Topological materials have become the focus of intense research in recent years, since they
exhibit fundamentally new physical phenomena with potential applications for novel devices …

In this review, we discuss recent progress in the explorations of topological materials
beyond topological insulators; specifically, we focus on topological crystalline insulators and …

The discoveries of intrinsically magnetic topological materials, including semimetals with a
large anomalous Hall effect and axion insulators,–, have directed fundamental research in …

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 …

We present a method for efficiently enumerating all allowed, topologically distinct, electronic
band structures within a given crystal structure in all physically relevant dimensions. The …

We propose MnBi 2 n Te 3 n+ 1 as a magnetically tunable platform for realizing various
symmetry-protected higher-order topology. Its canted antiferromagnetic phase can host …

We theoretically study three-dimensional topological semimetals (TSMs) with nodal lines
protected by crystalline symmetries. Compared to TSMs with point nodes, eg, Weyl …

Spatial symmetries in crystals may be distinguished by whether they preserve the spatial
origin. Here we study spatial symmetries that translate the origin by a fraction of the lattice …

We complete a classification of topological phases and their topological defects in crystalline
insulators and superconductors. We consider topological phases and defects described by …

The link between chemical orbitals described by local degrees of freedom and band theory,
which is defined in momentum space, was proposed by Zak several decades ago for …