相关论文: Quadrupole moments, edge polarizations, and corner…

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…

A formula for the corner charge in terms of the bulk quadrupole moment is derived for two-dimensional periodic systems. This is an analog of the formula for the surface charge density in terms of the bulk polarization. In the presence of an…

We analyze a special separable and chiral-symmetric model with a quantized quadrupole moment, extending the Benalcazar-Bernevig-Hughes model [Science 357, 61 (2017)]. Using nested-Wilson loop formalism, we give an exact expression for…

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…

The modern theory of charge polarization in solids is based on a generalization of Berry's phase. Its possible quantization lies at the heart of our understanding of all systems with topological band structures that were discovered over the…

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…

Topological invariants are a significant ingredient in the study of topological phases of matter that intertwines the supposedly contradicting concepts of bulk and boundary. The nature of the invariants differ depending on the dimension of…

Quadrupole topological phases, exhibiting protected boundary states that are themselves topological insulators of lower dimensions, have recently been of great interest. Extensions of these ideas from current tight binding models to…

We show that topological defects in quadrupole insulators do not host quantized fractional charges, contrary to what their Wannier representation indicates. In particular, we test the charge quantization hypothesis based on the Wannier…

Thanks to the nearsightedness principle, the low-energy electronic structure of solids can be represented by localized states such as the Wannier functions. Wannier functions are actively being applied to a wide range of phenomena in…

We study two-dimensional spinful insulating phases of matter that are protected by time-reversal and crystalline symmetries. To characterize these phases we employ the concept of corner charge fractionalization: Corners can carry charges…

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…

Higher-order topological insulators host gapless states on hinges or corners of three-dimensional crystals. Recent studies suggested that even topologically trivial insulators may exhibit fractionally quantized charges localized at hinges…

We describe a method to calculate the electronic properties of an insulator under an applied electric field. It is based on the minimization of an electric enthalpy functional with respect to the orbitals, which behave as Wannier functions…

Two-dimensional higher-order topological insulators can display a number of exotic phenomena such as half-integer charges localized at corners or disclination defects. In this paper, we analyze these phenomena, focusing on the paradigmatic…

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…

Measuring bipartite fluctuations of a conserved charge, such as the particle number, is a powerful approach to understanding quantum systems. When the measured region has sharp corners, the bipartite fluctuation receives an additional…

We consider the problem of constructing Wannier functions for Z_2 topological insulators in two dimensions. It is well known that there is a topological obstruction to the construction of Wannier functions for Chern insulators, but it has…

Higher-order topological insulators in two spatial dimensions display fractional corner charges. While fractional charges in one dimension are known to be captured by a many-body bulk invariant, computed by the Resta formula, a many-body…

Working in the Wannier representation, we derive an expression for the orbital magnetization of a periodic insulator. The magnetization is shown to be comprised of two contributions, an obvious one associated with the internal circulation…