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

Deep learning extraction of band structure parameters from density of states: a case study on trilayer graphene

The development of two-dimensional materials has resulted in a diverse range of novel, high-quality compounds with increasing complexity. A key requirement for a comprehensive quantitative theory is the accurate determination of these materials' band structure parameters. However, this task is challenging due to the intricate band structures and the indirect nature of experimental probes. In this work, we introduce a general framework to derive band structure parameters from experimental data using deep neural networks. We applied our method to the penetration field capacitance measurement of trilayer graphene, an effective probe of its density of states. First, we demonstrate that a trained deep network gives accurate predictions for the penetration field capacitance as a function of tight-binding parameters. Next, we use the fast and accurate predictions from the trained network to automatically determine tight-binding parameters directly from experimental data, with extracted parameters being in a good agreement with values in the literature. We conclude by discussing potential applications of our method to other materials and experimental techniques beyond penetration field capacitance.Comment: (v2): 12 pages, 6 figures, close to published version; (v1): 11 pages, 4 figure

Gate-Defined Topological Josephson Junctions in Bernal Bilayer Graphene

Recent experiments on Bernal bilayer graphene (BLG) deposited on monolayer WSe$_2$ revealed robust, ultra-clean superconductivity coexisting with sizable induced spin-orbit coupling. Here we propose BLG/WSe$_2$ as a platform to engineer gate-defined planar topological Josephson junctions, where the normal and superconducting regions descend from a common material. More precisely, we show that if superconductivity in BLG/WSe$_2$ is gapped and emerges from a parent state with inter-valley coherence, then Majorana zero modes can form in the barrier region upon applying weak in-plane magnetic fields. Our results spotlight a potential pathway for `internally engineered' topological superconductivity that minimizes detrimental disorder and orbital-magnetic-field effects.Comment: 7 pages, 4 figures, plus supplementary materia