Magnetic topological materials represent a class of compounds with properties that are
strongly influenced by the topology of their electronic wavefunctions coupled with the …

The quantum Hall (QH) effect, quantized Hall resistance combined with zero longitudinal
resistance, is the characteristic experimental fingerprint of Chern insulators—topologically …

Topological electronic materials, such as topological insulators, are distinct from trivial
materials in the topology of their electronic band structures that lead to robust …

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

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 …

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 …

Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic
excitations that are protected by topology and symmetry. As three-dimensional analogs of …

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 …

One of the intriguing properties characteristic to three-dimensional topological materials is
the topological magnetoelectric phenomena arising from a topological term called the θ …

The interplay between symmetry and topology leads to a rich variety of electronic topological
phases, protecting states such as the topological insulators and Dirac semimetals. Previous …