Fractional quantum Hall effect in semiconductor systems

TL;DR

This paper reviews the experimental observations and theoretical models of the fractional quantum Hall effect in GaAs semiconductors, emphasizing recent advances in understanding exotic quantum states and topological phenomena.

Contribution

It provides a comprehensive overview of experimental data and introduces new theoretical frameworks like parton and Dirac composite fermion theories for FQH states.

Findings

Experimental phenomenology of FQH in GaAs systems

Theoretical interpretations including trial wave functions and composite fermions

Recent developments like parton theory and entanglement in FQH states

Abstract

The fractional quantum Hall (FQH) effect refers to the strongly-correlated phenomena and the associated quantum phases of matter realized in a two-dimensional gas of electrons placed in a large perpendicular magnetic field. In such systems, topology and quantum mechanics conspire to give rise to exotic physics that manifests via robust quantization of the Hall resistance. In this chapter, we provide an overview of the experimental phenomenology of the FQH effect in GaAs-based semiconductor materials and present its theoretical interpretations in terms of trial wave functions, composite fermion quasiparticles, and enigmatic non-Abelian states. We also highlight some recent developments, including the parton theory and the Dirac composite fermion field theory of FQH states, the role of anisotropy and geometrical degrees of freedom, and quantum entanglement in FQH fluids.