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When interacting spins in condensed matter order ferromagnetically, their ground state wave function is topologically trivial. Nonetheless, in two dimensions, the ferromagnetic state can support spin excitations with nontrivial topology, an…
Topological insulators have been extended to higher-order versions that possess topological hinge or corner states in lower dimensions. However, their robustness against disorder is still unclear. Here, we theoretically investigate the…
A Chern metal is a two-dimensional metallic state of matter carrying chiral edge states. It can emerge as a doped Chern insulator, but theoretical studies have also predicted its emergence near a Kondo breakdown separating a metallic chiral…
We develop a unified view of topological phase transitions (TPTs) in solids by revising the classical band theory with the inclusion of topology. Re-evaluating the band evolution from an "atomic crystal" [a normal insulator (NI)] to a solid…
Three dimensional topological insulator crystals consist of an insulating bulk enclosed by metallic surfaces, and detailed theoretical predictions about the surface state band topology and spin texture are available. While several…
Symmetry plays a key role in classifying topological phases. Recent theory shows that in the presence of gauge fields, the algebraic structure of crystalline symmetries needs to be projectively represented, which enables unprecedented…
Topological insulators (TIs) and topological crystalline insulators (TCIs) are materials with unconventional electronic properties, making their discovery highly valuable for practical applications. However, such materials, particularly…
We propose searching for Chern insulators by depositing atomic layers of elements with large spin-orbit coupling (e.g., Bi) on the surface of a magnetic insulator. We argue that such systems will typically have isolated surface bands with…
Topological insulators are substances which are bulk insulators but which carry current via special "topologically protected" edge states. The understanding of long range topological order in these systems is built around the idea of a…
Granular conductors form an artificially engineered class of solid state materials wherein the microstructure can be tuned to mimic a wide range of otherwise inaccessible physical systems. At the same time, topological insulators (TIs) have…
Two-dimensional (2D) magnetic materials with nontrivial topological states have drawn considerable attention recently. Among them, 2D metal-organic frameworks (MOFs) are standing out due to their advantages, such as the easy synthesis in…
Bound electron-hole pairs in semiconductors known as excitons can form a coherent state at low temperatures akin to a BCS condensate. The resulting phase is known as the excitonic insulator and has superfluid properties. Here we…
Topological crystalline insulators (TCIs) are classified by topological invariants defined with respect to the crystalline symmetries of their gapped bulk. The bulk-boundary correspondence then links the topological properties of the bulk…
Topological materials host fascinating low dimensional gapless states at the boundary. As a prominent example, helical topological edge states (TESs) of two-dimensional topological insulators (2DTIs) and their stacked three-dimensional (3D)…
The higher order topological insulator (HOTI) has enticed enormous research interests owing to its novelty in supporting gapless states along the hinges of the crystal. Despite several theoretical predictions, enough experimental…
Chern insulators are band insulators which exhibit a gap in the bulk and gapless excitations in the edge. Detection of Chern insulators is a serious challenge in cold atoms since the Hall transport measurements are technically unrealistic…
The recent discovery of topological insulator (TI) offers new opportunities for the development of thermoelectrics, because many TIs (like Bi$_2$Te$_3$) are excellent thermoelectric (TE) materials. In this review, we will first describe the…
Non-Hermitian topology provides a research frontier for exploring topological phenomena, revealing novel topological effects and driving the development of emergent materials and platforms. Here, we explore the non-Hermitian Chern insulator…
We study the effect of electron-electron interactions in a spinful Chern insulator. For weak on-site repulsive interactions at half-filling, the system is a weakly correlated Chern insulator adiabatically connected to the noninteracting…
Electronic topological phases of matter, characterized by robust boundary states derived from topologically nontrivial bulk states, are pivotal for next-generation electronic devices. However, understanding their complex quantum phases,…