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

Current-phase relations of few-mode InAs nanowire Josephson junctions

Gate-tunable semiconductor nanowires with superconducting leads have great potential for quantum computation and as model systems for mesoscopic Josephson junctions. The supercurrent, $I$, versus the phase, $\phi$, across the junction is called the current-phase relation (CPR). It can reveal not only the amplitude of the critical current, but also the number of modes and their transmission. We measured the CPR of many individual InAs nanowire Josephson junctions, one junction at a time. Both the amplitude and shape of the CPR varied between junctions, with small critical currents and skewed CPRs indicating few-mode junctions with high transmissions. In a gate-tunable junction, we found that the CPR varied with gate voltage: Near the onset of supercurrent, we observed behavior consistent with resonant tunneling through a single, highly transmitting mode. The gate dependence is consistent with modeled subband structure that includes an effective tunneling barrier due to an abrupt change in the Fermi level at the boundary of the gate-tuned region. These measurements of skewed, tunable, few-mode CPRs are promising both for applications that require anharmonic junctions and for Majorana readout proposals

Images of Edge Current inﾠInAs/GaSbﾠQuantum Wells

Quantum spin Hall devices with edges much longer than several microns do not display ballistic transport; that is, their measured conductances are much less thanﾠe2/hﾠper edge. We imaged edge currents inﾠInAs/GaSbﾠquantum wells with long edges and determined an effective edge resistance. Surprisingly, although the effective edge resistance is much greater thanﾠh/e2, it is independent of temperature up to 30ﾠK within experimental resolution. Known candidate scattering mechanisms do not explain our observation of an effective edge resistance that is large yet temperature independent

Emergent Dirac gullies and gully-symmetry breaking quantum Hall states in ABA trilayer graphene

We report on quantum capacitance measurements of high quality, graphite- and hexagonal boron nitride encapsulated Bernal stacked trilayer graphene devices. At zero applied magnetic field, we observe a number of electron density- and electrical displacement-tuned features in the electronic compressibility associated with changes in Fermi surface topology. At high displacement field and low density, strong trigonal warping gives rise to emergent Dirac gullies centered near the corners of the hexagonal Brillouin and related by three fold rotation symmetry. At low magnetic fields of $B=1.25$~T, the gullies manifest as a change in the degeneracy of the Landau levels from two to three. Weak incompressible states are also observed at integer filling within these triplets Landau levels, which a Hartree-Fock analysis indicates are associated with Coulomb-driven nematic phases that spontaneously break rotation symmetry.Comment: Main text: 5 pages, 3 Figures. Supplements: 8 pages, 5 figure

Variation in superconducting transition temperature due to tetragonal domains in two-dimensionally doped SrTiO₃

Strontium titanate is a low-temperature, non-Bardeen-Cooper-Schrieffer superconductor that superconducts to carrier concentrations lower than in any other system and exhibits avoided ferroelectricity at low temperatures. Neither the mechanism of superconductivity in strontium titanate nor the importance of the structure and dielectric properties for the superconductivity are well understood. We studied the effects of twin structure on superconductivity in a 5.5-nm-thick layer of niobium-doped SrTiO$_{3}$ embedded in undoped SrTiO$_{3}$. We used a scanning superconducting quantum interference device susceptometer to image the local diamagnetic response of the sample as a function of temperature. We observed regions that exhibited a superconducting transition temperature $T_{c}$ $\gtrsim$ 10% higher than the temperature at which the sample was fully superconducting. The pattern of these regions varied spatially in a manner characteristic of structural twin domains. Our results emphasize that the anisotropic dielectric properties of SrTiO$_{3}$ are important for its superconductivity, and need to be considered in any theory of the mechanism of the superconductivity.Comment: 14 pages, 11 figures, Supplemental Information available at http://stanford.edu/group/moler/papers/Noad_STOsuperconductivity_SI.pd