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Register a new userHall conductance and the statistics of flux insertions in gapped interacting lattice systems
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We study charge transport for zero-temperature infinite-volume gapped lattice systems in two dimensions with short-range interactions. We show that the Hall conductance is locally computable and is the same for all systems which are in the same gapped phase. We provide a rigoro
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We provide a short proof of the quantisation of the Hall conductance for gapped interacting quantum lattice systems on the two-dimensional torus. This is not new and should be seen as an adaptation of the proof of [1], simplified by making the stronger assumption that the Hamiltonian remains gapped when threading the torus with fluxes. We argue why this assumption is very plausible. The conductance is given by Berrys curvature and our key auxiliary result is that the curvature is asymptotically constant across the torus of fluxes.
A weak superconducting proximity effect in the vicinity of the topological transition of a quantum anomalous Hall system has been proposed as a venue to realize a topological superconductor (TSC) with chiral Majorana edge modes (CMEMs). A recent experiment [Science 357, 294 (2017)] claimed to have observed such CMEMs in the form of a half-integer quantized conductance plateau in the two-terminal transport measurement of a quantum anomalous Hall-superconductor junction. Although the presence of a superconducting proximity effect generically splits the quantum Hall transition into two phase transitions with a gapped TSC in between, in this Rapid Communication we propose that a nearly flat conductance plateau, similar to that expected from CMEMs, can also arise from the percolation of quantum Hall edges well before the onset of the TSC or at temperatures much above the TSC gap. Our Rapid Communication, therefore, suggests that, in order to confirm the TSC, it is necessary to supplement the observation of the half-quantized conductance plateau with a hard superconducting gap (which is unlikely for a disordered system) from the conductance measurements or the heat transport measurement of the transport gap. Alternatively, the half-quantized thermal conductance would also serve as a smoking-gun signature of the TSC.
Twisted van der Waals materials open up novel avenues to control electronic correlation and topological effects. These systems contain the unprecedented possibility to precisely tune strong correlations, topology, magnetism, nematicity, and superconductivity with an external non-invasive electrostatic doping. By doing so, rich phase diagrams featuring an interplay of different states of correlated quantum matter can be unveiled. The nature of the superconducting order presents a recurring overarching open question in this context. In this work, we quantitatively assess the case of spin-fluctuation-mediated pairing for $Gamma$-valley twisted transition metal dichalcogenide homobilayers. We construct a low-energy honeycomb model on which basis we self-consistently and dynamically calculate a doping dependent phase diagram for the superconducting transition temperature $T_{mathrm{c}}$. A superconducting dome emerges with a maximal $T_{mathrm{c}}approx$ 0.1-1 K depending on twist angle. We qualitatively compare our results with conventional phonon-mediated superconductivity and discern clear fingerprints which are detectable in doping-dependent measurements of the superconducting transition temperature, providing direct access to probing the superconducting pairing mechanism in twisted Van der Waals materials.
We numerically investigate the properties of the quasihole excitations above the bosonic fractional Chern insulator state at filling $ u = 1/2$, in the specific case of the Harper-Hofstadter Hamiltonian with hard-core interactions. For this purpose we employ a Tree Tensor Network technique, which allows us to study systems with up to $N=18$ particles on a $16 times 16$ lattice and experiencing an additional harmonic confinement. First, we observe the quantization of the quasihole charge at fractional values and its robustness against the shape and strength of the impurity potentials used to create and localize such excitations. Then, we numerically characterize quasihole anyonic statistics by applying a discretized version of the relation connecting the statistics of quasiholes in the lowest Landau level to the depletions they create in the density profile [Macaluso et al., arXiv:1903.03011]. Our results give a direct proof of the anyonic statistics for quasiholes of fractional Chern insulators, starting from a realistic Hamiltonian. Moreover, they provide strong indications that this property can be experimentally probed through local density measurements, making our scheme readily applicable in state-of-the-art experiments with ultracold atoms and superconducting qubits.
Spin-dependent partial conductances are evaluated in a tight-binding description of electron transport in the presence of spin-orbit (SO) couplings, using transfer-matrix methods. As the magnitude of SO interactions increases, the separation of spin-switching channels from non-spin-switching ones is gradually erased. Spin-polarised incident beams are produced by including a Zeeman-like term in the Hamiltonian. The exiting polarisation is shown to exhibit a maximum as a function of the intensity of SO couplings. For moderate site disorder, and both weak and strong SO interactions, no evidence is found for a decay of exiting polarisation against increasing system length. With very low site disorder and weak SO couplings a spin-filter effect takes place, as polarisation {em increases} with increasing system length.
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