Z4 parafermions in an interacting quantum spin Hall Josephson junction coupled to an impurity spin

Z4 parafermions can be realized in a strongly interacting quantum spin Hall Josephson junction or in a spin Hall Josephson junction strongly coupled to an impurity spin. In this paper, we study a system that has both features, but with weak (repulsive) interactions and a weakly coupled spin. We show that for a strongly anisotropic exchange interaction, at low temperatures the system enters a strong coupling limit in which it hosts two Z4 parafermions, characterizing a fourfold degeneracy of the ground state. We construct the parafermion operators explicitly and show that they facilitate fractional e/2 charge tunneling across the junction. The dependence of the effective low- energy spectrum on the superconducting phase difference reveals an 8π periodicity of the supercurrent

Quantum quenches and driven dynamics in a single-molecule device

The nonequilibrium dynamics of molecular devices is studied in the framework of a generic model for single-molecule transistors: a resonant level coupled by displacement to a single vibrational mode. In the limit of a broad level and in the vicinity of the resonance, the model can be controllably reduced to a form quadratic in bosonic operators, which in turn is exactly solvable. The response of the system to a broad class of sudden quenches and ac drives is thus computed in a nonperturbative manner, providing an asymptotically exact solution in the limit of weak electron-phonon coupling. From the analytic solution we are able to (1) explicitly show that the system thermalizes following a local quantum quench, (2) analyze in detail the time scales involved, (3) show that the relaxation time in response to a quantum quench depends on the observable in question, and (4) reveal how the amplitude of long-time oscillations evolves as the frequency of an ac drive is tuned across the resonance frequency. Explicit analytical expressions are given for all physical quantities and all nonequilibrium scenarios under study.Comment: 23 pages, 13 figure

Parity Anomaly and Spin Transmutation in Quantum Spin Hall Josephson Junctions

We study the Josephson effect in a quantum spin Hall system coupled to a localized magnetic impurity. As a consequence of the fermion parity anomaly, the spin of the combined system of impurity and spin-Hall edge alternates between half-integer and integer values when the superconducting phase difference across the junction advances by 2π. This leads to characteristic differences in the splittings of the spin multiplets by exchange coupling and single-ion anisotropy at phase differences, for which time-reversal symmetry is preserved. We discuss the resulting 8π-periodic (or Z4) fractional Josephson effect in the context of recent experiments

Robust Majorana Conductance Peaks for a Superconducting Lead

Experimental evidence for Majorana bound states largely relies on measurements of the tunneling conductance. While the conductance into a Majorana state is in principle quantized to 2e2/h, observation of this quantization has been elusive, presumably due to temperature broadening in the normal-metal lead. Here, we propose to use a superconducting lead instead, whose gap strongly suppresses thermal excitations. For a wide range of tunneling strengths and temperatures, a Majorana state is then signaled by symmetric conductance peaks at eV=±Δ with quantized height G=(4−π)2e2/h. For a superconducting scanning tunneling microscope tip, Majorana states appear as spatial conductance plateaus while the conductance varies with the local wavefunction for trivial Andreev bound states. We discuss effects of nonresonant (bulk) Andreev reflections and quasiparticle poisoning

Bulk thermal transport coefficients in a quantum Hall system and the fundamental difference between thermal and charge response

We derive and calculate thermal transport coefficients for a quantum Hall system in the linear response regime, and show that they are exponentially small in the bulk, in contrast to the quantized value of the charge Hall coefficient, thus violating the Wiedemann-Franz law. This corroborates earlier reports about the essential difference between the charge and thermal quantum Hall effect, that originates from the different behavior of the corresponding U(1) and gravitational anomalies. We explicitly calculate the bulk currents when a temperature profile is applied within the bulk, and show that they are proportional to the second derivative of the respective gravitational potential (tidal force), and nonuniversal, in contrast to the charge current which is proportional to the first derivative of the electrochemical potential