non-Abelian-topology

Universal higher-order bulk-boundary correspondence of triple nodal points

Triple nodal points are degeneracies of energy bands in momentum space at which three Hamiltonian eigenstates coalesce at a single eigenenergy. For spinless particles, the stability of a triple nodal point requires two ingredients: rotation symmetry …

Non-Abelian topology reveals a relation between triple points and nodal links

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.

From triple-point materials to multiband nodal links

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 …

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 …

Alice strings in non-Hermitian systems

An Alice string is a topological defect with a very peculiar feature. When a defect with a monopole charge encircles an Alice string, the monopole charge changes sign. In this paper, we generalize this notion to the momentum space of periodic media …

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” …

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 …