The concept of topological energy bands and their manifestations have been demonstrated
in condensed matter systems as a fantastic paradigm toward unprecedented physical …

Topological materials discovery has evolved at a rapid pace over the past 15 years following
the identification of the first nonmagnetic topological insulators (TIs), topological crystalline …

In the presence of crystalline symmetries, certain topological insulators present a filling
anomaly: a mismatch between the number of electrons in an energy band and the number of …

Higher-order phases are characterized by corner or hinge modes that arise due to the
interesting interplay of localization mechanisms along two or more dimensions. In this work …

We show that the Wannier obstruction and the fragile topology of the nearly flat bands in
twisted bilayer graphene at magic angle are manifestations of the nontrivial topology of two …

Higher-order topological insulators are newly proposed topological phases of matter, whose
bulk topology manifests as localized modes at two-or higher-dimensional lower boundaries …

Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the
surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points …

Higher-order topology yields intriguing multidimensional topological phenomena, while
Weyl semimetals have unconventional properties such as chiral anomaly. However, so far …

Current understanding of higher-order topological insulators (HOTIs) is based primarily on
crystalline materials. Here, we propose that HOTIs can be realized in quasicrystals …

We propose a general principle for constructing higher-order topological (HOT) phases. We
argue that if a D-dimensional first-order or regular topological phase involves m Hermitian …