We find theoretically a new quantum state of matter-the valley-polarized quantum anomalous Hall state in silicene. In the presence of Rashba spin-orbit coupling and an exchange field, silicene hosts a quantum anomalous Hall state with Chern number C=2. We show that through tuning the Rashba spin-orbit coupling, a topological phase transition results in a valley-polarized quantum anomalous Hall state, i.e., a quantum state that exhibits the electronic properties of both the quantum valley Hall state (valley Chern number Cv=3) and quantum anomalous Hall state with C=-1. This finding provides a platform for designing dissipationless valleytronics in a more robust manner.
In this work, we investigate the bound-state problem in a one-dimensional spin-1 Dirac Hamiltonian with a flat band. It is found that the flat band has significant effects on the bound states. For example, for Dirac delta potential gδ(x), there exists one bound state for both the positive and negative potential strength g. Furthermore, when the potential is weak, the bound-state energy is proportional to the potential strength g. For square well potential, the flat band results in the existence of infinite bound states for arbitrarily weak potential. In addition, when the bound-state energy is very near the flat band, the energy displays a hydrogen atom-like spectrum, i.e. the bound-state energies are inversely proportional to the square of the natural number n (e.g., E
n
∝ 1/n
2, n = 1, 2, 3, …). Most of the above nontrivial behaviors can be attributed to the infinitely large density of states of the flat band and its ensuing 1/z singularity of the Green function. The combination of a short-ranged potential and flat band provides a new possibility to get an infinite number of bound states and a hydrogen atom-like energy spectrum. In addition, our findings provide some useful insights and further our understanding of the many-body physics of the flat band.
We present a general formula of the orbital magnetization of disordered systems based on the Keldysh Green's function theory in the gauge-covariant Wigner space. In our approach, the gauge invariance of physical quantities is ensured from the very beginning, and the vertex corrections are easily included. Our formula applies not only for insulators but also for metallic systems where the quasiparicle behavior is usually strongly modified by the disorder scattering. In the absence of disorders, our formula recovers the previous results obtained from the semiclassical theory and the perturbation theory. As an application, we calculate the orbital magnetization of a weakly disordered two-dimensional electron gas with Rashba spin-orbit coupling. We find that for the short range disorder scattering, its major effect is to the shifting of the distribution of orbital magnetization corresponding to the quasiparticle energy renormalization.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.