Gapless layered three-dimensional fractional quantum Hall states

摘要

Using the parton construction, we build a three-dimensional (3D) multilayerfractional quantum Hall state with average filling \nu = 1/3 per layer that isqualitatively distinct from a stacking of weakly coupled Laughlin states. Thestate supports gapped charge e/3 fermionic quasiparticles that can propagateboth within and between the layers, in contrast to the quasiparticles in amultilayer Laughlin state which are confined within each layer. Moreover, thestate has gapless neutral collective modes, a manifestation of an emergent"photon", which is minimally coupled to the fermionic quasiparticles. Thesurface sheath of the multilayer state resembles a chiral analog of theHalperin-Lee-Read state, which is protected against gap forming instabilitiesby the topological character of the bulk 3D phase. We propose that this statemight be present in multilayer systems in the "intermediate tunneling regime",where the interlayer tunneling strength is on the same order as the Coulombenergy scale. We also find that the parton construction leads to a candidatestate for a bilayer \nu = 1/3 system in the intermediate tunneling regime. Thecandidate state is distinct from both a bilayer of \nu=1/3 Laughlin states andthe single layer \nu = 2/3 state, but is nonetheless a fully gapped fractionalquantum Hall state with charge e/3 anyonic quasiparticles.