Topology of Band-Like Excitations in Frustrated Magnets and Their Experimental Signatures

One of the most important revolutions in physics during the latter half of the 20thcentury must surely be the introduction of topology. Beginning with the discovery of the integer quantum Hall effect, modern condensed matter theory has now dis-covered a new class of phases with unconventional transport properties. The theory of topologically non-trivial electronic bands in solids is now extremely well-studied. Questions of where similar physics may arise with magnetic excitations have there-fore also gained attention. Magnons and other pseudo-particle spin-excitations forma diverse cast with distinct properties that may be important in quantum metrology or even quantum logic tasks and simulation. In this thesis, we investigate the band-topology of such excitations and their experimental signatures. In our study of the bilayer kagome Heisenberg model we investigate the unconventional excitations of a quantum paramagnet. We show that the Z2 topological invariant known from the time-reversal invariant quantum spin Hall system of electrons makes an appearance here. These are comparable, but not analogous to Krämers pairs in electron transport, and they can be characterized in a similar fashion, but they do not enjoy the same symmetry protection under time-reversal due to their bosonic nature. We describe how bond-nematic terms appear which destroy the Z2 phase. We also study the monolayer spin-polarized kagome Heisenberg model. Our representation theory of the bands allows for the determination of degeneracies as well as interactions which give rise to non-trivial band-gaps. We show how one may associate certain features in the neutron scattering spectra with topological ex-citations. We show that pinch-points and half-moon features found ubiquitously in neutron scattering experiments will undergo characteristic distortions when those bands carry Chern numbers. Our work paves the way for a more systematic experimental characterization and treatment of topologically gapped magnetic excitations and motivates experimental investigation of the spin Nernst effect in for instance quantum dimer mate-rials, or possibly in certain ferro-quadrupolar ordered solids.Okinawa Institute of Science and Technology Graduate Universit