict the melting temperature of quantum Hall electron bubble crystals, validating defect-mediated melting as a predictive framework.

Contribution

It provides a quantitative match between theory and experiment for melting temperatures in quantum Hall bubble phases, integrating elasticity theory with topological defect unbinding.

Findings

Theoretical melting temperatures match experimental data across multiple Landau levels.

Transport measurements effectively probe topological defect energetics.

The approach can be extended to other electronic crystal systems.

Abstract

A two-dimensional crystal melts via the proliferation and unbinding of topological defects, yet quantitatively predicting the melting temperature $T_m$ in real systems is challenging. Here we resolve this discrepancy in quantum Hall electron bubble phases by combining Corbino-geometry transport experiment in an ultraclean GaAs/AlGaAs quantum well for Landau levels 2 to 5 with Hartree--Fock elasticity and the full Kosterlitz--Thouless--Halperin--Nelson--Young melting criterion including the finite-temperature renormalization-group calculation. The theoretically obtained $T_m$ quantitatively captures the measured solid-liquid phase transition boundaries across all probed ranges, validating the bubble-crystal interpretation and establishing defect--mediated melting as a predictive framework for strongly interacting electronic solids. This agreement further supports using bulk transport to probe the energetics of topological defects and screening in quantum Hall physics, and the approach is readily extendable to other electronic crystals, including the generalized Wigner crystal in moir\'e Chern bands.