We extend the theory of dipole moments in crystalline insulators to higher multipole
moments. As first formulated in Benalcazar et al.[Science 357, 61 (2017) SCIEAS 0036-8075 …

Since the discovery of topological insulators and semimetals, there has been much research
into predicting and experimentally discovering distinct classes of these materials, in which …

The intense theoretical and experimental interest in topological insulators and semimetals
has established band structure topology as a fundamental material property. Consequently …

In a flat band superconductor, bosonic excitations can disperse while unpaired electrons are
immobile. To study this strongly interacting system, we construct a family of multi-band …

In a partially filled flat Bloch band electrons do not have a well defined Fermi surface and
hence the low-energy theory is not a Fermi liquid. Nevertheless, under the influence of an …

Understanding the relationship between quantum geometry and topological invariants is a
central problem in the study of topological states. In this work, we establish the relationship …

The topological phases of two-dimensional time-reversal symmetric insulators are classified
by a Z 2 topological invariant. Usually, the invariant is introduced and calculated by …

The fundamental building blocks in band theory are band representations—bands whose
infinitely numbered Wannier functions are generated (by action of a space group) from a …

Abstract Time Reversal Symmetry (TRS) broken topological phases provide gapless surface
states protected by topology, regardless of additional internal symmetries, spin or valley …

We provide a constructive proof of exponentially localized Wannier functions and related
Bloch frames in 1-and 2-dimensional time-reversal symmetric (TRS) topological insulators …