The Berry phase provides a modern formulation of electric polarization in crystals. We
extend this concept to higher electric multipole moments and determine the necessary …

The theory of electric polarization in crystals defines the dipole moment of an insulator in
terms of a Berry phase (geometric phase) associated with its electronic ground state,. This …

Recent theoretical studies have extended the Berry phase framework to account for higher
electric multipole moments; quadrupole and octupole topological phases have been …

Higher-order topological insulators are a new class of topological phases of matter,
originally conceived for electrons in solids. It has been suggested that the ZN Berry phase …

We investigate disorder-driven topological phase transitions in quantized electric
quadrupole insulators in two dimensions. We show that chiral symmetry can protect the …

The modern theory of charge polarization in solids, is based on a generalization of Berry's
phase. The possibility of the quantization of this phase, arising from parallel transport in …

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 …

Berry phase associated with energy bands in crystals can lead to quantised observables like
quantised dipole polarizations in one-dimensional topological insulators. Recent theories …

Topological multipole insulators are a class of higher-order topological insulators (HOTIs) in
which robust fractional corner charges appear due to a quantized electric multipole moment …

Spectral measurements of boundary-localized topological modes are commonly used to
identify topological insulators. For high-order insulators, these modes appear at boundaries …