We study the topological properties and transport in the Bernevig-Hughes-Zhang (BHZ) model undergoing a slow quench between different topological regimes. Due to the closing of the band gap during the quench, the system ends up in an excited state. For quenches governed by a Hamiltonian that preserves the symmetries present in the BHZ model (time-reversal, inversion, and conservation of spin projection), the Z2 invariant remains equal to the one evaluated in the initial state. The bulk spin Hall conductivity does change and its time average approaches that of the ground state of the final Hamiltonian. The deviations from the ground-state spin Hall conductivity as a function of the quench time follow the Kibble-Zurek scaling. We also consider the breaking of the timereversal symmetry, which restores the correspondence between the bulk invariant and the transport properties after the quench. arXiv:1802.05572v3 [cond-mat.mes-hall]

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If simple guidelines could be established for understanding how quantum interference (QI) can be exploited to control the flow of electricity through single molecules, then new functional molecules, which exploit room-temperature QI could be rapidly identified and subsequently screened. Recently it was demonstrated that conductance ratios of molecules with aromatic cores, with different connectivities to electrodes, can be predicted using a simple and easy-to-use “magic number theory.” In contrast with counting rules and “curly-arrow” descriptions of destructive QI, magic number theory captures the many forms of constructive QI, which can occur in molecular cores. Here we address the question of how conductance ratios are affected by electron-electron interactions. We find that due to cancellations of opposing trends, when Coulomb interactions and screening due to electrodes are switched on, conductance ratios are rather resilient. Consequently, qualitative trends in conductance ratios of molecules with extended pi systems can be predicted using simple ‘non-interacting’ magic number tables, without the need for large-scale computations. On the other hand, for certain connectivities, deviations from non-interacting conductance ratios can be significant and therefore such connectivities are of interest for probing the interplay between Coulomb interactions, connectivity and QI in single-molecule electron transport.

We considered various types of potential noise in gates controlling non-adiabatic holonomic transformations of spin-qubits in one and two-dimensional systems with the Rashba interaction. It is shown how exact results can be derived for deviations of spin rotation angle and fidelity of the qubit transformation after a completed transformation. Errors in initial values of gate potentials and timedependent drivings are considered and exact results for white gate noise are derived and analysed in detail. It is demonstrated how the drivings can be tuned to optimise the final fidelity of the transformation and to minimise the variances of qubit transformations.

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We investigate slow quenches in Chern insulators in ribbon geometry. We consider the Qi-Wu-Zhang model and slowly ramp the parameters (large time of the quench τ ) from a non-topological (Chern number = 0) to a topological regime (Chern number = 0). In contrast to the Haldane model considered in [Phys. Rev. B 93, 241406(R) (2016)] earlier, the in-gap state degeneracy point is pinned to an inversion symmetric momentum, which changes the behavior drastically. The density of excitations in the in-gap states scales with the quench time as τ −1/2 as the ramp becomes slow, and the Kibble-Zurek mechanism applies. Despite the slower scaling of the density of in-gap excitations with τ , the Hall conductance after the quench deviates from that of the ground state of the final Hamiltonian by an amount that drops as τ −1 . :1905.12691v1 [cond-mat.str-el] arXiv

We consider exactly solvable manipulation of spin-qubits confined in a moving harmonic trap and in the presence of the time dependent Rashba interaction. Non-adiabatic Anandan phase for cyclic time evolution is compared to the Wilczek-Zee adiabatic counterpart. It is shown that the ratio of these two phases can for a chosen system be any real number. Next we demonstrate the possibility of arbitrary qubit transformation in a ring with spin-orbit interaction. Finally, we present an example of exact analysis of spin-orbit dynamics influenced by the Ornstein-Uhlenbeck coloured noise. a

We study the influence of a thermal environment on a nonadiabatic spin-flip driving protocol of spin-orbit qubits. The driving protocol operates by moving the qubit, trapped in a harmonic potential, along a nanowire in the presence of a time-dependent spin-orbit interaction. We consider the harmonic degrees of freedom to be weakly coupled to a thermal bath. We find an analytical expression for the Floquet states and derive the Lindblad equation for a strongly nonadiabatically driven qubit. The Lindblad equation corrects the dynamics of an isolated qubit with Lamb shift terms and a dissipative behavior. Using the Lindblad equation, the influence of a thermal environment on the spin-flip protocol is analyzed.