相关论文: Microscopic theory of Chern polarization via cryst…
Chern insulators present a topological obstruction to a smooth gauge in their Bloch wave functions that prevents the construction of exponentially-localized Wannier functions - this makes the electric polarization ill-defined. Here, we show…
Recently, it has been shown how topological phases of matter with crystalline symmetry and $U(1)$ charge conservation can be partially characterized by a set of many-body invariants, the discrete shift $\mathscr{S}_{\text{o}}$ and electric…
Recently, it has been established that Chern insulators possess an intrinsic two-dimensional electric polarization, despite having gapless edge states and non-localizable Wannier orbitals. This polarization, $\vec{P}_{\text{o}}$, can be…
We extend the Berry-phase concept of polarization to insulators having a non-zero value of the Chern invariant. The generalization to such Chern insulators requires special care because of the partial occupation of chiral edge states. We…
A feature of the "modern theory" is that electric polarization is not well-defined in a metallic ground state. A different approach invokes the general existence of a complete set of exponentially localized Wannier functions, with respect…
We derive macroscopic expressions for the polarization and orbital magnetization of a Chern insulator in its zero-temperature ground state using a previously developed formalism for treating microscopic polarization and magnetization fields…
Fractional Chern insulators (FCI) with crystalline symmetry possess topological invariants that fundamentally have no analog in continuum fractional quantum Hall (FQH) states. Here we demonstrate through numerical calculations on model wave…
The concept of the Zak phase lies at the core of the modern theory of electric polarization. It is defined using the components of the Bloch wave functions in a certain basis, which is not captured by the standard expression for Berry…
The construction of optimally localized Wannier functions (and Wannier functions in general) for a Chern insulator has been considered to be impossible owing to the fact that the second moment of such functions is generally infinite. In…
We derive the macroscopic charge and current densities of a Chern insulator initially occupying its electronic ground state as it responds to a finite-frequency electric field; we use a previously developed formalism based on microscopic…
Chern insulators are band insulators exhibiting a nonzero Hall conductance but preserving the lattice translational symmetry. We conclusively show that a partially filled Chern insulator at 1/3 filling exhibits a fractional quantum Hall…
In this paper, we derive a general formula for the quantized fractional corner charge in two-dimensional C_n-symmetric higher-order topological insulators. We assume that the electronic states can be described by the Wannier functions and…
A powerful result of topological band theory is that nontrivial phases manifest obstructions to constructing localized Wannier functions. In Chern insulators, it is impossible to construct Wannier functions that respect translational…
Robust fractional charge localized at disclination defects has been recently found as a topological response in $C_{6}$ symmetric 2D topological crystalline insulators (TCIs). In this article, we thoroughly investigate the fractional charge…
The bulk polarization is a $\mathbb{Z}_2$ topological invariant characterizing non-interacting systems in one dimension with chiral or particle-hole symmetries. We show that the bulk polarization can always be determined from the…
In insulators, the method of Marzari and Vanderbilt [Phys. Rev. B {\bf 56}, 12847 (1997)] can be used to generate maximally localized Wannier functions whose centers are related to the electronic polarization. In the case of layered…
Chern insulators are band insulators which exhibit a gap in the bulk and gapless excitations in the edge. Detection of Chern insulators is a serious challenge in cold atoms since the Hall transport measurements are technically unrealistic…
We examine the density-functional theory of macroscopic insulators, obtained in the large-cluster limit or under periodic boundary conditions. For polar crystals, we find that the two procedures are not equivalent. In a large-cluster case,…
We show that two-dimensional band insulators, with vanishing bulk polarization, obey bulk-and-edge to corner charge correspondence stating that the knowledge of the bulk and the two corresponding ribbon band structures uniquely determines…
The modern theory of polarization allows for the determination of the macroscopic end charge of a truncated one-dimensional insulator, modulo the charge quantum $e$, from a knowledge of bulk properties alone. A more subtle problem is the…