Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDisorder Effects in Topological States -- Brief Review of the Recent Developments
103
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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$^{-3}$ of Coulomb impurities. It is believed that a MBS device can function only if the amplitude of long-range fluctuations of the random Coulomb potential $Gamma$ is smaller than the subband gap $Delta$. Here we calculate $Gamma$ for recently experimentally studied large-dielectric-constant (Bi$_{1-x}$Sb$_x$)$_2$Te$_{3}$ wires in a small-dielectric-constant environment (no superconductor). We show that provided by such a dielectric-constant contrast, the confinement of electric field of impurities within the wire allows more distant impurities to contribute into $Gamma$, leading to $Gamma sim 3Delta$. We also calculate a TI wire resistance as a function of the Fermi level and carrier concentration due to scattering on Coulomb and neutral impurities, and do not find observable discrete subband-spectrum related oscillations at $N gtrsim 10^{18}$ 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 surface Dirac points by the random potential of abundant Coulomb impurities. We show that in a typical TI film with large dielectric constant $sim 50$ sandwiched between two low dielectric constant layers, the Rytova-Chaplik-Entin-Keldysh modification of the Coulomb potential of a charge impurity allows a larger number of the film impurities to contribute to $Gamma$. As a result, $Gamma$ is large and independent of the TI film thickness $d$ for $d > 5$ nm. In thinner films $Gamma$ grows with decreasing $d$ due to reduction of screening by the hybridization gap. We study the surface conductivity away from the neutrality point and at the neutrality point. In the latter case, we find the maximum TI film thickness at which the hybridization gap is still able to make a TI film insulating and allow observation of the quantum spin Hall effect, $d_{max} sim 7$ nm.
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 is because non-transitive interactions have paramount role on maintaining biodiversity and adequate human intervention into ecological systems requires deeper understanding of related dynamical processes. In this perspective article we overview different aspects of biodiversity, with focus on how it can be maintained based on mathematical modeling of last years. We also briefly discuss the potential links to evolutionary game models of social systems, and finally, give an overview about potential prospects for future research.
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 because their total norm converges. One model of this type is based on the 2D Gross-Pitaevskii equation (GPE) which combines the attractive potential ~ 1/r^2 and the quartic self-repulsive nonlinearity, induced by the Lee-Huang-Yang effect (quantum fluctuations around the mean-field state). The GPE demonstrates suppression of the 2D quantum collapse, driven by the attractive potential, and emergence of a stable ground state (GS), whose density features an integrable singularity ~1/r^{4/3} at r --> 0. Modes with embedded angular momentum exist too, and they have their stability regions. A counter-intuitive peculiarity of the model is that the GS exists even if the sign of the potential is reversed from attraction to repulsion, provided that its strength is small enough. This peculiarity finds a relevant explanation. The other model outlined in the review includes 1D, 2D, and 3D GPEs, with the septimal (seventh-order), quintic, and cubic self-repulsive terms, respectively. These equations give rise to stable singular solitons, which represent the GS for each dimension D, with the density singularity ~1/r^{2/(4-D). Such states may be considered as a result of screening of a bare delta-functional attractive potential by the respective nonlinearity.
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 chiral symmetric lattice with disordered gain and loss. The increasing disorder strength can drive a transition from trivial to topological insulators, characterizing by the change of topological winding number defined by localized states in the gapless and complex bulk spectra. The non-Hermitian critical behaviors are characterized by the biorthogonal localization length of zero energy edge modes, which diverges at the critical transition point and establishes the bulk-edge correspondence. Furthermore, we show that the bulk topology may be experimentally accessed by measuring the biorthogonal chiral displacement $mathcal{C}$, which converges to the winding number through time-averaging and can be extracted from proper Ramsey-interference sequences. We propose a scheme to implement and probe such non-Hermitian disorder driven topological insulators using photons in coupled micro-cavities.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
