Related papers: Topologically coupled energy bands in molecules
The Atiyah-Patodi-Singer(APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. The mathematical set-up for this theorem is, however, not directly related to the physical fermion…
Topological quantum chemistry (TQC) is a successful framework for identifying (noninteracting) topological materials. Based on the symmetry eigenvalues of Bloch eigenstates at maximal momenta, which are attainable from first principles…
Elementary band representations are the fundamental building blocks of atomic limit band structures. They have the defining property that at partial filling they cannot be both gapped and trivial. Here, we give two examples -- one each in a…
Although the richness of spatial symmetries has led to a rapidly expanding inventory of possible topological crystalline (TC) phases of electrons, physical realizations have been slow to materialize due to the practical difficulty to…
We report a detailed experimental study of the band structure of the recently discovered topological material $\textrm{Hf}_{2}\textrm{Te}_2\textrm{P}$. Using the combination of scanning tunneling spectroscopy and angle-resolved…
The electronic structure at the interface between a topological band insulator and a Mott insulator is studied within layer dynamical mean field theory. To represent the bulk phases of these systems, we use the generalized…
Topological physics opens up a plethora of exciting phenomena allowing to engineer disorder-robust unidirectional flows of light. Recent advances in topological protection of electromagnetic waves suggest that even richer functionalities…
Vector bundle cohomology represents a key ingredient for string phenomenology, being associated with the massless spectrum arising in string compactifications on smooth compact manifolds. Although standard algorithmic techniques exist for…
A topological phase can be engineered in quantum physics from the Bloch sphere of a spin-1/2 showing an hedgehog structure as a result of a radial magnetic field. We elaborate on a relation between the formation of an entangled wavefunction…
The screened electron-electron interaction in a multi-band electron system is calculated within the random phase approximation and in the tight-binding representation. The obtained dielectric matrix contains, beside the usual site-site…
A finit periodic $\delta-\delta'$ comb was solved by the help of both classical approach based on a direct solving of a Sr\"{odinger} equation and a quantum wave impedance method. It was demonstrated that the violation of a periodicity…
The topological nature of the Mott-Hubbard state in strongly correlated systems is treated. These systems are described in terms of spin-charge separation, i.e. spinon-holon deconfinement in the gauge field. Analogies with the quantum Hall…
Using topological band theory analysis we show that the nonsymmorphic symmetry operations in hexagonal lattices enforce Weyl points at the screw-invariant high-symmetry lines of the band structure. The corepresentation theory and…
We present a theoretical study of single-particle and many-body properties of twisted bilayer WSe$_2$. For single-particle physics, we calculate the band topological phase diagram and electron local density of states (LDOS), which are found…
We construct and characterize tight binding Hamiltonians which contain a completely flat topological band made of continuum lowest Landau level wavefunctions sampled on a lattice. We find an infinite family of such Hamiltonians, with simple…
Volkov-Pankratov surface bands arise in smooth topological interfaces, i.e. interfaces between a topological and a trivial insulator, in addition to the chiral surface state imposed by the bulk-surface correspondence of topological…
We calculate correlation functions of exactly-solvable one-dimensional flat-band models by utilizing the "molecular-orbital" representation. The models considered in this paper have a gapped ground state with flat-band being fully occupied,…
We review the Atiyah-Singer Index theorem and some applications. Only basic knowledge of differential geometry and Lie groups is required.
We propose a general principle for the low-energy theory of narrow bands with concentrated Berry curvature and Fubini-Study metric in the form of a map to Anderson-"+" models composed of heavy fermions hybridizing and interacting with…
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…