ﻻ يوجد ملخص باللغة العربية
Disorder inevitably exists in realistic samples, manifesting itself in various exotic properties for the topological states. In this paper, we summarize and briefly review work completed over the last few years, including our own, regarding recent developments in several topics about disorder effects in topological states. For weak disorder, the robustness of topological states is demonstrated, especially for both quantum spin Hall states with $Z_2=1$ and size induced nontrivial topological insulators with $Z_2=0$. For moderate disorder, by increasing the randomness of both the impurity distribution and the impurity induced potential, the topological insulator states can be created from normal metallic or insulating states. These phenomena and their mechanisms are summarized. For strong disorder, the disorder causes a metal-insulator transition. Due to their topological nature, the phase diagrams are much richer in topological state systems. Finally, the trends in these areas of disorder research are discussed.
Three-dimensional topological insulator (TI) nanowires with quantized surface subband spectra are studied as a main component of Majorana bound states (MBS) devices. However, such wires are known to have large concentration $N sim 10^{19}$ cm$^{-3}$
Thin films of topological insulators (TI) attract large attention because of expected topological effects from the inter-surface hybridization of Dirac points. However, these effects may be depleted by unexpectedly large energy smearing $Gamma$ of su
Lotkas seminal work (A.J. Lotka A., Proc. Natl. Acad. Sci. U.S.A. 6 (1920) 410) on certain rhythmic relations is already one hundred years old, but the research activity about pattern formations due to cyclical dominance is more vibrant than ever. It
This article provides a focused review of recent findings which demonstrate, in some cases quite counter-intuitively, the existence of bound states with a singularity of the density pattern at the center, while the states are physically meaningful be
Recent studies of disorder or non-Hermiticity induced topological insulators inject new ingredients for engineering topological matter. Here we consider the effect of purely non-Hermitian disorders, a combination of these two ingredients, in a 1D chi