Related papers: Non-Commutative Geometry in Higher Dimensional Qua…
We show that the quantum anomalous Hall effect almost always occurs in magnetic topological insulator thin films whenever the top and bottom surface layer magnetizations are parallel, independent of the interior layer magnetization…
A three-dimensional (3D) topological insulator (TI) is a quantum state of matter with a gapped insulating bulk yet a conducting surface hosting topologically-protected gapless surface states. One of the most distinct electronic transport…
The quantized version of the anomalous Hall effect has been predicted to occur in magnetic topological insulators, but the experimental realization has been challenging. Here, we report the observation of the quantum anomalous Hall (QAH)…
We study a system of electrons moving on a noncommutative plane in the presence of an external magnetic field which is perpendicular to this plane. For generality we assume that the coordinates and the momenta are both noncommutative. We…
Topologically protected surface modes of classical waves hold the promise to enable a variety of applications ranging from robust transport of energy to reliable information processing networks. The integer quantum Hall effect has delivered…
The quantum anomalous Hall effect (QAHE) is a topological state of matter with a quantized Hall resistance. It has been observed in some two-dimensional insulating materials such as magnetic topological insulator films and twisted bilayer…
Quantum anomalous Hall (QAH) insulator is the key material to study emergent topological quantum effects, but its ultralow working temperature limits experiments. Here, by first-principles calculations, we find a family of stable…
Quantum anomalous Hall (QAH) insulator is a topological phase which exhibits chiral edge states in the absence of magnetic field. The celebrated Haldane model is the first example of QAH effect, but difficult to realize. Here, we predict…
The discovery of the quantum spin Hall effect and topological insulators more than a decade ago has revolutionized modern condensed matter physics. Today, the field of topological states of matter is one of the most active and fruitful…
We resolve several puzzles related to the electromagnetic response of topological superconductors in 3+1 dimensions. In particular we show by an analytical calculation that the interface between a topological and normal superconductor does…
The recent observations of nonlinear Hall effect in time-reversal symmetry protected systems and on the surface of three-dimensional topological insulators due to an in-plane magnetic field have attracted immense experimental and…
We investigate the Kondo effect in the two-dimensional electron system with a non-trivial quadratic energy band crossing point. We show that the Kondo effect can induce a new hybrid topological insulator phase which is a coexistence state…
We report transport studies of Mn-doped Bi2Te3 topological insulator (TI) films with accurately controlled thickness grown by molecular beam epitaxy. We find that films thicker than 5 quintuple-layer (QL) exhibit the usual anomalous Hall…
We study a general problem how the gap in a nonmagnetic band insulator closes by tuning a parameter. We review our recent results on the classification of all the possible gap closing in two and three dimensions. We show that they accompany…
Can a generic magnetic insulator exhibit a Hall current? The quantum anomalous Hall effect (QAHE) is one example of an insulating bulk carrying a quantized Hall conductivity and other insulators (with zero Chern number) present zero Hall…
We study three dimensional generalizations of the quantum spin Hall (QSH) effect. Unlike two dimensions, where the QSH effect is distinguished by a single $Z_2$ topological invariant, in three dimensions there are 4 invariants…
In this chapter, we report the recent progress in the understanding of the rich mathematical structures of topological insulators in the framework of index theory and noncommutative geometry.
The quantum anomalous Hall effect in magnetic topological insulators has been recognized as a promising platform for applications in quantum metrology. The primary reason for this is the electronic conductance quantization at zero external…
In recent attempts to observe axion electrodynamics, much effort has focused on trilayer heterostructures of magnetic topological insulators, and in particular on the examination of a so-called zero Hall plateau, which has misguidedly been…
Theintertwining of electron-hole correlation and nontrivial topology is known to give rise to exotic topological excitonic insulators. Here, we show that the involvement of quantum geometry can characterize more exotic excitonic phases…