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A peculiar feature of the majority of three dimensional topological insulator surface states studied experimentally thus far, namely their particle-hole asymmetry, makes quantum oscillations (Shubnikov de Haas and de Haas van Alphen…
We consider the combined effect of a gap and a Zeeman interaction on the helical Dirac fermions which exist on the surface of a topological insulator. Magneto-optical properties, the magnetization, Hall effect and the density of states are…
We reconsider the problem of surface states spectrum in type One Dirac metals. We find that the surface states, despite being gapped, always form branches terminating at Dirac points. Furthermore, we consider evolution of the surface states…
We discuss the Chern number spectrum of ultra-cold fermions in square optical lattices as a function of artificial magnetic, Zeeman and spin-orbit fields that can be tuned independently. We show the existence of topological quantum phase…
The surface of a topological insulator is a closed two dimensional manifold. The surface states are described by the Dirac Hamiltonian in curved two dimensional spaces. For a slab-like sample with a magnetic field perpendicular to its top…
We study the quantum Hall effect in the surface states of topological insulator in the presence of a perpendicular magnetic field in the framework of edge states. Motion of Dirac fermions will form descrete Landau levels, among which a…
Quantum anomalous Hall (QAH) insulators are two-dimensional (2D) insulating states exhibiting properties similar to those of quantum Hall states but without external magnetic field. They have quantized Hall conductance $\sigma^H=Ce^2/h$,…
A quantum anomalous Hall state with high Chern number has so far been realized in multiplayer structures consisting of alternating magnetic and undoped topological insulator layers. However, in previous proposals, the Chern number can be…
Chern insulator phase is shown to emerge in two-dimensional arrays of polariton rings where time-reversal symmetry is broken due to the application of an out-of-plane magnetic field. The interplay of Zeeman splitting with the photonic…
Here we study the systematic evolution of the topological properties of a Chern insulator in presence of an electronic dispersion that can be tuned smoothly from being Dirac-like till a semi-Dirac one and beyond. The band structure under…
We investigate how a magnetic field induces one-dimensional edge channels when the two-dimensional surface states of three-dimensional topological insulators become gapped. The Hall effect, measured by contacting those channels, remains…
We derive the diagram of the topological phases accessible within a generic Hamiltonian describing quantum anomalous Hall effect for photons and electrons in honeycomb lattices in presence of a Zeeman field and Spin-Orbit Coupling (SOC).…
Starting from a minimal model for a 2D nodal loop semimetal, we study the effect of chiral mass gap terms. The resulting Dirac loop anomalous Hall insulator's Chern number is the phase winding number of the mass gap terms on the loop. We…
We study the interaction between a ferromagnetically ordered medium and the surface states of a topological insulator with a general surface termination. This interaction is strongly crystal face dependent and can generate chiral states…
Periodically driven systems can host so called anomalous topological phases, in which protected boundary states coexist with topologically trivial Floquet bulk bands. We introduce an anomalous version of reflection symmetry protected…
The quantum anomalous Hall effect is a intriguing topological nontrivial phase arising from spontaneous magnetization and spin-orbit coupling. However, the tremendously harsh realizing requirements of the quantum anomalous Hall effects in…
The surface of a three-dimensional topological electron system often hosts symmetry-protected gapless surface states. With the effect of electron interactions, these surface states can be gapped out without symmetry breaking by a surface…
We study the quantum Hall effect of Dirac fermions on the surface of a Wilson-Dirac type topological insulator thin film in the strong topological insulating phase. Although a magnetic field breaks time reversal symmetry of the bulk, the…
Different from the two-dimensional (2D) topological insulator, the 2D topological crystalline insulator (TCI) phase disappears when the mirror symmetry is broken, e.g., upon placing on a substrate. Here, based on a new family of 2D TCIs -…
Topological insulators lacking time-reversal symmetry can exhibit the quantum anomalous Hall effect. Odd-layer thick MnBi$_2$Te$_4$ is a promising platform due to its intrinsic magnetic nature, however, quantization is rarely observed in…