Fractional Chern insulator edges and layer-resolved lattice contacts

Fractional Chern insulators (FCIs) realized in fractional quantum Hall systems subject to a periodic potential are topological phases of matter for which space group symmetries play an important role. In particular, lattice dislocations in an FCI can host topology-altering non-Abelian topological defects, known as genons. Genons are of particular interest for their potential application to topological quantum computing. In this work, we study FCI edges and how they can be used to detect genons. We find that translation symmetry can impose a quantized momentum difference between the edge electrons of a partially-filled Chern band. We propose {\it layer-resolved lattice contacts}, which utilize this momentum difference to selectively contact a particular FCI edge electron. The relative current between FCI edge electrons can then be used to detect the presence of genons in the bulk FCI. Recent experiments have demonstrated graphene is a viable platform to study FCI physics. We describe how the lattice contacts proposed here could be implemented in graphene subject to an artificial lattice, thereby outlining a path forward for experimental dectection of non-Abelian topological defects.Comment: 5+7 pages, 10 figures, v2: modified figure

Topological exciton Fermi surfaces in two-component fractional quantized Hall insulators

A wide variety of two-dimensional electron systems (2DES) allow for independent control of the total andrelative charge density of two-component fractional quantum Hall (FQH) states. In particular, a recent experimenton bilayer graphene (BLG) observed a continuous transition between a compressible and incompressiblephase at total filling νT =12as charge is transferred between the layers, with the remarkable property that theincompressible phase has a finite interlayer polarizability. We argue that this occurs because the topologicalorder of νT =12systems supports a novel type of interlayer exciton that carries Fermi statistics. If the fermionicexcitons are lower in energy than the conventional bosonic excitons (i.e., electron-hole pairs), they can form anemergent neutral Fermi surface, providing a possible explanation of an incompressible yet polarizable state atνT =12. We perform exact diagonalization studies which demonstrate that fermionic excitons are indeed lowerin energy than bosonic excitons. This suggests that a “topological exciton metal” hidden inside a FQH insulatormay have been realized experimentally in BLG. We discuss several detection schemes by which the topologicalexciton metal can be experimentally probed

Evidence for a topological "exciton Fermi sea" in bilayer graphene

The quantum Hall physics of bilayer graphene is extremely rich due to the interplay between a layer degree of freedom and delicate fractional states. Recent experiments show that when an electric field perpendicular to the bilayer causes Landau levels of opposing layers to cross in energy, a even-denominator Hall plateau can coexist with a finite density of inter-layer excitons. We present theoretical and numerical evidence that this observation is due to a new phase of matter - a Fermi sea of topological excitons