Electron band structures, which describe the energy-momentum relation for electrons in solids, can exhibit robust crossings called "nodes". Such nodes famously occur in graphene or in Weyl semimetals, and often facilitate special transport phenomena, such as the decrease of resistivity of Weyl semimetals in applied parallel magnetic field.
We study a class of topological materials which in their momentum-space band structure exhibit threefold degeneracies known as triple points. Focusing specifically on $\mathcal{PT}$-symmetric crystalline solids with negligible spin-orbit coupling, we …
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 …