Related papers: Excess charges as a probe of one-dimensional topol…
Topological phases of matter have garnered significant interest over the past two decades for two main reasons: their identification, via topological invariants, relies on the quantum geometry of the Bloch states, bringing attention to an…
This paper provides a pedagogical introduction to recent developments in geometrical and topological band theory following the discovery of graphene and topological insulators. Amusingly, many of these developments have a connection to…
In this article we extend the celebrated Berry-phase formulation of electric polarization in crystals to higher electric multipole moments. We determine the necessary conditions under which, and minimal models in which, the quadrupole and…
Although topological materials have recently seen tremendous development, their applications have remained elusive. Simultaneously, there exists considerable interest in pushing the limits of topological materials, including the exploration…
We introduce new classes of gapped topological phases characterized by quantized crystalline-electromagnetic responses, termed "multipolar Chern insulators". These systems are characterized by nonsymmorphic momentum-space symmetries and…
There is considerable evidence, based on large $N_c$ chiral dynamics, holographic QCD, and Monte Carlo studies, that the QCD vacuum is permeated by discrete quasivacua separated by domain walls across which the local value of the…
For a wide class of noninteracting tight-binding models in one dimension we present an analytical solution for all scattering and edge states on a half-infinite system. Without assuming any symmetry constraints we consider models with…
We propose a new theory to characterize equilibrium topological phase with non-equilibrium quantum dynamics by introducing the concept of high-order topological charges, with novel phenomena being predicted. Through a dimension reduction…
The quasiclassical dynamics is studied for charge carriers moving on the surface of 3D topological insulator of Bi2Te3 type and subjected to static magnetic field. The effects connected to the symmetry changes of electron isoenergetic…
Topological crystalline insulators (TCIs) can exhibit unique, quantized electric phenomena such as fractional electric polarization and boundary-localized fractional charge. This quantized fractional charge is the generic observable for…
We study the quantization of the excess charge on $N$ localized (ultra-screened) impurities in $d$-dimensional crystalline insulating systems. Solving Dyson's equation, we demonstrate that such charges are topological, by expressing them as…
We study single-channel continuum models of one-dimensional insulators induced by periodic potential modulations which are either terminated by a hard wall (the boundary model) or feature a single region of dislocations and/or impurity…
A (2+1)D topologically ordered phase may or may not have a gappable edge, even if its chiral central charge $c_-$ is vanishing. Recently, it is discovered that a quantity regarded as a "higher" version of chiral central charge gives a…
We study topological properties of one-dimensional nonlinear bichromatic superlattices and unveil the effect of nonlinearity on topological states. We find the existence of nontrivial edge solitions, which distribute on the boundaries of…
Topological photonics has received extensive attention from researchers because it provides brand new physical principles to manipulate light. Band topology of optical materials is characterized using the Berry phase defined by Bloch…
The interacting bosons in one-dimensional inversion-symmetric superlattices are investigated from the topological aspect. The complete phase diagram is obtained by an atomic-limit analysis and quantum Monte Carlo simulations and comprises…
Modern theory of electric polarization is formulated by the Berry phase, which, when quantized, leads to topological phases of matter. Such a formulation has recently been extended to higher electric multipole moments, through the discovery…
We predict novel topological phases with broken time-reversal symmetry supporting the coexistence of opposite chiral edge states, which are fundamentally different from the photonic spin-Hall, valley-Hall, and higher-order topological…
Most natural and artificial materials have crystalline structures from which abundant topological phases emerge [1-6]. The bulk-edge correspondence, widely-adopted in experiments to determine the band topology from edge properties, however,…
Crystalline symmetry can be used to predict bulk and surface properties of topological phases. For non-interacting cases, symmetry-eigenvalue analysis of Bloch states at high symmetry points in the Brillouin zone simplifies the calculation…