The quantum spin Hall （QSH） effect is considered to be unstable to perturbations violating the time-reversal （TR） symmetry. We review some recent developments in the search of the QSH effect in the absence of the TR symmetry. The possibility to realize a robust QSH effect by artificial removal of the TR symmetry of the edge states is explored. As a useful tool to characterize topological phases without the TR symmetry, the spin-Chern number theory is introduced.
The electric-pulse-induced resistive switching effect is studied for Tio.s5Cro.15Ox （TCO） films grown on Ir-Si substrates by pulsed laser deposition. Such a TCO device exhibits bipolar switching behaviour with an electric-pulse- induced resistance ratio as large as about 1000% and threshold voltages smaller than 2 V. The resistive switching characteristics may be understood by resistance changes of a Schottky junction composed of a metal and an n-type semiconductor, and its nonvolatility is attributed to the movement of oxygen vacancies near the interface.
The Chern number is often used to distinguish different topological phases of matter in two-dimensional electron systems. A fast and efficient coupling-matrix method is designed to calculate the Chern number in finite crystalline and disordered systems. To show its effectiveness, we apply the approach to the Haldane model and the lattice Hofstadter model, and obtain the correct quantized Chern numbers. The disorder-induced topological phase transition is well reproduced, when the disorder strength is increased beyond the critical value. We expect the method to be widely applicable to the study of topological quantum numbers.
