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Topological transport is determined by global properties of physical media where it occurs and is characterized by quantized amounts of adiabatically transported quantities. Discovered for periodic potentials it was also explored in…
The abstract notion of topology has led to profound insights into real materials. Notably, the surface and edges of topological materials can host physics, such as unidirectional charge or spin transport, that is unavailable in isolated…
In flat-band systems, destructive interference leads to the localization of non-interacting particles and forbids their motion through the lattice. However, in the presence of interactions the overlap between neighbouring single-particle…
Hopf insulators are intriguing three-dimensional topological insulators characterized by an integer topological invariant. They originate from the mathematical theory of Hopf fibration and epitomize the deep connection between knot theory…
Presence of entangled states is explicitly shown in Topological insulator (TI) $Bi_2Te_3$. The surface and bulk state are found to have the different structures of entanglement. The surface states live as maximally entangled states in the…
We study one-dimensional topological models with dimerization and trimerization and show that these models can be generated using interaction or optical superlattice. The topological properties of these models are demonstrated by the…
Based on a quasi-one-dimensional limit of quantum Hall states on a thin torus, we construct a model of interaction-induced topological pumping which mimics the Hall response of the bosonic integer quantum Hall (BIQH) state. The…
We consider ferromagnetic instabilities of two-dimensional helical Dirac fermions hosted on the surface of three-dimensional topological insulators. We investigate ways to increase the role of interactions by means of modifying the bulk…
The vertical, tip-to-tip arrangement of neighboring caudal fins, common in densely packed fish schools, has received much less attention than staggered or side-by-side pairings. We explore this configuration using a canonical system of two…
The Thouless theory of quantum pumps establishes the conditions for quantized particle transport per cycle, and determines its value. When describing the pump from a moving reference frame, transported and existing charges transform, though…
We study the topological properties of quantum states for the spinless particle hopping in a Mobius ladder. This system can be regarded as a molecular device possibly engineered from the aromatic Mobius annulenes, which enjoys a pseudo-spin…
Our understanding of topological insulators is based on an underlying crystalline lattice where the local electronic degrees of freedom at different sites hybridize with each other in ways that produce nontrivial band topology, and the…
We design an interaction-driven topological insulator for fermionic cold atoms in an optical lattice, that is, we pose the question of whether we can realize in a continuous space a spontaneous symmetry breaking induced by the inter-atom…
We study the scattering theory of delicate topological insulators (TIs), which are novel topological phases beyond the paradigm of the tenfold way, topological quantum chemistry, and the symmetry indicator method. We demonstrate that the…
The transport of energy through 1-dimensional (1D) waveguiding channels can be affected by sub-wavelength disorder, resulting in undesirable localization and backscattering phenomena. However, quantized disorder-resilient transport is…
There are two prominent applications of the mathematical concept of topology to the physics of materials: band topology, which classifies different topological insulators and semimetals, and topological defects that represent immutable…
We investigate whether there could exist topological invariants of gapped 2D materials related to dissipationless thermoelectric transport at low temperatures. We give both macroscopic and microscopic arguments showing that thermoelectric…
In Thouless pumping, although non-flat band has no effects on the quantization of particle transport, it induces wave-packet dispersion which hinders the practical applications of Thouless pumping. Indeed, we find that the dispersion mainly…
Topological insulators are noninteracting, gapped fermionic systems which have gapless boundary excitations. They are characterized by topological invariants, which can be written in many different ways, including in terms of Green's…
Using Cluster Perturbation Theory we calculate Green's functions, quasi-particle energies and topological invariants for interacting electrons on a 2-D honeycomb lattice, with intrinsic spin-orbit coupling and on-site e-e interaction. This…