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 …

The modern scope of fermiology encompasses not just the classical geometry of Fermi
surfaces but also the geometry of quantum wave functions over the Fermi surface. This …

We present a general methodology toward the systematic characterization of crystalline
topological insulating phases with time-reversal symmetry. In particular, taking the two …

In this work, we examine the topological phases that can arise in triangular lattices with
disconnected elementary band representations. We show that, although these phases may …

We present a framework to systematically address topological phases when finer
partitionings of bands are taken into account, rather than only considering the two …

We study the bulk and boundary properties of fragile topological insulators (TIs) protected by
inversion symmetry, mostly focusing on the class A of the Altland-Zirnbauer classification …

We study a two-dimensional tight-binding model of a topological crystalline insulator (TCI)
protected by rotation symmetry. The model is built by stacking two Chern insulators with …

We study the homotopy classification of symmetry representations to describe the bulk
topological invariants protected by the combined operation of a twofold rotation C 2 z and …

Establishing the fundamental relation between the homotopy invariants and the band
topology of Hamiltonians has played a critical role in the recent development of topological …

Being Wannierizable is not the end of the story for topological insulators. We introduce a
family of topological insulators that would be considered trivial in the paradigm set by the …