Half-filled Landau level, topological insulator surfaces, and three dimensional quantum spin liquids

TL;DR

This paper connects the physics of half-filled Landau levels, topological insulator surfaces, and quantum spin liquids, providing new insights into particle-hole symmetry and composite fermion behavior in two and three dimensions.

Contribution

It offers a physical understanding of particle-hole symmetric composite fermions via topological insulator surface states and revises the phenomenology of composite Fermi liquids with novel transport properties.

Findings

Particle-hole symmetric composite fermions can be understood as electrically neutral dipoles.

Composite Fermi liquids violate the Wiedemann-Franz law significantly.

Insights suggest new ways to realize correlated topological insulator surfaces.

Abstract

We synthesize and partly review recent developments relating the physics of the half-filled Landau level in two dimensions to correlated surface states of topological insulators in three dimensions. The latter are in turn related to the physics of certain three dimensional quantum spin liquid states. The resulting insights provide an interesting answer to the old question of how particle-hole symmetry is realized in composite fermion liquids. Specifically the metallic state at filling $\nu = \frac{1}{2}$ - described originally in pioneering work by Halperin , Lee, and Read as a liquid of composite fermions - was proposed recently by Son to be described by a particle-hole symmetric effective field theory distinct from that in the prior literature. We show how the relation to topological insulator surface states leads to a physical understanding of the correctness of this proposal. We develop a simple picture of the particle-hole symmetric composite fermion through a modification of older pictures as electrically neutral "dipolar" particles. We revisit the phenomenology of composite fermi liquids (with or without particle-hole symmetry), and show that their heat/electrical transport dramatically violates the conventional Wiedemann-Franz law but satisfies a modified one. We also discuss the implications of these insights for finding physical realizations of correlated topological insulator surfaces.