band-theory

Emerging avenues in band theory: multigap topology and hyperbolic lattices

One of the cornerstones of condensed matter physics, the description of wave functions on periodic lattices in terms of energy bands of Bloch states, serves as the unifying thread in this thesis. This description is often referred to as band theory. …

Triple nodal points characterized by their nodal-line structure in all magnetic space groups

We analyze triply degenerate nodal points [or triple points (TPs) for short] in energy bands of crystalline solids. Specifically, we focus on spinless band structures, i.e., when spin-orbit coupling is negligible, and consider TPs formed along …

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 …

Delicate topology protected by rotation symmetry: Crystalline Hopf insulators and beyond

Pontrjagin's seminal topological classification of two-band Hamiltonians in three momentum dimensions is hereby enriched with the inclusion of a crystallographic rotational symmetry. The enrichment is attributed to a new topological invariant which …

Delicate topological insulators: a new world of phases between trivial and fragile

Topological band theory studies the behavior of non-interacting electrons in solids that is protected by topological invariants and is therefore robust against system perturbations. Among many topics that are important for characterizing topological …

Exceptional Topological Insulators

We introduce the exceptional topological insulator (ETI), a non-Hermitian topological state of matter that features exotic non-Hermitian surface states which can only exist within the three-dimensional topological bulk embedding. We show how this …

Theorists discover new paradigm of topological band structures

After the experimental discovery of topological insulators, the notion of what actually constitutes a topological band insulator has been refined in many ways. In their recent work, Aleksandra Nelson, Titus Neupert, Tomáš Bzdušek and Aris Alexandradinata extend the paradigm of topological insulators to areas which were previously thought to contain only trivial insulators.

Multicellularity of delicate topological insulators

Being Wannierizable is not the end of the story for topological insulators. We introduce a family of topological insulators that would be considered trivial in the paradigm set by the tenfold way, topological quantum chemistry, and the method of …

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 …