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Topologically trivial insulators can be classified into atomic insulators (AIs) and obstructed atomic insulators (OAIs) depending on whether the Wannier charge centers are localized or not at spatial positions occupied by atoms. An OAI can…
Topological insulators are unique devices supporting unidirectional edge states at their interfaces. Due to topological protection, such edge states persist in the presence of disorder and do not experience backscattering upon interaction…
In this paper, we explore the localization features of wave functions in a family of mosaic quasiperiodic chains obtained by continuously interpolating between two limits: the mosaic Aubry-Andr\'{e} (AA) model, known for its exact mobility…
Spin-orbit (SO) coupling -- the interaction between a quantum particle's spin and its momentum -- is ubiquitous in nature, from atoms to solids. In condensed matter systems, SO coupling is crucial for the spin-Hall effect and topological…
The newly discovered topological crystalline insulators (TCIs) harbor a complex band structure involving multiple Dirac cones. These materials are potentially highly tunable by external electric field, temperature or strain and could find…
Band-topology is traditionally analyzed in terms of gauge-invariant observables associated with crystalline Bloch wavefunctions. Recent work has demonstrated that many of the free fermion topological characteristics survive even in an…
We investigate the possibility of realizing a disorder-induced topological Floquet spectrum in two-dimensional periodically-driven systems. Such a state would be a dynamical realization of the topological Anderson insulator. We establish…
As an exotic quantum condensed matter, the topological insulator (TI) is a bulk-insulating material with a Dirac-type conducting surface state. Such dissipationless transport of topological surface states (TSSs) is protected by the…
Electric circuits are known to realize topological quadrupole insulators. We explore electric circuits made of capacitors and inductors forming the breathing Kagome and pyrochlore lattices. They are known to possess three phases (trivial…
We investigate the possibility of using structural disorder to induce a topological phase in a solid state system. Using first-principles calculations, we introduce structural disorder in the trivial insulator BiTeI and observe the…
Most common types of symmetry breaking in quasi-one-dimensional electronic systems possess a combined manifold of states degenerate with respect to both the phase $\theta$ and the amplitude $A$ sign of the order parameter $A\exp(i\theta)$.…
Topological insulators (TIs) present a neoteric class of materials, which support delocalised, conducting surface states despite an insulating bulk. Due to their intriguing electronic properties, their optical properties have received…
Recent theories and experiments have suggested that strong spin-orbit coupling effects in certain band insulators can give rise to a new phase of quantum matter, the so-called topological insulator, which can show macroscopic entanglement…
In the binary-alloy with composition A$_x$B$_{1-x}$ of two atoms with ionic energy scales $\pm\Delta$, an apparent Ander- son insulator (AI) is obtained as a result of randomness in the position of atoms. Using our recently developed…
Recently, the structural disorder-induced topological phase transitions in periodic systems have attracted much attention. However, in aperiodic systems such as quasicrystalline systems, the interplay between structural disorder and band…
Topological insulators (TIs) have attracted much attention due to their spin-polarized surface and edge states, whose origin in symmetry gives them intriguing quantum-mechanical properties. Robust control over the chemical potential of TI…
An excitonic insulator (EI) is an unconventional quantum phase of matter in which excitons, bound pairs of electrons and holes, undergo Bose--Einstein condensation, forming a macroscopic coherent state. While its existence was first…
We report the discovery of several classes of novel topological insulators (TIs) with hybrid-order boundary states generated from the first-order TIs with additional crystalline symmetries. Unlike the current studies on hybrid-order TIs…
We study the Kondo effect induced by a topological soliton in a one-dimensional Dirac system with the sign-changing mass term. The soliton hosts a localized zero mode whose spatially extended wavefunction leads to a momentum-dependent…
We investigate the role of quantum fluctuations in topological quantum phase transitions of quantum spin Hall insulators and quantum anomalous Hall insulators. Employing the variational cluster approximation to obtain the single-particle…