We present a framework to systematically address topological phases when finer partitionings of bands are taken into account, rather than only considering the two subspaces spanned by valence and conduction bands. Focusing on …
Weyl semimetals in three-dimensional crystals provide the paradigm example of topologically protected band nodes. It is usually taken for granted that a pair of colliding Weyl points annihilate whenever they carry opposite chiral charge. In stark …
Nodal lines inside the momentum space of three-dimensional crystalline solids are topologically stabilized by a $\pi$-flux of Berry phase. Nodal-line rings in $\mathcal{PT}$-symmetric systems with negligible spin-orbit coupling (here described as …
We revisit the problem of classifying topological band structures in non-Hermitian systems. Recently, a solution has been proposed, which is based on redefining the notion of energy band gap in two different ways, leading to the so-called “point-gap” …
Topological semimetals are characterized by topologically protected band-structure nodes. One prominent example is the Weyl semimetal, characterized by Weyl points carrying topological Chern numbers. In this dissertation, we explore the topology of …
Weyl points in three spatial dimensions are characterized by a Z-valued charge—the Chern number—which makes them stable against a wide range of perturbations. A set of Weyl points can mutually annihilate only if their net charge vanishes, a property …
We show that the Nielsen-Ninomiya no-go theorem still holds on a Floquet lattice: there is an equal number of right-handed and left-handed Weyl points in a three-dimensional Floquet lattice. However, in the adiabatic limit, where the time evolution …
According to a widely held paradigm, a pair of Weyl points with opposite chirality mutually annihilate when brought together. In contrast, we show that such a process is strictly forbidden for Weyl points related by a mirror symmetry, provided that …
Weyl points in three spatial dimensions are characterized by a Z-valued charge—the Chern number—which makes them stable against a wide range of perturbations. A set of Weyl points can mutually annihilate only if their net charge vanishes, a property …
The band theory of solids is arguably the most successful theory of condensed-matter physics, providing a description of the electronic energy levels in various materials. Electronic wavefunctions obtained from the band theory enable a topological …