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

Understand

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.