The Quantum Hall Effect: Novel Excitations and Broken Symmetries

TL;DR

This paper provides a comprehensive introduction to the quantum Hall effects, emphasizing novel excitations, broken symmetries, and detailed theoretical descriptions of quantum Hall ferromagnetism and spin textures.

Contribution

It offers new pedagogical insights into effective field theories for broken symmetry states and topological spin textures in quantum Hall systems.

Findings

Derivation of effective field theories for broken symmetry states

Discussion of skyrmion and meron spin textures

Analysis of quantum Hall ferromagnetism in single and double-layer systems

Abstract

These pedagogical lecture notes present a general introduction to most aspects of the integer and fractional quantum Hall effects. This is followed by an extensive discussion of quantum Hall ferromagnetism, both for spins in single-layer systems and `pseudospins' in double-layer systems. The effective field theories describing various broken symmetry states and `skyrmion' and `meron' spin textures are derived and discussed in some detail. Pedagogical presentations on Berry phases and lowest Landau level projection are included in appendices.