Top-down patterning of topological surface and edge states using a focused ion beam.

The conducting boundary states of topological insulators appear at an interface where the characteristic invariant ℤ2 switches from 1 to 0. These states offer prospects for quantum electronics; however, a method is needed to spatially-control ℤ2 to pattern conducting channels. It is shown that modifying Sb2Te3 single-crystal surfaces with an ion beam switches the topological insulator into an amorphous state exhibiting negligible bulk and surface conductivity. This is attributed to a transition from ℤ2 = 1 → ℤ2 = 0 at a threshold disorder strength. This observation is supported by density functional theory and model Hamiltonian calculations. Here we show that this ion-beam treatment allows for inverse lithography to pattern arrays of topological surfaces, edges and corners which are the building blocks of topological electronics.

Newton's second law in spin-orbit torque.

Spin-orbit torque (SOT) refers to the excitation of magnetization dynamics via spin-orbit coupling (SOC) under the application of a charged current. In this work, we introduce a simple and intuitive description of the SOT in terms of spin force. In Rashba SOC system, the damping-like SOT can be expressed as [Formula: see text], in analogy to the classical torque-force relation, where R c is the effective radius characterizing the Rashba splitting in the momentum space. As a consequence, the magnetic energy is transferred to the conduction electrons, which dissipates through Joule heating at a rate of [Formula: see text], with j e being the applied current. Finally, we propose an experimental verification of our findings via measurement of the anisotropic magnetoresistance effect.

Effect of surface state hybridization on current-induced spin-orbit torque in thin topological insulator films.

We investigate the thickness optimization for maximum current-induced spin-orbit torque (SOT) generated by topological surface states (TSS's) in a bilayer system comprising of a ferromagnetic layer coupled to a thin topological insulator (TI) film. We show that by reducing the TI thickness, two competing effects on the SOT are induced: (i) the torque strength is stronger as the bulk contribution is decreased; (ii) on the other hand, the torque strength becomes suppressed due to increasing hybridization of the surface states. The latter is attributed to the opposite helicities of the coupled TSS's. We theoretically model the interplay of these two effects and derive the optimal TI thickness to maximize the spin torque, which is estimated to be about 3-5 nm for typical Bi2Se3 films.

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 [formula in text] instead of [formula in text], and Rashba heavy hole [formula in text] instead of [formula in text]. This renewed treatment suggests a need to re-derive and re-calculate previously studied SHE conductivity.