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While one of the most important and intriguing features of the topological insulators is the presence of edge states, the closed-form expressions for the edge states of some famous topological models are still lacking. Here, we focus on the…
The higher-order corner modes for quantum anomalous Hall insulators in $C_3$ symmetry broken honeycomb lattice have been engineered recently. Here we consider an extended Haldane model in presence of inversion symmetry breaking sub-lattice…
Twisted bilayer graphene offers a unique bilayer two-dimensional-electron system where the layer separation is only in sub-nanometer scale. Unlike Bernal-stacked bilayer, the layer degree of freedom is disentangled from spin and valley,…
In an ideal InAs/GaSb bilayer of appropriate dimension in-plane electron and hole bands overlap and hybridize, and a topologically non-trivial, or quantum spin Hall (QSH) insulator, phase is predicted to exist. The in-plane dispersion's…
Electron tunneling through a single magnetic barrier in a HgTe topological insulator has been theoretically investigated. We find that the perpendicular magnetic field would not lead to spin-flip of the edge states due to the conservation…
Recently, the topological classification of electronic states has been extended to a new class of matter known as topological crystalline insulators. Similar to topological insulators, topological crystalline insulators also have…
Topological insulators are well-known for their topological edge states, which are protected by the non-trivial bulk topology and characterized by gapless Wannier bands, a phenomenon known as the bulk-boundary correspondence. However,…
A study of spinless matter fermions coupled to a constrained $\mathbb{Z}_{2}$ lattice gauge theory on a triangular ladder is presented. The triangular unit cell and the ladder geometry strongly modify the physics, as compared to previous…
We present a new theoretical approach to the study of $\nu=1$ quantum Hall bilayer that is based on a systematic mapping of the microscopic Hamiltonian to an anisotropic SU(4) spin model on a lattice. To study the properties of this model…
Moir\'e superlattices have emerged as a premier platform for simulating the Hubbard model, yet achieving high tunability in square-lattice systems remains a key challenge. We demonstrate that $\Gamma$-valley twisted square homobilayers…
Inspired by recent discovery of correlated insulating states in twisted bilayer graphene (TBG), we study a two-orbital Hubbard model on the honeycomb lattice with two electrons per unit cell. Based on the real-space density matrix…
A simplified model of a metallic spin-type photonic topological insulator on a rhombic lattice is presented and analyzed. Instead of the more commonly used hexagonal unit cells, a reduced symmetry rhombus is employed, which is both simpler…
The coexistence of ferroelectric and topological orders in two-dimensional (2D) atomic crystals allows non-volatile and switchable quantum spin Hall states. Here we offer a general design principle for 2D bilayer heterostructures that can…
The interplay between topology and correlations can generate a variety of quantum phases, many of which remain to be explored. Recent advances have identified monolayer WTe2 as a promising material for doing so in a highly tunable fashion.…
We show how quasi-one-dimensional correlated insulating states arise at two-thirds filling in organometallic multinuclear coordination complexes described by layered decorated honeycomb lattices. The interplay of spin-orbit coupling and…
Based on a combination of $k \cdot p$ theory, band topology analysis and electronic structure calculations, we predict the (111) thin films of the SnTe class of three-dimensional (3D) topological crystalline insulators realize the quantum…
Recent discoveries have spurred the theoretical prediction and experimental realization of novel materials that have topological properties arising from band inversion. Such topological insulators are insulating in the bulk but have…
We report on the coexistence of both normal and topological insulating phases in InAs/GaSb bilayer quantum well induced by the built-in electric field tuned optically and electrically. The emergence of topological and normal insulating…
The quantum spin Hall insulator bismuthene, a two-third monolayer of bismuth on SiC(0001), is distinguished by helical metallic edge states that are protected by a groundbreaking 800 meV topological gap, making it ideal for room temperature…
We propose a two-orbital Hubbard model on an emergent honeycomb lattice to describe the low-energy physics of twisted bilayer graphene. Our model provides a theoretical basis for studying metal-insulator transition, Landau level degeneracy…