The hallmark of the spin-Hall insulator is the presence of gapless edge states of different spins moving in opposite directions. Through analytical solutions in a model calculation for a strip of finite width, we find that edge states on the two sides can couple together to produce a gap in the spectrum, destroying the quantum spin-Hall effect. The application of a magnetic field can however modify and even remove the gap by shifting the momenta of the edge states relative to each other.

Current understanding of higher-order topological insulators (HOTIs) is based primarily on crystalline materials. Here, we propose that HOTIs can be realized in quasicrystals. Specifically, we show that two distinct types of second-order topological insulators (SOTIs) can be constructed on the quasicrystalline lattices (QLs) with different tiling patterns. One is derived by using a Wilson mass term to gap out the edge states of the quantum spin Hall insulator on QLs. The other is the quasicrystalline quadrupole insulator (QI) with a quantized quadrupole moment. We reveal some unusual features of the corner states (CSs) in the quasicrystalline SOTIs. We also show that the quasicrystalline QI can be simulated by a designed electrical circuit, where the CSs can be identified by measuring the impedance resonance peak. Our findings not only extend the concept of HOTIs into quasicrystals but also provide a feasible way to detect the topological property of quasicrystals in experiments. arXiv:1904.09932v4 [cond-mat.mes-hall]

The magnetization reversal in a single molecular magnet ͑SMM͒ weakly coupled to an electrode with spin-dependent splitting of chemical potentials ͑spin bias͒ is theoretically investigated by means of the rate equation. A microscopic mechanism for the reversal is demonstrated by the avalanche dynamics at the reversal point. The magnetization as a function of the spin bias shows hysteresis loops tunable by the gate voltage and varying with temperature. The nondestructive measurement to the orientation of giant spin in SMM is presented by measuring the fully polarized electric current in the response to a small spin bias. For Mn 12 ac molecule, its small transverse anisotropy only slightly violates the results above. The situation when there is an angle between the easy axis of the SMM and the spin-quantization direction of the electrode is also studied. PACS number͑s͒: 75.50.Xx, 75.60.Jk, 72.25.Hg V 2 . The horizontal lines in the SMM region correspond to resonant energies to add an extra electron into the SMM via transitions from state ͉0,m͘ to ͉1,m Ϯ 1 2 ͘ − , which is tunable with respect to S ↑/↓ by the gate voltage V g .