band-theory

Geometric approach to fragile topology beyond symmetry indicators

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 …

Non-Abelian reciprocal braiding of Weyl nodes and its manifestations in ZrTe

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 …

Non-Abelian topology of nodal-line rings in $\mathcal{PT}$-symmetric systems

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 …

Homotopy characterization of non-Hermitian Hamiltonians

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” …

Conversion and braiding rules of band-structure nodes

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 …

Non-Abelian band topology in noninteracting metals

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 …

Three-dimensional chiral lattice fermion in Floquet systems

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 …

Conversion rules for Weyl points and nodal lines in topological media

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 …

Robust doubly charged nodal lines and nodal surfaces in centrosymmetric systems

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 …

Nodal-chain metals

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 …