Effect of spin–orbit coupling on spectral and transport properties of tubular electron gas in InAs nanowires

We constructed the Hamiltonian of spin–orbit splitting for carriers of a tubular electron gas in InAs nanowires. The spectral problem is solved using an exact numerical diagonalization. It is shown that the contribution of k-linear Dresselhaus-like spin–orbit (SO) coupling leads to renormalization of the so-called SO-gaps and appearance of anticrossings in subband spectrum. These features can be detected in ballistic transport.     

On Harmonic Approximation for Large Josephson Junction Coupling Charge Qubits

We revisit the harmonic approximation (HA) for a large Josephson junction interacting with some charge qubits through the variational approach for the quantum dynamics of the junction-qubit coupling system. By making use of numerical calculation and analytical treatment, the conditions under which HA works well can be precisely presented to control the parameters implementing the two-qubit quantum logical gate through the couplings to the large junction with harmonic oscillator Hamiltonian.     

Cooperative dynamics of coupled motor–cargoes system with stochastic interactions in the crowded environment

In this study, we investigate the cooperative transport behaviors of coupled motor–cargoes system, in which multiple passive cargoes stochastically interact with one active Brownian motor. The environment with stochastic interactions is characterized by the concentration (reflecting the cargo’s number in unit volume) and switching rate (reflecting the interacting stability between motor and cargoes), based on which the stationary multiple-state process can be employed to describe the fluctuating-cargo state in the coupled system. By analyzing the average probability current of decoupled system in the thermodynamic limit, we effectively study the possibility of cooperative transport through stochastic cargoes to behave rich dynamical behaviors, including the directed current, current reversal, stochastic resonance (SR) and stochastic inhibition (SI), inverse SR and SI, even without the effect of external driving force. Based on numerical results, we systematically discuss the transport dependence on various parameters, including the cargo concentration in the crowded environment, cargo capacity of the motor, driving amplitude of external periodic force, and medium temperature. Obviously, the sensitivity of transport process to parameter changes can be used by the environment to regulate its cargo traffic, which also provides latent support for manipulating the transport performance and optimizing the coupled structure in artificial nano-machines.     

Magnetic flux control of chiral Majorana edge modes in topological superconductor

We study the transport of chiral Majorana edge modes (CMEMs) in a hybrid quantum anomalous Hall insulator-topological superconductor (QAHI-TSC) system in which the TSC region contains a Josephson junction and a cavity. The Josephson junction undergoes a topological transition when the magnetic flux through the cavity passes through half-integer multiples of magnetic flux quantum. For the trivial phase, the CMEMs transmit along the QAHI-TSC interface as without magnetic flux. However, for the nontrivial phase, a zero-energy Majorana state appears in the cavity, leading to that a CMEM can resonantly tunnel through the Majorana state to a different CMEM. These findings may provide a feasible scheme to control the transport of CMEMs by using the magnetic flux and the transport pattern can be customized by setting the size of the TSC.     

Role of conserved quantities in Fourier's law for diffusive mechanical systems

Energy transport can be influenced by the presence of other conserved quantities. We consider here diffusive systems where energy and the other conserved quantities evolve macroscopically on the same diffusive space–time scale. In these situations, the Fourier law depends also on the gradient of the other conserved quantities. The rotor chain is a classical example of such systems, where energy and angular momentum are conserved. We review here some recent mathematical results about the diffusive transport of energy and other conserved quantities, in particular for systems where the bulk Hamiltonian dynamics is perturbed by conservative stochastic terms. The presence of the stochastic dynamics allows us to define the transport coefficients (thermal conductivity) and in some cases to prove the local equilibrium and the linear response argument necessary to obtain the diffusive equations governing the macroscopic evolution of the conserved quantities. Temperature profiles and other conserved quantities profiles in the non-equilibrium stationary states can be then understood from the non-stationary diffusive behavior. We also review some results and open problems on the two step approach (by weak coupling or kinetic limits) to the heat equation, starting from mechanical models with only energy conserved.     

Interfacial spin Hall current in a Josephson junction with Rashba spin—orbit coupling

We theoretically investigate the spin transport properties of the Cooper pairs in a conventional Josephson junction with Rashba spin-orbit coupling considered in one of the superconducting leads.It is found that an angle-resolved spin supercurrent flows through the junction and a nonzero interfacial spin Hall current driven by the superconducting phase difference also appears at the interface.The physical origin of this is that the Rashba spin-orbit coupling can induce a triplet order parameter in the s-wave superconductor.The interfacial spin Hall current dependences on the system parameters are also discussed.     

Spin-resolved edge states transport in a normal/ferromagnetic/normal topological insulator junction: The role of interface

The spin-resolved edge states transport in a normal/ferromagnetic/normal topological insulator (TI) junction is investigated numerically. It is shown that the transport properties of the hybrid junction strongly depend on the interface shape. For the junction with two sharp interfaces, a nonzero spin conductance can be generated besides the spin-split energy windows. Moreover, the axial symmetries of the in-plane spin conductance amplitude are broken. The underlying physics is attributed to the sharp-interface-induced quantum interference effect. However, for the hybrid junction with two smooth interfaces, a non-zero spin conductance can only be achieved in the spin-split energy windows. Further, the axial symmetries of the in-plane spin conductance amplitude recover. These findings may not only benefit to further apprehend the spin-dependent edge states transport in the hybrid TI junctions but also provide some theoretical bases to the application of the topological spintronics devices.     

Interplay of spin–orbit coupling and superconducting correlations in germanium telluride thin films

There is much current interest in combining superconductivity and spin–orbit coupling in order to induce the topological superconductor phase and associated Majorana‐like quasiparticles which hold great promise towards fault‐tolerant quantum computing. Experimentally these effects have been combined by the proximity‐coupling of super‐conducting leads and high spin–orbit materials such as InSb and InAs, or by controlled Cu‐doping of topological insu‐lators such as Bi₂Se₃. However, for practical purposes, a single‐phase material which intrinsically displays both these effects is highly desirable. Here we demonstrate coexisting superconducting correlations and spin–orbit coupling in molecular‐beam‐epitaxy‐grown thin films of GeTe. The former is evidenced by a precipitous low‐temperature drop in the electrical resistivity which is quelled by a magnetic field, and the latter manifests as a weak antilocalisation (WAL) cusp in the magnetotransport. Our studies reveal several other intriguing features such as the presence of two‐dimensional rather than bulk transport channels below 2 K, possible signatures of topological superconductivity, and unexpected hysteresis in the magnetotransport. Our work demonstrates GeTe to be a potential host of topological SC and Majorana‐like excitations, and to be a versatile platform to develop quantum information device architectures. (© 2016 The Authors. Phys. Status Solidi RRL published by WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Driven dissipative dynamics and topology of quantum impurity systems

In this review, we provide an introduction to and an overview of some more recent advances in real-time dynamics of quantum impurity models and their realizations in quantum devices. We focus on the Ohmic spin–boson and related models, which describe a single spin-1/2 coupled with an infinite collection of harmonic oscillators. The topics are largely drawn from our efforts over the past years, but we also present a few novel results. In the first part of this review, we begin with a pedagogical introduction to the real-time dynamics of a dissipative spin at both high and low temperatures. We then focus on the driven dynamics in the quantum regime beyond the limit of weak spin–bath coupling. In these situations, the non-perturbative stochastic Schrödinger equation method is ideally suited to numerically obtain the spin dynamics as it can incorporate bias fields $h_z(t)$ of arbitrary time-dependence in the Hamiltonian. We present different recent applications of this method: (i) how topological properties of the spin such as the Berry curvature and the Chern number can be measured dynamically, and how dissipation affects the topology and the measurement protocol, (ii) how quantum spin chains can experience synchronization dynamics via coupling with a common bath. In the second part of this review, we discuss quantum engineering of spin–boson and related models in circuit quantum electrodynamics (cQED), quantum electrical circuits, and cold-atoms architectures. In different realizations, the Ohmic environment can be represented by a long (microwave) transmission line, a Luttinger liquid, a one-dimensional Bose–Einstein condensate or a chain of superconducting Josephson junctions. We show that the quantum impurity can be used as a quantum sensor to detect properties of a bath at minimal coupling, and how dissipative spin dynamics can lead to new insight in the Mott–superfluid transition.     

Exponential Relaxation to Equilibrium for a One-Dimensional Focusing Non-Linear Schrödinger Equation with Noise

We construct generalized grand-canonical- and canonical Gibbs measures for a Hamiltonian system described in terms of a complex scalar field that is defined on a circle and satisfies a nonlinear Schrödinger equation with a focusing nonlinearity of order p < 6. Key properties of these Gibbs measures, in particular absence of “phase transitions” and regularity properties of field samples, are established. We then study a time evolution of this system given by the Hamiltonian evolution perturbed by a stochastic noise term that mimics effects of coupling the system to a heat bath at some fixed temperature. The noise is of Ornstein–Uhlenbeck type for the Fourier modes of the field, with the strength of the noise decaying to zero, as the frequency of the mode tends to ∞. We prove exponential approach of the state of the system to a grand-canonical Gibbs measure at a temperature and “chemical potential” determined by the stochastic noise term.     

Manifestation of Hamiltonian chaos in dissipative atomic transport in a standing-wave laser field

We simulate atomic ballistic transport in a standing-wave laser field in the framework of a Monte Carlo stochastic wavefunction approach in which the coherent Hamiltonian evolution is interrupted at random times by spontaneous emission events. It is shown in numerical experiments and confirmed analytically that the character of spatial and momentum diffusion of spontaneously emitting atoms changes abruptly in the atom-laser detuning regime where the deterministic Hamiltonian dynamics has been shown to be chaotic. Thus, we find a manifestation of underlying Hamiltonian chaos in the diffusive-like center-of-mass motion which can be observed in real experiments. The article is published in the original.     

Phase-dependent electron transport through a quantum wire on a surface

Electron transport through a quantum wire in the presence of external periodic energy-level modulations with different on-site phases is studied within the time evolution operator method for a tight-binding Hamiltonian. It is found that in the presence of spatial symmetry of the system and no source-drain and static gate voltages the pumping current can be generated. Moreover, for a wire which is tunnel-coupled to the underlying substrate, the current flowing through an unbiased wire does not fade away but increases with the wire-surface coupling. For randomly chosen phases at every wire site two regimes of the phase-averaged current are found which are related to small and high wire density of states.     

Topological and Nontopological Edge States Induced by Qubit-Assisted Coupling Potentials

In the usual Su–Schrieffer–Heeger (SSH) chain, the topology of the energy spectrum is divided into two categories in different parameter regions. Here, the topological and nontopological edge states induced by qubit-assisted coupling potentials in circuit quantum electrodynamics (QED) lattice modeled as a SSH chain are studied. It is found that, when the coupling potential added on only one end of the system raises to a certain extent, the strong coupling potential will induce a new topologically nontrivial phase accompanied by the appearance of a nontopological edge state, and the novel phase transition leads to the inversion of odd–even effect directly. Furthermore, the topological phase transitions when two unbalanced coupling potentials are injected into both ends of the circuit QED lattice are studied, and it is found that the system exhibits three distinguishing phases with multiple flips of energy bands. These phases are significantly different from the previous phase induced via unilateral coupling potential due to the existence of a pair of nontopological edge states. The scheme provides a feasible and visible method to induce different topological and nontopological edge states through controlling the qubit-assisted coupling potentials in circuit QED lattice both in experiment and theory.     

Andreev reflection at the edge of a two-dimensional electron system with strong spin-orbit coupling

We experimentally investigate transport properties of a single planar junction between the niobium superconductor and the edge of a two-dimensional electron system in a narrow In_0.75Ga_0.25As quantum well with strong Rashba-type spin-orbit coupling. We experimentally demonstrate suppression of Andreev reflection at low biases at ultralow temperatures. From the analysis of temperature and magnetic field behavior, we interpret the observed suppression as a result of a spin-orbit coupling. There is also an experimental sign of the topological superconductivity realization in the present structure.     

Quantum signal transmission through a single-qubit chain

A system of a two-level atom of an impurity (qubit) inserted into a periodic chain coupled to the continuum is studied with the use of the effective non-Hermitian Hamiltonian. Exact solutions are derived for the quasistationary eigenstates, their complex energies, and transport properties. Due to the presence of the qubit, two long-lived states corresponding to the ground and excited states of the qubit emerge outside the Bloch energy band. These states remain essentially localized at the qubit even in the limit of sufficiently strong coupling between the chain and the environment when the super-radiant states are formed. The transmission through the chain is studied as a function of the continuum coupling strength and the chain-qubit coupling; the perfect resonance transmission takes place through isolated resonances at weak and strong continuum coupling, while the transmission is lowered in the intermediate regime.     

Selective effects of noise by stochastic multi-resonance in coupled cells system

By investigating a stochastic model for intracellular calcium oscillations proposed by Höfer, we have analyzed the transmission behavior of calcium signaling in a one-dimensional two-way coupled hepatocytes system. It is shown that when the first cell is subjected to the external noise, the output signal-to-noise ratio (SNR) in the cell exhibits two maxima as a function of external noise intensity, indicating the occurrence of stochastic bi-resonance (SBR). It is more important that when cells are coupled together, the resonant behavior in the 1st cell propagates along the chain with different features through the coupling effect. The cells whose locations are comparatively close to or far from the 1st cell can show SBR, while the cells located in the middle position can display stochastic multi-resonance (SMR). Furthermore, the number of cells that can show SMR increases with coupling strength enhancing. These results indicate that the cells system may make an effective choice in response to external signaling induced by noise, through the mechanism of SMR by adjusting coupling strength.     

Theory of resonant tunneling through quantum dots in the presence of electron-phonon interaction

Structures where the electrons of a two-dimensional electron gas are confined to disconnected regions can be fabricated by the use of appropriate gate geometries. The transport between these electrostatically defined quantum dots takes place by tunneling. Using the tunneling Hamiltonian approach we present a theoretical model of the system including electron-phonon interaction. The relevant coupling constants are determined from realistic wave functions for the expected confinement potentials. The phonon part of the Hamiltonian is diagonalized using a canonical transformation. Starting from the determination of the transmission matrix for the interacting system we calculate the current-voltage characteristics for different temperatures and phonon coupling strengths.     

Singular reduction of implicit Hamiltonian systems

This paper develops the theory of singular reduction for implicit Hamiltonian systems admitting a symmetry Lie group. The reduction is performed at a singular value of the momentum map. This leads to a singular reduced topological space which is not a smooth manifold. A topological Dirac structure on this space is defined in terms of a generalized Poisson bracket and a vector space of derivations, both being defined on a set of smooth functions. A corresponding Hamiltonian formalism is described. It is shown that solutions of the original system descend to solutions of the reduced system. Finally, if the generalized Poisson bracket is nondegenerate, then the singular reduced space can be decomposed into a set of smooth manifolds called pieces. The singular reduced system restricts to a regular reduced implicit Hamiltonian system on each of these pieces. The results in this paper naturally extend the singular reduction theory as previously developed for symplectic or Poisson Hamiltonian systems.     

二维势场中弹性耦合粒子的定向输运研究

建立了二维势场中弹性耦合粒子的输运模型, 其中一维上加交流驱动及噪声, 另一维上不加驱动及噪声, 分析讨论了过阻尼情形下系统和外部参量对定向流的影响. 结果表明, 粒子可以通过相互耦合使一个方向上输入的驱动能量转化到垂直方向上, 从而使无能量输入的方向产生定向流. 适当的弹簧自由长度及耦合强度可以使定向流达到极值, 特别是当耦合强度及噪声强度固定时, 定向流会随弹簧自由长度的变化而振荡, 出现多峰现象. 研究还发现, 定向流随噪声强度的变化出现随机共振现象. 当产生定向流方向上的势的不对称度达到一定程度时会出现流反转现象. 关键词： 弹性耦合 定向输运 随机共振 流反转     

Nonlocal transport properties of topological insulator F/I/SC/I/F junction with perpendicular magnetization

We investigate theoretically the nonlocal transport properties in a ferromagnet/insulator/superconductor/insulator/ferromagnet (F/I/SC/I/F) junction with perpendicular magnetization formed on a topological insulator. The nonlocal conductance through the junction depends strongly on whether the perpendicular magnetizations of the two ferromagnets are in a parallel or an antiparallel alignment. This stems from the fact that on the surface of three dimensional topological insulator the exchange field acts as vector potential and from spin-momentum locking property of the topological insulator surface states. It is found that the nonlocal conductance as a function of barrier strength of the I regions exhibits a quantum switch on-off property.