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We study the Dirac quasiparticles in $d$-dimensional lattice systems of electrons in the presence of domain walls ($d=1$), vortices ($d=2$), or hedgehogs ($d=3$) of superconducting and/or insulating, order parameters, which appear as mass…

Low energy excitation of surface states of a three-dimensional topological insulator (3DTI) can be described by Dirac fermions. By using a tight-binding model, the transport properties of the surface states in a uniform magnetic field is…

We predict pseudo topological insulators that have been previously overlooked. We determine some conditions under which robust pseudo topological edge states appear and illustrate our idea on the Su-Schrieffer-Heeger (SSH) model with extra…

Proximity-induced superconductivity in low-dimensional systems offers a powerful pathway to engineer topological superconducting phases in, otherwise, non-superconducting systems. These exotic phases are of fundamental and technological…

A wide class of materials that were discovered to carry a topologically protected phase order has led to a highly active area of research called topological insulators. This phenomenon has radically changed our thinking because of their…

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…

We investigate the topological phase derived by time-reversal breaking fields in a nonsymmorphic symmetry-protected two-dimensional Dirac semimetal. When the nonsymmorphic symmetry is preserved even in the presence of the field, the…

In investigating the topological electronic structures of monolayer $\alpha$-phase group V elements, we uncover a new topological phase, which is invisible in the symmetry-based topological quantum chemistry (TQC) as well as symmetry…

We investigate interacting Su-Schrieffer-Heeger (SSH) chains with two- and three-site unit cells using density matrix renormalization group (DMRG) simulations. By selecting appropriate filling fractions and sweeping across interaction…

Graphene is famous for being a host of 2D Dirac fermions. However, spin-orbit coupling introduces a small gap, so that graphene is formally a quantum spin hall insulator. Here we present symmetry-protected 2D Dirac semimetals, which feature…

We propose a new concept of two-dimensional (2D) Dirac semiconductor which is characterized by the emergence of fourfold degenerate band crossings near the band edge and provide a generic approach to realize this novel semiconductor in the…

Topological insulators are a novel state of matter that share a common feature: their spectral bands are associated with a nonlocal integer-valued index, commonly manifesting through quantized bulk phenomena and robust boundary effects. In…

Large-gap quantum spin Hall insulators are promising materials for room-temperature applications based on Dirac fermions. Key to engineer the topologically non-trivial band ordering and sizable band gaps is strong spin-orbit interaction.…

Quantum materials that host a flat band, such as pseudospin-1 lattices and magic-angle twisted bilayer graphene, can exhibit drastically new physical phenomena including unconventional superconductivity, orbital ferromagnetism, and Chern…

We identify the possibility of realizing higher order topological (HOT) phases in noncrystalline or amorphous materials. Starting from two and three dimensional crystalline HOT insulators, accommodating topological corner states, we…

Semi-Dirac materials in 2D present an anisotropic dispersion relation, linear along one direction and quadratic along the perpendicular one. This study explores the topological properties and the influence of disorder in a 2D semi-Dirac…

Discrete degrees of freedom, such as spin and orbital, can provide intriguing strategies to manipulate electrons, photons, and phonons. With a spin degree of freedom, topological insulators have stimulated intense interests in…

Topological insulators are transformative quantum solids with immune-to-disorder metallic surface states having Dirac band structure. Ubiquitous charged bulk defects, however, pull the Fermi energy into the bulk bands, denying access to…

A higher-order topological insulator is a new concept of topological states of matter, which is characterized by the emergent boundary states whose dimensionality is lower by more than two compared with that of the bulk, and draws a…

We study with first-principles methods the interplay between bulk and surface Dirac fermions in three dimensional Dirac semimetals. By combining density functional theory with the coherent potential approximation, we reveal a topological…