Related papers: Quantized Electric Multipole Insulators
The modern theory of electric polarization in crystals associates the dipole moment of an insulator with a Berry phase of its electronic ground state [1, 2]. This concept constituted a breakthrough that not only solved the long-standing…
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 extend the theory of dipole moments in crystalline insulators to higher multipole moments. In this paper, we expand in great detail the theory presented in Ref. 1, and extend it to cover associated topological pumping phenomena, and a…
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…
Recent theoretical studies have extended the Berry phase framework to account for higher electric multipole moments, quadrupole and octupole topological phases have been proposed. Although the two-dimensional quantized quadrupole insulators…
The Berry phase associated with energy bands in crystals can lead to quantized quantities, such as the quantization of electric dipole polarization in an insulator, known as a one-dimensional (1D) topological insulator (TI) phase. Recent…
Recently extended from the modern theory of electric polarization, quantized multipole topological insulators (QMTIs) describe higher-order multipole moments, lying in nested Wilson loops, which are inherently quantized by lattice…
Quadrupole topological insulators are a new class of topological insulators with quantized quadrupole moments, which support protected gapless corner states. The experimental demonstrations of quadrupole-topological insulators were reported…
The topological phases of matter are characterized using the Berry phase, a geometrical phase, associated with the energy-momentum band structure. The quantization of the Berry phase, and the associated wavefunction polarization, manifest…
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…
Quantized electric quadrupole insulators have recently been proposed as novel quantum states of matter in two spatial dimensions. Gapped otherwise, they can feature zero-dimensional topological corner mid-gap states protected by the bulk…
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 study the orbital magnetic quadrupole moment (MQM) in three dimensional higher-order topological phases. Much like electric quadrupole moment, which is associated with a charge response on the boundaries of a finite sample, the diagonal…
The modern theory of electric polarization has recently been extended to higher multipole moments, such as quadrupole and octupole moments. The higher electric multipole insulators are essentially topological crystalline phases protected by…
We investigate disorder-driven topological phase transitions in quantized electric quadrupole insulators. We show that chiral symmetry can protect the quantization of the quadrupole moment $q_{xy}$, such that the higher-order topological…
Conventional topological insulators support boundary states that have one dimension lower than the bulk system that hosts them, and these states are topologically protected due to quantized bulk dipole moments. Recently, higher-order…
Quantized bulk quadrupole moment has unveiled a nontrivial boundary state, exhibiting lower-dimensional topological edge states and simultaneously hosting the in-gap corner modes of zero dimension. All state-of-the-art strategies for…
We propose the entanglement dipole polarization to describe the topological quadrupole phase. The quadrupole moment can be regarded as a pair of the dipole moment, in which the total dipole moment is canceled. The entanglement polarization,…
When the crystalline symmetries that protect a higher-order topological phase are not preserved at the boundaries of the sample, gapless hinge modes or in-gap corner states cannot be stabilized. Therefore, careful engineering of the sample…
Higher-order topological insulators are a new class of topological phases of matter, originally conceived for electrons in solids. It has been suggested that $\mathbb{Z}_N$ Berry phase (Berry phase quantized into $2\pi/N$) is a useful tool…