相关论文: Asymmetric real topology of conduction and valence…
Band topology of materials describes the extent Bloch wavefunctions are twisted in momentum space. Such descriptions rely on a set of topological invariants, generally referred to as topological charges, which form a characteristic class in…
In this article, we review the recent progress in the study of topological phases in systems with space-time inversion symmetry $I_{\text{ST}}$. $I_{\text{ST}}$ is an anti-unitary symmetry which is local in momentum space and satisfies…
Symmetry-protected topological phases have been a central theme in condensed matter physics and beyond over the past two decades. Most efforts have focused on topological classifications of physical systems under given symmetries, while the…
The use of topological invariants to describe geometric phases of quantum matter has become an essential tool in modern solid state physics. The first instance of this paradigmatic trend can be traced to the study of the quantum Hall…
The study of topological property of band insulators is an interesting branch of condensed matter physics. Two types of topologically nontrivial insulators have been extensively studied. The first type is characterized by a nonzero TKNN…
We study the topological band theory of time reversal invariant topological insulators and interpret the topological $\mathbb{Z}_2$ invariant as an obstruction in terms of Stiefel--Whitney classes. The band structure of a topological…
The interplay between symmetry and topology in electronic band structures has been one of the central subjects in condensed-matter physics. Recently, it has been getting clear that a wide variety of useful information about the band…
Sixty years ago, Karplus and Luttinger pointed out that quantum particles moving on a lattice could acquire an anomalous transverse velocity in response to a force, providing an explanation for the unusual Hall effect in ferromagnetic…
The study of topology of energy bands in solid has always been interesting and fruitful. Historically, Thouless et al proposed the TKNN number or Chern number of the energy bands to explain the quantization of Hall conductance in the…
The main aim of this article is to study the topology of real Bott towers as special and interesting examples of real toric varieties. We first give a presentation of the fundamental group of a real Bott tower and show that the fundamental…
This paper provides a mathematical perspective on fragile topology phenomena in condensed matter physics. In dimension $d \leq 3$, vanishing Chern classes of bundles of Bloch eigenfunctions characterize operators with exponentially…
Topological band theory establishes a standardized framework for classifying different types of topological matters. Recent investigations have shown that hyperbolic lattices in non-Euclidean space can also be characterized by hyperbolic…
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…
The ground state of translationally-invariant insulators comprise bands which can assume topologically distinct structures. There are few known examples where this distinction is enforced by a point-group symmetry alone. In this paper we…
We study translationally-invariant insulators with inversion symmetry that fall outside the established classification of topological insulators. These insulators are not required to have gapless boundary modes in the energy spectrum.…
Topological phase transitions are typically characterized by abrupt changes in a quantized invariant. Here we report a contrasting paradigm in non-Hermitian parity-time symmetric systems, where the topological invariant remains conserved,…
Weyl semimetals have been theoretically predicted to become topological metals with anomalous Hall conductivity in amorphous systems. However, measuring the anomalous Hall conductivity in realistic materials, particularly those with…
We study amorphous systems with completely random sites and find that, through constructing and exploring a concrete model Hamiltonian, such a system can host an exotic phase of topological amorphous metal in three dimensions. In contrast…
Real band topology often appears in systems with space-time inversion symmetry and is characterized by invariants such as the Euler and second Stiefel-Whitney classes. Here, we examine the generic band topology of Bogoliubov de-Gennes (BdG)…
Topological invariants in band theory are often formulated assuming that Bloch wave functions are smoothly defined over the Brillouin zone (BZ). However, first-principles band calculations typically provide Bloch states only at discrete…