Related papers: Band Representations and Topological Quantum Chemi…
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…
Gapless surface states of time reversal invariant topological insulators are protected by the anti-unitary nature of the time reversal operation. Very recently, this idea was generalized to magnetic structures, in which time reversal…
We develop a framework to describe a wide class of flat-band models, with and without a translational symmetry, by using "molecular orbitals" introduced in the prior work (HATSUGAI Y. and MARUYAMA I., \textit{EPL}, \textbf{95}, (2011)…
The topological classification of gapped band structures depends on the particular definition of topological equivalence. For translation-invariant systems, stable equivalence is defined by a lack of restrictions on the numbers of occupied…
Strongly correlated analogues of topological insulators have been explored in systems with purely on-site symmetries, such as time-reversal or charge conservation. Here, we use recently developed tensor network tools to study a quantum…
We examine the interplay of symmetry and topological order in $2+1$ dimensional topological phases of matter. We present a definition of the \it topological symmetry \rm group, which characterizes the symmetry of the emergent topological…
In this review, We discussed the theoretical foundation and experimental discovery of different topological electronic states of material in condensed matter. At first, we briefly reviewed the conventional electronic states, which have been…
Complex band structure generalizes conventional band structure by also considering wavevectors with complex components. In this way, complex band structure describes both the bulk-propagating states from conventional band structure and the…
The method of the space dependent basis is applied to study electronic spinors in a crystal. The crystal in the momentum space is described by the Brillouine zone which might contains obstructions or degeneracies for which requires…
We characterize non-Hermitian band structures by symmetry indicator topological invariants. Enabled by crystalline inversion symmetry, these indicators allow us to short-cut the calculation of conventional non-Hermitian topological…
How do we uniquely identify a quantum phase, given its ground state wave-function? This is a key question for many body theory especially when we consider phases like topological insulators, that share the same symmetry but differ at the…
Although topological band theory has been used to discover and classify a wide array of novel topological phases in insulating and semi-metal systems, it is not well-suited to identifying topological phenomena in metallic or gapless…
The aim of the present survey paper is to provide an accessible introduction to a new chapter of representation theory - harmonic analysis for noncommutative groups with infinite-dimensional dual space. I omitted detailed proofs but tried…
The past years have seen rapid progress in the classification of topological materials. These diagnostical methods are increasingly getting explored in the pertinent context of magnetic structures. We report on a general class of electronic…
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 present comparatively simple two-dimensional and three-dimensional checkerboard-like optical lattices possessing nontrivial topological properties. By simple tuning of the parameters these lattices can have a topological insulating…
We construct Quantum Representation Theory which describes quantum analogue of representations in frame of "non-commutative linear geometry" developed by Manin. To do it we generalise the internal hom-functor to the case of adjunction with…
We develop and study a generalization of commutative rings called bands, along with the corresponding geometric theory of band schemes. Bands generalize both hyperrings, in the sense of Krasner, and partial fields in the sense of Semple and…
Topological superconductors are exotic phases of matter featuring robust surface states that could be leveraged for topological quantum computation. A useful guiding principle for the search of topological superconductors is to relate the…
We introduce a novel class of interaction-enabled topological crystalline insulators in two- and three-dimensional electronic systems, which we call "topological crystalline magnet." It is protected by the product of the time-reversal…