Quantum computing through electron propagation in edge states of quantum spin Hall systems

We propose to implement quantum computing by the on-demand control of the wave packets propagation in helical edge channels of the quantum spin Hall systems (QSHs). Two non-commutative single-qubit gates are realized by the gate voltages applied on the edge channels. The two-qubit controlled phase gate is implemented by the capacitive Coulomb interaction between two adjacent edge channels from two parallel QSHs. A universal set of quantum gates thus can be realized in an all-electrical way. It is also shown that the fidelity and the purity of the controlled phase gate can reach a high value, with both the time delay and the finite width of the wave packets taken into account.     

Electrical manipulation and measurement of spin properties of quantum spin Hall edge states

We study the effects of a gate-controlled Rashba spin-orbit coupling to quantum spin Hall edge states in HgTe quantum wells. A uniform Rashba coupling can be employed in tuning the spin orientation of the edge states while preserving the time-reversal symmetry. We introduce a sample geometry where the Rashba coupling can be used in probing helicity by purely electrical means without requiring spin detection, application of magnetic materials or magnetic fields. In the considered setup a tilt of the spin orientation with respect to the normal of the sample leads to a reduction in the two-terminal conductance with current-voltage characteristics and temperature dependence typical of Luttinger liquid constrictions.     

Electron spin transitions in quantum Hall systems

A system of two-dimensional electron gas in a strong magnetic field exhibits a remarkable phenomenon known as the fractional quantum Hall effect. Rapid advances in experimental techniques and intense theoretical work for well over a decade have significantly contributed to our understanding of the mechanism behind the effect. It is now a well established fact that electron correlations are largely responsible for the occurrence of this phenomenon. In recent years, theoretical and experimental investigations have revealed that those electron correlations, which are responsible for the quantum Hall effect, are also the reason for various spin transitions in the system. In this review, we systematically follow the theoretical studies of the role spin degree of freedom play in the quantum Hall effect regime and also describe several ingenious experiments reported in recent years which are in good agreement with the emerging theoretical picture.     

Nanomagnet coupled to quantum spin Hall edge: An adiabatic quantum motor

The precessing magnetization of a magnetic islands coupled to a quantum spin Hall edge pumps charge along the edge. Conversely, a bias voltage applied to the edge makes the magnetization precess. We point out that this device realizes an adiabatic quantum motor and discuss the efficiency of its operation based on a scattering matrix approach akin to Landauer–Büttiker theory. Scattering theory provides a microscopic derivation of the Landau–Lifshitz–Gilbert equation for the magnetization dynamics of the device, including spin-transfer torque, Gilbert damping, and Langevin torque. We find that the device can be viewed as a Thouless motor, attaining unit efficiency when the chemical potential of the edge states falls into the magnetization-induced gap. For more general parameters, we characterize the device by means of a figure of merit analogous to the ZT value in thermoelectrics.     

Electron entanglement detected by quantum spin Hall systems

We propose a promising electron entanglement detector consisting of two quantum spin Hall systems weakly coupled to a superconductor. The detection of electron spins along various polarization directions, which is a prerequisite for testing Bell's inequality on solid state spins, can be achieved in an all-electrical-controlled manner utilizing the helical edge states. It is found that the violation of Bell's inequality exists in a large range of the tunneling parameters, which can be realized in mercury telluride quantum wells.     

Helical nuclear spin order in a strip of stripes in the quantum Hall regime

We investigate nuclear spin effects in a two-dimensional electron gas in the quantum Hall regime modeled by a weakly coupled array of interacting quantum wires. We show that the presence of hyperfine interaction between electron and nuclear spins in such wires can induce a phase transition, ordering electrons and nuclear spins into a helix in each wire. Electron-electron interaction effects, pronounced within the one-dimensional stripes, boost the transition temperature up to tens to hundreds of millikelvins in GaAs. We predict specific experimental signatures of the existence of nuclear spin order, for instance for the resistivity of the system at transitions between different quantum Hall plateaus.     

Reconstruction of the quantum Hall edge

The sharp quantum Hall edge present for hard confinement is shown to have two modes that go soft as the confining potential softens. This signals a second order transition to a reconstructed edge that is either a depolarized spin-texture edge or a polarized charge density wave edge.     

Reprint of : Nanomagnet coupled to quantum spin Hall edge: An adiabatic quantum motor

The precessing magnetization of a magnetic islands coupled to a quantum spin Hall edge pumps charge along the edge. Conversely, a bias voltage applied to the edge makes the magnetization precess. We point out that this device realizes an adiabatic quantum motor and discuss the efficiency of its operation based on a scattering matrix approach akin to Landauer–Büttiker theory. Scattering theory provides a microscopic derivation of the Landau–Lifshitz–Gilbert equation for the magnetization dynamics of the device, including spin-transfer torque, Gilbert damping, and Langevin torque. We find that the device can be viewed as a Thouless motor, attaining unit efficiency when the chemical potential of the edge states falls into the magnetization-induced gap. For more general parameters, we characterize the device by means of a figure of merit analogous to the ZT value in thermoelectrics.     

Exact exponents for the spin quantum Hall transition in the presence of multiple edge channels

Critical properties of quantum Hall systems are affected by the presence of extra edge channels-those that are present, in particular, at higher plateau transitions. We study this phenomenon for the case of the spin quantum Hall transition. Using supersymmetry, we map the corresponding network model to a classical loop model, whose boundary critical behavior was recently determined exactly. We verify predictions of the exact solution by extensive numerical simulations.     

Time-reversal-symmetry-broken quantum spin Hall effect

The quantum spin Hall (QSH) state of matter is usually considered to be protected by time-reversal (TR) symmetry. We investigate the fate of the QSH effect in the presence of the Rashba spin-orbit coupling and an exchange field, which break both inversion and TR symmetries. It is found that the QSH state characterized by nonzero spin Chern numbers C(±) = ±1 persists when the TR symmetry is broken. A topological phase transition from the TR-symmetry-broken QSH phase to a quantum anomalous Hall phase occurs at a critical exchange field, where the bulk band gap just closes. It is also shown that the transition from the TR-symmetry-broken QSH phase to an ordinary insulator state cannot happen without closing the band gap.     

Multiprobe quantum spin Hall bars

We analyze electron transport in multiprobe quantum spin Hall (QSH) bars using the Büttiker formalism and draw parallels with their quantum Hall (QH) counterparts. We find that in a QSH bar the measured resistance changes upon introducing side voltage probes, in contrast to the QH case. We also study four- and six-terminal geometries and derive the expressions for the resistances. For these our analysis is generalized from the single-channel to the multi-channel case and to the inclusion of backscattering originating from a constriction placed within the bar.     

Spin-orbit gauge and quantum spin Hall effect

We have shown that the non-Abelian spin-orbit gauge field strength of the Rashba and Dresselhaus interactions, when split into two Abelian field strengths, the Hamiltonian of the system can be re-expressed as a Landau level problem with a particular relation between the two coupling parameters. The quantum levels are created with up and down spins with opposite chirality and leads to the quantum spin Hall effect.     

Imaging of Coulomb-driven quantum Hall edge states

The edges of a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime are divided into alternating metallic and insulating strips, with their widths determined by the energy gaps of the QHE states and the electrostatic Coulomb interaction. Local probing of these submicrometer features, however, is challenging due to the buried 2DEG structures. Using a newly developed microwave impedance microscope, we demonstrate the real-space conductivity mapping of the edge and bulk states. The sizes, positions, and field dependence of the edge strips around the sample perimeter agree quantitatively with the self-consistent electrostatic picture. The evolution of microwave images as a function of magnetic fields provides rich microscopic information around the ν=2 QHE state.     

Molecular tuning of quantum Hall edge states

Hybrid organic/inorganic devices may find applications as sensors and in futuristic molecular-electronic devices. Here, we demonstrate molecular control of vertical transport in semiconductor superlattices in strong magnetic fields by adsorption of organic molecules onto the sidewalls of a GaAs/AlGaAs device. The molecules have identical attachment groups functionalized by end groups with different electronegativities. For magnetic fields in quantized Hall states, we find that the adsorbate substantially modifies the network of edge states that carries the electrical current. The data indicate that molecules with appropriately chosen end groups can enhance or decrease the vertical conductivity of the edge state system.     

Electron correlations at the fractional quantum Hall edge

This paper reviews tunnel spectroscopy of fractional quantum Hall edges using cleaved-edge overgrown devices. Beginning with an intuitive introduction to various experimental and theoretical aspects, the device structure is reviewed, and the experimental result of a continuum of power-law tunneling exponents is revisited. The unanticipated behavior of the exponent with fractional filling factor is described, and all subsequent theoretical explanations for these results are laid out for comparison. Finally, we propose new directions for experimentally resolving the remaining questions.     

Spin-charge separation in the quantum spin Hall state

The quantum spin Hall state is a topologically nontrivial insulator state protected by the time-reversal symmetry. We show that such a state always leads to spin-charge separation in the presence of a pi flux. Our result is generally valid for any interacting system. We present a proposal to experimentally observe the phenomenon of spin-charge separation in the recently discovered quantum spin Hall system.     

Nondissipative spin Hall effect via quantized edge transport

The spin Hall effect in a two-dimensional electron system on honeycomb lattice with both intrinsic and Rashba spin-orbit couplings is studied numerically. Integer quantized spin Hall conductance is obtained at the zero Rashba coupling limit when electron Fermi energy lies in the energy gap created by the intrinsic spin-orbit coupling, in agreement with recent theoretical prediction. While nonzero Rashba coupling destroys electron spin conservation, the spin Hall conductance is found to remain near the quantized value, being insensitive to disorder scattering, until the energy gap collapses with increasing the Rashba coupling. We further show that the charge transport through counterpropagating spin-polarized edge channels is well quantized, which is associated with a topological invariant of the system.