Two-dimensional surface charge transport in topological insulators

We construct a theory of charge transport by the surface states of topological insulators in three dimensions. The focus is on the experimentally relevant case when the electron doping is such that the Fermi energy $\varepsilon_F$ and transport scattering time $\tau$ satisfy $\varepsilon_F \tau/\hbar \gg 1$, but sufficiently low that $\varepsilon_F$ lies below the bottom of the conduction band. Our theory is based on the spin density matrix and takes the quantum Liouville equation as its starting point. The scattering term is determined accurately to linear order in the impurity density. We consider scattering by charged impurities and short-range scatterers such as surface roughness. We calculate also the polarization function in topological insulators, emphasizing the differences from graphene. We find that the main contribution to the conductivity is $\propto n_i^{-1}$, where $n_i$ is the impurity density, and will have different carrier density dependencies for different forms of scattering. Two different contributions to this conductivity are traced to the scalar and spin-dependent terms in the Hamiltonian and their relative weight depends on the doping density. Our results contain all contributions to the conductivity to orders zero and one in the impurity density. We discuss also a way to determine the dominant scattering angles by studying the ratio of the transport relaxation time to the Bloch lifetime as a function of the Wigner-Seitz radius $r_s$. We also discuss the effect on the surface states of adding metallic contacts. Comment: 16 pages, 3 figure

Spin precession and alternating spin polarization in spin-3/2 hole systems

The spin density matrix for spin-3/2 hole systems can be decomposed into a sequence of multipoles which has important higher-order contributions beyond the ones known for electron systems [R. Winkler, Phys. Rev. B \textbf{70}, 125301 (2004)]. We show here that the hole spin polarization and the higher-order multipoles can precess due to the spin-orbit coupling in the valence band, yet in the absence of external or effective magnetic fields. Hole spin precession is important in the context of spin relaxation and offers the possibility of new device applications. We discuss this precession in the context of recent experiments and suggest a related experimental setup in which hole spin precession gives rise to an alternating spin polarization.Comment: 4 pages, 2 figures, to appear in Physical Review Letter

Anisotropic Pauli Spin Blockade of Holes in a GaAs Double Quantum Dot

Electrically defined semiconductor quantum dots are attractive systems for spin manipulation and quantum information processing. Heavy-holes in both Si and GaAs are promising candidates for all-electrical spin manipulation, owing to the weak hyper- fine interaction and strong spin-orbit interaction. However, it has only recently become possible to make stable quantum dots in these systems, mainly due to difficulties in device fabrication and stability. Here we present electrical transport measurements on holes in a gate-defined double quantum dot in a GaAs/AlxGa1−xAs heterostructure. We observe clear Pauli spin blockade and demonstrate that the lifting of this spin blockade by an external magnetic field is highly anisotropic. Numerical calculations of heavy-hole transport through a double quantum dot in the presence of strong spin-orbit coupling show quantitative agreement with experimental results and suggest that the observed anisotropy can be explained by both the anisotropic effective hole g-factor and the surface Dresselhaus spin-orbit interaction

Integrated silicon qubit platform with single-spin addressability, exchange control and robust single-shot singlet-triplet readout

Silicon quantum dot spin qubits provide a promising platform for large-scale quantum computation because of their compatibility with conventional CMOS manufacturing and the long coherence times accessible using $^{28}$Si enriched material. A scalable error-corrected quantum processor, however, will require control of many qubits in parallel, while performing error detection across the constituent qubits. Spin resonance techniques are a convenient path to parallel two-axis control, while Pauli spin blockade can be used to realize local parity measurements for error detection. Despite this, silicon qubit implementations have so far focused on either single-spin resonance control, or control and measurement via voltage-pulse detuning in the two-spin singlet-triplet basis, but not both simultaneously. Here, we demonstrate an integrated device platform incorporating a silicon metal-oxide-semiconductor double quantum dot that is capable of single-spin addressing and control via electron spin resonance, combined with high-fidelity spin readout in the singlet-triplet basis.Comment: 10 pages, 4 figure

Geometrical phase effects on the Wigner distribution of Bloch electrons

We investigate the dynamics of Bloch electrons using a density operator method and connect this approach with previous theories based on wave packets. We study non-interacting systems with negligible disorder and strong spin-orbit interactions, which have been at the forefront of recent research on spin-related phenomena. We demonstrate that the requirement of gauge invariance results in a shift in the position at which the Wigner function of Bloch electrons is evaluated. The present formalism also yields the correction to the carrier velocity arising from the Berry phase. The gauge-dependent shift in carrier position and the Berry phase correction to the carrier velocity naturally appear in the charge and current density distributions. In the context of spin transport we show that the spin velocity may be defined in such a way as to enable spin dynamics to be treated on the same footing as charge dynamics. Aside from the gauge-dependent position shift we find additional, gauge-covariant multipole terms in the density distributions of spin, spin current and spin torque.Comment: 12 pages, 3 figure

Ultra-low carrier concentration and surface dominant transport in Sb-doped Bi2Se3 topological insulator nanoribbons

A topological insulator is a new state of matter, possessing gapless spin-locking surface states across the bulk band gap which has created new opportunities from novel electronics to energy conversion. However, the large concentration of bulk residual carriers has been a major challenge for revealing the property of the topological surface state via electron transport measurement. Here we report surface state dominated transport in Sb-doped Bi2Se3 nanoribbons with very low bulk electron concentrations. In the nanoribbons with sub-10nm thickness protected by a ZnO layer, we demonstrate complete control of their top and bottom surfaces near the Dirac point, achieving the lowest carrier concentration of 2x10^11/cm2 reported in three-dimensional (3D) topological insulators. The Sb-doped Bi2Se3 nanostructures provide an attractive materials platform to study fundamental physics in topological insulators, as well as future applications.Comment: 5 pages, 4 figures, 1 tabl