Z. B. Siu

Gauge Physics of Spin Hall Effect

Spin Hall effect (SHE) has been discussed in the context of Kubo formulation, geometric physics, spin orbit force, and numerous semi-classical treatments. It can be confusing if the different pictures have partial or overlapping claims of contribution to the SHE. In this article, we present a gauge-theoretic, time-momentum elucidation, which provides a general SHE equation of motion, that unifies under one theoretical framework, all contributions of SHE conductivity due to the kinetic, the spin orbit force (Yang-Mills), and the geometric (Murakami-Fujita) effects. Our work puts right an ambiguity surrounding previously partial treatments involving the Kubo, semiclassical, Berry curvatures, or the spin orbit force. Our full treatment shows the Rashba 2DEG SHE conductivity to be instead of −, and Rashba heavy hole instead of −. This renewed treatment suggests a need to re-derive and re-calculate previously studied SHE conductivity.

Topological state transport in topological insulators under the influence of hexagonal warping and exchange coupling to in-plane magnetizations

A hexagonal warping term has been proposed recently to explain the experimentally observed 2D equal energy contours of the surface states of the topological insulator Bi2Te3. Differing from the Dirac fermion Hamiltonian, the hexagonal warping term leads to the opening up of a band gap by an in-plane magnetization. We study the transmission between two Bi2Te3 segments subjected to different in-plane magnetizations and potentials. The opening up of a bandgap, and the accompanying displacement and distortion of the constant energy surfaces from their usual circular shapes by the in-plane magnetizations, modify the transverse momentum overlap between the two Bi2Te3 segments, and strongly modulate the transmission profile. The strong dependence of the TI surface state transport of Bi2Te3 on the magnetization orientation of an adjacent ferromagnetic layer may potentially be utilized in, e.g., a memory readout application.

Quantum anomalous Hall effect in topological insulator memory

We theoretically investigate the quantum anomalous Hall effect (QAHE) in a magnetically coupled three-dimensional-topological insulator (3D-TI) system. We apply the generalized spin-orbit coupling Hamiltonian to obtain the Hall conductivity σxy of the system. The underlying topology of the QAHE phenomenon is then analyzed to show the quantization of σxy and its relation to the Berry phase of the system. Finally, we analyze the feasibility of utilizing σxy as a memory read-out in a 3D-TI based memory at finite temperatures, with comparison to known magnetically doped 3D-TIs.

Spin-bias driven field effect transistor

We propose a spin field effect transistor driven by spin biases which are externally generated in the source and drain electrodes. We employed the Keldysh non-equilibrium Green’s function formalism to evaluate the charge and spin currents through the transistor, and verify the operation of the transistor as predicted by a semiclassical model. Our calculations show that in the “off” state, both the charge and spin currents are suppressed. In the “on” state, the device allows only the spin current to pass through but not charge current, thus potentially improving the energy efficiency of the device.

Electron Transport at the Interface Between a Ferromagnetic Insulator and a Topological Insulator

We perform a theoretical study of the electron transport through a normal metal-topological insulator-normal metal (NM-TI-NM) system, where a ferromagnetic insulator (FI) layer is deposited on top of the TI. The spin conductance of the system is analyzed as a function of parameters such as the strength of exchange coupling between the surface states of the TI and the magnetic moments of the FI layer, as well as the dimension of the TI channel. We find that the strength of the spin conductance can be optimized by tuning the parameters.

Spin current generator based on topological insulator coupled to ferromagnetic insulators

We propose a spin current generator based on a topological insulator current-in-plane spin valve, consisting of a 3D topological insulator sandwiched between two ferromagnetic insulator layers. The “on” and “off” states of the spin current can be toggled by switching the magnetization configuration of the two ferromagnetic insulator layers which are coupled to the surface states of the topological insulator.

The Hartman effect in Weyl semimetals

The group delay and dwell time are theoretically investigated in Weyl semimetals in the presence and absence of a magnetic field. The Hartman effect, which denotes the independence of group delay time on barrier length, is observed in Weyl semimetals when the incident angle and electron energy exceed certain critical values. We discuss the influence of the incident azimuthal angle, incident electron energy, and barrier length on the group delay time. Additionally, we found that the Hartman effect is also influenced by the magnetic field due to the direction dependence of the dwell time. This suggests some possible means to control the group delay time in applications involving Weyl semimetal-based devices.

Electric field tunable Landau levels of Weyl semimetals in the absence of magnetic fields

Weyl semimetals have emerged as the three-dimensional counterpart of graphene with linear energy dispersion along all three directions [1,2].

Transport in magnetized nanocylindrical topological insulators

In this work we study the surface states of a topological insulator (TI) cylinder with a magnetization in the radial, azimuthal and axial directions. We derive the eigenenergies and eigenstates, and show that a state with a quantum number associated with the orbital angular momentum incident at a junction between a source TI cylinder and a coaxial drain TI cylinder can only be transmitted and reflected into states with the same quantum number. For cylinders magnetized only in the radial direction, this leads to markedly different behavior in the transmission depending on whether the source magnetization is smaller or larger than the drain magnetization. For azimuthal magnetizations, it results in perfect transmission between two cylinders magnetized to different extents in the azimuthal direction. The restriction of transmission and reflection to states with the same quantum number gives rise to a step-like increment in the transmission from an unmagnetized cylinder to one with an axial magnetization as the energy and magnetization are varied.

Self-consistent magnetization dynamics of a ferromagnetic quantum dot driven by a spin bias

We present an iterative scheme which combines the non-equilibrium Green’s function (NEGF) for evaluating the quantum spin transport in a ferromagnetic quantum dot device and the Landau-Lifshitz (LL) equation for modeling the magnetization dynamics of the dot. For a given initial magnetization, the spin polarization of current and the resulting spin torque in the dot are calculated using the NEGF formalism. The torque acts on the magnetic moment of the dot, and the resultant magnetization dynamics is obtained from the LL equation. The new value of the dot’s magnetization is then used as an input for the next round of NEGF calculation, and the whole process is repeated iteratively. The spin torque is thus calculated self-consistently with the dynamics of the magnetic moment of the dot. We apply this self-consistent iterative scheme to study the magnetization dynamics in an exemplary quantum dot system with an induced spin bias in the leads under varying damping conditions.