Related papers: Topology invisible to eigenvalues in obstructed at…
The vacuum of a band system, with respect to particles or holes, can become topologically nontrivial when the exceptional points of the non-hermitian Hamiltonian spread over the whole Brillouin zone. The coalescence of the eigenstates…
Energy bands of non-Hermitian crystalline systems are described in terms of the generalized Brillouin zone (GBZ) having unique features which are absent in Hermitian systems. In this paper, we show that in one-dimensional non-Hermitian…
Electronic bands in crystals are described by an ensemble of Bloch wave functions indexed by momenta defined in the first Brillouin Zone, and their associated energies. In an insulator, an energy gap around the chemical potential separates…
In this lecture for the Nobel symposium, we review previous research on a class of translational-invariant insulators without spin-orbit coupling. These may be realized in intrinsically spinless systems such as photonic crystals and…
The discovery of topological phases has ushered in a new era of condensed matter physics and revealed a variety of natural and artificial materials. They obey the bulk-boundary correspondence (BBC), which guarantees the emergence of…
We examine different topological phases in three-dimensional non-centrosymmetric superconductors with time-reversal symmetry by using three different types of topological invariants. Due to the bulk boundary correspondence, a non-zero value…
The multipartite non-Hermitian Su-Schrieffer-Heeger model is explored as a prototypical example of one-dimensional systems with several sublattice sites for unveiling intriguing insulating and metallic phases with no Hermitian counterparts.…
We study phase diagrams of charge-conserving `class A' non-interacting fermions, focusing on the trivial phase in various dimensions. Such phases are usually termed `featureless' to distinguish them from those others with either…
To date, almost all of the discussions on topological insulators (TIs) have focused on two- and three-dimensional systems. One-dimensional (1D) TIs manifested in real materials, in which localized spin states may exist at the end or near…
Topologically trivial insulators are classified into two primary categories: unobstructed and obstructed atomic insulators. While both types can be described by exponentially localized Wannier orbitals, a defining feature of obstructed…
We address the conditions required for a $\mathbb{Z}$ topological classification in the most general form of the non-Hermitian Su-Schrieffer-Heeger (SSH) model. Any chirally-symmetric SSH model will possess a "conjugated-pseudo-Hermiticity"…
The electronic properties in a solid depend on the specific form of the wave-functions that represent the electronic states in the Brillouin zone. Since the discovery of topological insulators, much attention has been paid to the…
By using a second quantized formulation of level crossing, which does not assume adiabatic approximation, a convenient formula for geometric terms including off-diagonal terms is derived. The analysis of geometric phases is reduced to a…
The quantum metric encodes the geometric structure of Bloch wave functions and governs a wide range of physical responses. Its Brillouin-zone integral, the quantum weight, appears in the structure factor and provides lower bounds on…
The discovery of novel topological phase advances our knowledge of nature and stimulates the development of applications. In non-Hermitian topological systems, the topology of band touching exceptional points is very important. Here we…
The integration of artificial intelligence (AI) into fundamental science has opened new possibilities to address long-standing scientific challenges rooted in mathematical limitations. For example, topological invariants are used to…
We show topological configurations of the complex-valued spectra in gapped non-Hermitian systems. These arise when the distinctive EPs in the energy Riemann sheets of such models are annihilated after threading them across the boundary of…
Topological crystalline phases in electronic structures can be generally classified using the spatial symmetry characters of the valence bands and mapping them onto appropriate symmetry indicators. These mappings have been recently applied…
In this article, we provide a pedagogical review of the theory of topological quantum chemistry and topological crystalline insulators. We begin with an overview of the properties of crystal symmetry groups in position and momentum space.…
We review the recent, mainly theoretical, progress in the study of topological nodal line semimetals in three dimensions. In these semimetals, the conduction and the valence bands cross each other along a one-dimensional curve in the…