Gapless layered three-dimensional fractional quantum Hall states

Abstract

Using the parton construction, we build a three-dimensional (3D) multilayer fractional quantum Hall state with average filling \nu = 1/3 per layer that is qualitatively distinct from a stacking of weakly coupled Laughlin states. The state supports gapped charge e/3 fermionic quasiparticles that can propagate both within and between the layers, in contrast to the quasiparticles in a multilayer Laughlin state which are confined within each layer. Moreover, the state has gapless neutral collective modes, a manifestation of an emergent "photon", which is minimally coupled to the fermionic quasiparticles. The surface sheath of the multilayer state resembles a chiral analog of the Halperin-Lee-Read state, which is protected against gap forming instabilities by the topological character of the bulk 3D phase. We propose that this state might be present in multilayer systems in the "intermediate tunneling regime", where the interlayer tunneling strength is on the same order as the Coulomb energy scale. We also find that the parton construction leads to a candidate state for a bilayer \nu = 1/3 system in the intermediate tunneling regime. The candidate state is distinct from both a bilayer of \nu=1/3 Laughlin states and the single layer \nu = 2/3 state, but is nonetheless a fully gapped fractional quantum Hall state with charge e/3 anyonic quasiparticles.Comment: 11 pages, 1 figur

Layer Construction of 3D Topological States and String Braiding Statistics

“…A similar setting was considered in Ref. [79] in which a stacked layer of Laughlin states is coupled and gapless photon modes emerge. To realize these layer-constructed systems in experiment, the crystal graphite should be a good candidate material.…”

“…When we move toward the strongly correlated regime of graphite under a magnetic field, this setting can, in principle, allow us to realize the system proposed in Ref. [79]. For our layer-constructed 3D topological state, since each layer in this construction is nonchiral, we can start directly with stacked layers of graphene, namely, graphite crystal, without the external magnetic field.…”

Fractional topological phases in three-dimensional coupled-wire systems

“…A critical phase could for instance be composed of fractionally charged fermionic 3D quasiparticles (somewhat related ideas are discussed in Refs. 27,59). This scenario is supported by the quasiparticles at the Luther-Emery-type points considered in Sec.…”

“…23 In the latter, inter layer couplings can stabilize many-layer versions of Halperin bilayer states, [24][25][26] or exotic phases with fractionally charged fermionic 3D quasiparticles. 27 Other coupled-layer constructions 28,29 can also exhibit string-like excitations, which in general allow for non-trivial 3D braiding.…”

Noncommutative geometry for three-dimensional topological insulators

“…One approach to capture universal physics arising from topological interacting electron systems in (2+1) [20][21][22][23][24][25][26][27] and (3+1) [28][29][30] dimensions of space and time is via the parton construction. A fractional phase of electrons is obtained by constructing integer filled bands of "partons", which are then "glued" together by very strong gauge-mediated interactions so as to assemble together the physical electron.…”