Coupled-wire descriptions of unconventional quantum states in twisted nanostructures

Abstract

Coupled-wire description has been developed as a powerful framework for providing bosonic descriptions of strongly correlated quantum matter, with early applications to systems such as the cuprates and the integer and fractional quantum Hall states. In this topical review, we discuss recent developments of coupled-wire description in nanoscale systems, where it emerges not only as a theoretical tool but also as a highly tunable physical platform. In these nanoscale realizations, coupled-wire networks are formed by one-dimensional channels embedded in two-dimensional materials, most prominently in moir\'e and twisted structures. Such networks host a broad range of unconventional states of matter, including superconductivity, charge density waves, spin density waves, Mott insulating phases, Anderson insulating phases, quantum spin Hall states, quantum anomalous Hall states, and their fractionalized counterparts. The ability to electrically control interaction strength, confinement, and coupling between wires makes these systems qualitatively different from earlier realizations and allows continuous tuning between competing phases. Notably, recent work has demonstrated that the coupled-wire framework in moir\'e networks completes the trio of quantum Hall phenomena, encompassing quantum Hall, quantum spin Hall, and quantum anomalous Hall states, together with their fractional analogues. This development highlights coupled-wire networks in nanoscale materials as a versatile and experimentally relevant setting for exploring the interplay of topology, strong correlations, and low-dimensional physics.