In solid state conductors, linear response to a steady electric field is normally dominated by Bloch state occupation number changes. Recently it has been realized that, for a number of important physical observables, the dominant response is electric-field induced coherence between Bloch states in different bands. Examples include the anomalous and spin-Hall effects, spin torques in magnetic conductors, and the minimum conductivity and chiral anomaly in Weyl and Dirac semimetals. Here we first discuss the framework of a general quantum kinetic theory of linear response to an electric field which can be applied to solids with arbitrarily complicated band structures and includes the inter-band coherence response and the Bloch-state repopulation responses on an equal footing. We demonstrate that the inter-band response in conductors consists primarily of two terms: an intrinsic contribution due to the entire Fermi sea that captures, among other effects, the Berry curvature contribution to wave-packet dynamics, and an anomalous contribution caused by scattering that is sensitive to the presence of the Fermi surface. Next we discuss an important interband coherence effect on Hall transport. Classical charge transport, such as longitudinal and Hall currents in weak magnetic fields, is usually not affected by quantum phenomena. Yet relativistic quantum mechanics is at the heart of the spin-orbit interaction, which has been at the forefront of efforts to realize spin-based electronics, new phases of matter and topological quantum computing. In this work we demonstrate that quantum spin dynamics induced by the spin-orbit interaction are directly observable in classical charge transport. We determine the Hall coefficient RH of two-dimensional hole systems at low magnetic fields and show that it has a sizable spin-orbit contribution, which depends on the density p, is independent of temperature, is a strong function of the top gate electric field, and can reach 30% of the total. We provide a general method for extracting the spin-orbit parameter from magnetotransport data, applicable even at higher temperatures where Shubnikov-de Haas oscillations and weak antilocalisation are difficult to observe. Our work will enable experimentalists to measure spin-orbit parameters without requiring large magnetic fields, ultralow temperatures, or optical setups.
High-fidelity two-qubit entanglement operations pose new challenges for spin qubits. Although spin orbit-coupling (SOC) can simplify entanglement via electric fields and microwave photons, it exposes conventional spin qubits to electrical noise. Here we devise a gate-tunable single-acceptor spin-orbit qubit in silicon having a sweet spot where the electric dipole spin resonance (EDSR) is maximized, and the qubit is simultaneously insensitive to dephasing from low-frequency electrical noise. The sweet spot protects the qubit during rapid single-qubit EDSR and two-qubit dipole-dipole mediated operations, and is only obtained by treating SOC non-perturbatively. More than 10000 one-qubit and 1000 two-qubit operations are possible in the predicted relaxation time, as necessary for surface codes. Moreover, circuit quantum electrodynamics with single dopants is feasible in this scheme, including dispersive single-spin readout, cavity-mediated two-qubit entangement, and strong Jaynes-Cummings coupling. Our approach provides a scalable route for controlling electrical and photon-mediated interactions between spins of individual dopants in silicon.
Topological insulators (TI) have revolutionised our understanding of insulating behaviour. They are insulators in the bulk but conducting along their surfaces, thanks to surface states in which the spin and the charge are strongly coupled by means of the spin-orbit interaction. Much of the recent research on TI focuses on overcoming the transport bottleneck , namely the fact that surface state transport is overwhelmed by bulk transport stemming from unintentional doping. The key to overcoming this bottleneck is identifying unambiguous signatures of surface state transport. This talk will discuss one such signature, which is manifest in the coherent backscattering of electrons in TI. Because of the strong spin-orbit coupling in TI one expects to observe weak antilocalisation rather than weak localisation, meaning that coherent backscattering increases the electrical conductivity . The features of this effect, however, are rather subtle, because in TI the impurities have strong spin-orbit coupling as well, greatly increasing the complexity of the problem . I will show that spin-orbit coupled impurities introduce an additional time scale, which is expected to be shorter than the dephasing time, and the resulting conductivity has a logarithmic dependence on the carrier number density, a behaviour hitherto unknown in 2D electron systems. The result we predict is directly observable experimentally and would provide a smoking gun test of surface transport. Furthermore, I will also discuss the effect of electron-electron interactions on transport in this regime.
 D. Culcer, Physica E 44, 860 (2012).
 G. Tkachov and E. M. Hankiewicz, Phys. Rev. B 84, 035444 (2011).
 W. Liu, , P. Adroguer, X. Bi, E. M. Hankiewicz, and D. Culcer, to be published.