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One of the most striking features of quantum mechanics is the appearance of phases of matter with topological origins. These phases result in remarkably robust macroscopic phenomena such as the edge modes in integer quantum Hall systems,…
For a disordered two-dimensional model of a topological insulator (such as a Kane-Mele model with disordered potential) with small coupling of spin invariance breaking term (such as the Rashba coupling), it is proved that the spin edge…
Motivated by surprises in recent experimental findings, we study transport in a model of a quantum Hall edge system with a gate-voltage controlled constriction. A finite backscattered current at finite edge-bias is explained from a…
The quantum Hall effect was originally observed in a two-dimensional electron gas forming Landau levels when exposed to a strong perpendicular magnetic field and was later generalized to Chern insulators without net magnetization. Here,…
Topologically nontrivial band structure of a material may give rise to special states that are confined to the material's boundary and protected against disorder and scattering. Quantum spin Hall effect (QSHE) is a paradigmatic example of…
We addressed quantization phenomena in transport and vortex/precession-motion of low-dimensional systems, stationary quantization of confined motion in phase space due to oscillatory dynamics or compacti fication of space and time for…
We generalize the idea of the quantized Hall current to count gapless edge states in topological materials, applying equally well to theories in different dimensions, with or without continuous symmetries in the bulk or chiral anomalies on…
The discovery of robust transport via topological states in electronic, photonic and phononic materials has deepened our understanding of wave propagation in condensed matter with prospects for critical applications of engineered…
Based on very general arguments we show that for any geometry of the experiment, in the regime when the measurement leads to a quantized Hall conductivity, almost the entire current injected into the sample is carried by the bulk states.…
Time-dependent perturbations can drive a trivial two-dimensional band insulator into a quantum Hall-like phase, with protected nonequilibrium states bound to its edges. We propose an experiment to probe the existence of these topological…
The twin discoveries of the quantum Hall effect, in the 1980's, and of topological band insulators, in the 2000's, were landmarks in physics that enriched our view of the electronic properties of solids. In a nutshell, these discoveries…
The beauty of quantum Hall (QH) effect is the metrological precision of Hall resistance quantization that originates from the topological edge states. Understanding the factors that lead to quantization breakdown not only provides important…
The quantization of transport and its resilience to backscattering are key features for leveraging topological matter in applications that demand stringent noise mitigation, such as metrology and quantum information processing. Due to the…
The thermal Hall effect has emerged as a fundamental tool for probing exotic quasiparticles and topological order, particularly in magnetic insulators where electronic conduction is suppressed. Much like skyrmions, which are characterized…
As a new quantum state, topological insulators have become the focus of condensed matter and material science. The open system research of topological insulators has aroused the interest of many researchers. Recently, many aspects,…
The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Recently, a new class of topological insulators has been proposed. These topological insulators have an insulating gap in…
We provide a characterization of tunneling between coupled topological insulators in 2D and 3D under the influence of a ferromagnetic layer. We explore conditions for such systems to exhibit integer quantum Hall physics and localized…
Topology provides an essential concept for achieving unchanged (or protected) quantum properties in the presence of perturbations. A challenge facing realistic applications is that the level of protection displayed in real systems is…
Confinement of small-gapped fractional quantum Hall states facilitates quasiparticle manipulation and is an important step towards quasiparticle interference measurements. Demonstrated here is conduction through top gate defined, narrow…
The quantum Hall effect is a remarkable manifestation of quantized transport in a two-dimensional electron gas. Given its technological relevance, it is important to understand its development in realistic nanoscale devices. In this work we…