Topological viewpoint of two-dimensional group III-V and IV-IV compounds in the presence of electric field and spin-orbit coupling by density functional theory and tight-binding model

Using the tight-binding model and density functional theory, the topological invariant of the two-dimensional (2D) group III-V and IV-IV compounds are studied in the absence and the presence of an external perpendicular electric field and spin-orbit coupling. It will be recognized that a critical value of these parameters changes the topological invariant of 2D graphene-like compounds. The significant effects of an external electric field and spin-orbit coupling are considered to the two-center overlap integrals of the Slater-Koster model involved in band structures, changing band-gap, and tuning the topological phase transition between ordinary and quantum spin Hall regime. These declare the good consistency between two theories: tight-binding and density functional. So, this study reveals topological phase transition in these materials. Our finding paves a way to extend an effective Hamiltonian, and may instantly clear some computation aspects of the study in the field of spintronic based on the first-principles methods.

Topological phase transition in cavity optomechanical system with periodical modulation

We investigate the topological phase transition and the enhanced topological effect in cavity optomechanical system with periodical modulation. By calculating the steady-state equations of the system, the steady-state conditions of cavity fields and the restricted conditions of effective optomechanical couplings are demonstrated. It is found that the cavity optomechanical system can be modulated to different topological Su-Schrieffer-Heeger (SSH) phases via designing the optomechanical couplings legitimately. Meanwhile, combining the effective optomechanical couplings and the probability distributions of gap states, we reveal the topological phase transition between trivial SSH phase and nontrivial SSH phase via adjusting the decay rates of cavity fields. Moreover, we find that the enhanced topological effect of gap states can be achieved by enlarging the size of system and adjusting the decay rates of cavity fields.

Topological phase transition associated with structural phase transition in ternary half Heusler compound LiAuBi.

In this article, we report detailed theoretical investigations of topological phases in a new non-centrosymmetric half Heusler compound LiAuBi upto a pressure of 30 GPa. It is found that the compound forms into a dynamically stable face centered cubic (FCC) lattice structure of space group F ¯43m (216) at ambient pressure. The compound is topologically non-trivial at ambient pressure, but undergoes a quantum phase transition to trivial topological phase at 23.4 GPa. However, the detailed investigations show a structural phase transition from FCC lattice (space group 216) to a honeycomb lattice (space group 194) at 13 GPa, which is also associated with a non-trivial to trivial topological phase transition. Further investigations show that the compound also carries appreciable thermoelectric properties at ambient pressure. The figure of merit (ZT) increases from 0.21 at room temperature to a maximum value of 0.22 at 500K. The theoretical findings show its potential for practical applications in spintronics as well as thermoelectricity, therefore LiAuBi needs to be synthesized and investigated experimentally for its applications.

Majorana/Andreev crossover and the fate of the topological phase transition in inhomogeneous nanowires

Majorana bound states (MBS) and Andreev bound states (ABS) in realistic Majorana nanowires setups have similar experimental signatures which make them hard to distinguishing one from the other. Here, we characterize the continuous Majorana/Andreev crossover interpolating between fully-separated, partially-separated, and fully-overlapping Majorana modes, in terms of global and local topological invariants, fermion parity, quasiparticle densities, Majorana pseudospin and spin polarizations, density overlaps and transition probabilities between opposite Majorana components. We found that in inhomogeneous wires, the transition between fully-overlapping trivial ABS and nontrivial MBS does not necessarily mandate the closing of the bulk gap of quasiparticle excitations, but a simple parity crossing of partially-separated Majorana modes (ps-MM) from trivial to nontrivial regimes. We demonstrate that fully-separated and fully-overlapping Majorana modes correspond to the two limiting cases at the opposite sides of a continuous crossover: the only distinction between the two can be obtained by estimating the degree of separations of the Majorana components. This result does not contradict the bulk-edge correspondence: Indeed, the field inhomogeneities driving the Majorana/Andreev crossover have a length scale comparable with the nanowire length, and therefore correspond to a nonlocal perturbation which breaks the topological protection of the MBS.