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

How quickly can anyons be braided? Or: How I learned to stop worrying about diabatic errors and love the anyon

Topological phases of matter are a potential platform for the storage and processing of quantum information with intrinsic error rates that decrease exponentially with inverse temperature and with the length scales of the system, such as the distance between quasiparticles. However, it is less well-understood how error rates depend on the speed with which non-Abelian quasiparticles are braided. In general, diabatic corrections to the holonomy or Berry's matrix vanish at least inversely with the length of time for the braid, with faster decay occurring as the time-dependence is made smoother. We show that such corrections will not affect quantum information encoded in topological degrees of freedom, unless they involve the creation of topologically nontrivial quasiparticles. Moreover, we show how measurements that detect unintentionally created quasiparticles can be used to control this source of error.Comment: 33 pages, 18 figures, version 3: extended results to general anyon braidin

Vortex-enabled Andreev processes in quantum Hall-superconductor hybrids

Quantum Hall-superconductor heterostructures provide possible platforms for intrinsically fault-tolerant quantum computing. Motivated by several recent experiments that successfully integrated these phases, we investigate transport through a proximitized integer quantum Hall edge--paying particular attention to the impact of vortices in the superconductor. By examining the downstream conductance, we identify regimes in which sub-gap vortex levels mediate Andreev processes that would otherwise be frozen out in a vortex-free setup. Moreover, we show that at finite temperature, and in the limit of a large number of vortices, the downstream conductance can average to zero, indicating that the superconductor effectively behaves like a normal contact. Our results highlight the importance of considering vortices when using transport measurements to study superconducting correlations in quantum Hall-superconductor hybrids.Comment: 16 pages, 9 figure

Fragility of the Fractional Josephson Effect in Time-Reversal-Invariant Topological Superconductors

Time-reversal-invariant topological superconductor (TRITOPS) wires host Majorana Kramers pairs that have been predicted to mediate a fractional Josephson effect with 4π periodicity in the superconducting phase difference. We explore the TRITOPS fractional Josephson effect in the presence of time-dependent “local mixing” perturbations that instantaneously preserve time-reversal symmetry. Specifically, we show that just as such couplings render braiding of Majorana Kramers pairs nonuniversal, the Josephson current becomes either aperiodic or 2π periodic (depending on conditions that we quantify) unless the phase difference is swept sufficiently quickly. We further analyze topological superconductors with T² = +1 time-reversal symmetry and reveal a rich interplay between interactions and local mixing that can be experimentally probed in nanowire arrays

Anomalous exciton transport in response to a uniform, in-plane electric field

Excitons are neutral objects, that, naively, should have no response to a uniform, electric field. Could the Berry curvature of the underlying electronic bands alter this conclusion? In this work, we show that Berry curvature can indeed lead to anomalous transport for excitons in 2D materials subject to a uniform, in-plane electric field. By considering the constituent electron and hole dynamics, we demonstrate that there exists a regime for which the corresponding anomalous velocities are in the same direction. We establish the resulting center of mass motion of the exciton through both a semiclassical and fully quantum mechanical analysis, and elucidate the critical role of Bloch oscillations in achieving this effect. We identify transition metal dichalcogenide heterobilayers as candidate materials to observe the effect

Survival of the fractional Josephson effect in time-reversal-invariant topological superconductors

Time-reversal-invariant topological superconductor (TRITOPS) wires host Majorana Kramers pairs that have been predicted to mediate a fractional Josephson effect with 4π periodicity in the superconducting phase difference. We explore the TRITOPS fractional Josephson effect in the presence of time-dependent `local mixing' perturbations that instantaneously preserve time-reversal symmetry. Specifically, we show that just as such couplings render braiding of Majorana Kramers pairs non-universal, the Josephson current becomes either aperiodic or 2π-periodic (depending on conditions that we quantify) unless the phase difference is swept sufficiently quickly. We further analyze topological superconductors with T² = +1 time-reversal symmetry and reveal a rich interplay between interactions and local mixing that can be experimentally probed in nanowire arrays

Torsorial actions on G-crossed braided tensor categories

We develop a method for generating the complete set of basic data under the torsorial actions of $H^2_{[\rho]}(G,\mathcal{A})$ and $H^3(G,\text{U}(1))$ on a $G$-crossed braided tensor category $\mathcal{C}_G^\times$, where $\mathcal{A}$ is the set of invertible simple objects in the braided tensor category $\mathcal{C}$. When $\mathcal{C}$ is a modular tensor category, the $H^2_{[\rho]}(G,\mathcal{A})$ and $H^3(G,\text{U}(1))$ torsorial action gives a complete generation of possible $G$-crossed extensions, and hence provides a classification. This torsorial classification can be (partially) collapsed by relabeling equivalences that appear when computing the set of $G$-crossed braided extensions of $\mathcal{C}$. The torsor method presented here reduces these redundancies by systematizing relabelings by $\mathcal{A}$-valued $1$-cochains. We also use our methods to compute the composition rule of these torsor functors.Comment: 34 pages, several figures; v2: added Sec V, VI, and minor correction