Interplay of disorder and interaction in quantum Hall systems: from fractional quantum Hall liquids to Wigner crystals and amorphous solids

Abstract

We investigate the interplay of disorder and interaction in two-dimensional electron systems in a strong magnetic field, focusing on the transition between Wigner crystals and fractional quantum Hall liquids. We first study classical Wigner crystals with charged impurities, revealing an evolution from a coherent crystal to local crystalline domains with short-range order and eventually to an amorphous state as impurity concentration increases. We then analyze noninteracting quantum electron crystals created by periodic potentials, showing that their structure factor exhibits both peaks and rings, distinct from classical Wigner crystals. Finally, we explore fractional quantum Hall liquids with random short-range disorder and quenched charged impurities, demonstrating that the ground state can evolve from an incompressible liquid to a localized ordered state and eventually to an amorphous state as disorder strength increases. In general, we find that random charged impurities lead to longer-range crystalline ordering than the short-range random disorder. Our findings highlight the rich interplay between disorder and interaction in quantum Hall systems and provide insights into experimental observations of these phenomena. By qualitative comparison with a recent STM experiment [Nature \textbf{628}, 287 (2024)], we conclude that the 2D system crosses over from an incompressible homogeneous fractional quantum Hall liquid to a generic locally ordered solid and eventually to a disordered amorphous solid at large disorder.