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The theory of topological insulators and superconductors has mostly focused on non-interacting and gapped systems. This review article discusses topological phases that are either gapless or interacting. We discuss recent progress in…
Recently, a new class of second-order topological insulators (SOTIs) characterized by an electronic dipole has been theoretically introduced and proposed to host topological corner states. As a novel topological state, it has been…
As a promising candidate system to realize topological superconductivity, the system of a 3D topological insulator (TI) grown on top of the s-wave superconductor has been extensively studied. To access the topological superconductivity…
We demonstrate that the terahertz/infrared radiation induced photogalvanic effect, which is sensitive to the surface symmetry and scattering details, can be applied to study the high frequency conductivity of the surface states in…
There has been considerable interest in exploiting the spin degrees of freedom of electrons for potential information storage and computing technologies. Topological insulators (TI), a class of quantum materials, have special gapless…
Substituting magnetic ions with nonmagnetic ions is a new way to study dilution. Using determinant quantum Monte Carlo calculations, we investigate an interacting Dirac fermion model with the on-site Coulomb repulsion being randomly zero on…
Correlated transition metal oxides present exciting prospects as switches or memory and storage devices owing to the possibility to control electronic properties using various external stimuli. While their complex behaviour is known to stem…
Two-dimensional (2D) topological insulator (TI) have been recognized as a new class of quantum state of matter. They are distinguished from normal 2D insulators with their nontrivial band-structure topology identified by the $Z_2$ number as…
Topological insulators (TIs) are characterized by an insulating bulk and symmetry protected bound state on their boundaries. A "strong" topological insulator is characterized by robust conducting states on \emph{all} boundaries protected by…
Topological insulators and semimetals as well as unconventional iron-based superconductors have attracted major recent attention in condensed matter physics. Previously, however, little overlap has been identified between these two vibrant…
Strong nonmagnetic impurities on the surface of three-dimensional topological insulators (TIs) generate localized resonance peaks close to the Dirac point. We show that this results in a strongly reduced critical Coulomb interaction…
The three-dimensional (3D) topological insulator is a novel quantum state of matter where an insulating bulk hosts a linearly-dispersing surface state, which can be viewed as a sea of massless Dirac fermions protected by the time-reversal…
The surface state of a three-dimensional topological insulator forms a two-dimensional massless Dirac electron system. In Dirac electron systems, Coulomb interaction is not screened due to the small density of states at the Fermi energy and…
Topological states may be protected by a lattice symmetry in a class of topological semi-metals. In three spatial dimensions, the Berry flux around gapless excitations in momentum space defines a chirality concretely, so a protecting…
Magnetically doped topological insulators (TIs) exhibit two distinct phases: the quantum anomalous Hall (QAH) phase when the Fermi level resides within the surface gap, and a metallic phase outside the gap. The QAH phase hosts…
Topological insulators (TIs) constitute a new class of materials with unique properties resulting from the relativistic-like character and topological protection of their surface states. Theory predicts these to exhibit a rich variety of…
Two-dimensional (2D) topological insulators (TIs), a new state of quantum matter, are promising for achieving the low-power-consuming electronic devices owning to the remarkable robustness of their conducting edge states against…
Motivated by recent studies which show that topological phases may emerge in strongly correlated electron systems, we theoretically study the strong electron correlation effect in a three-dimensional topological insulator, which effective…
Surface states refer to electronic states emerging as a solid material terminates at a surface, and can be present in many systems. Despite their spatial proximity to material surfaces, surface states have been largely overlooked in…
The interplay between topology and interactions on the edge of a two dimensional topological insulator with time reversal symmetry is studied. We consider a simple non-interacting system of three helical channels with an inherent…