Topological Phonons in Graphite
Around 500°C (67 meV), lattice fluctuations propagating through the hexagonal carbon layers of graphite share some properties with relativistic particles of quantum electrodynamics.
Congratulations to Nikita Andriushin, first author of our new paper “Phonon Topology and Winding of Spectral Weight in Graphite”, Phys. Rev. Lett. 131, 246601 (2023)!
Carbon monolayers, known as graphene, are well known for their special electronic properties. The origin of these effects lies in the hexagonal atomic structure, which crystallographers perceive as two trigonal sublattices. Electronic states associated with either sublattice cannot hybridize, which leads to linear band crossings at certain points in momentum space. The dynamics of the charge carriers around these points topologically resemble the behaviour of massless “Dirac” fermions of quantum electrodynamics.
Since these consequences of the hexagonal structure do not depend on quantum statistics, they do not only affect fermionic degrees of freedom. Indeed, dispersive lattice fluctuations (phonons) in graphene show similar linear band crossings. Given their bosonic character, the unusual dispersion of these excitations will, in general, not dominate physical properties - but is already inspiring exciting new concepts in the design and manipulation of acoustic waves.
In this study, we used inelastic x-ray scattering (IXS) and electronic structure calculations to investigate the phonon topology, not of graphene but of graphite, its familiar three-dimensional analogue.
Left: On a closed loop around a phonon (pseudo-) Dirac point in momentum space, the structure factor of lattice fluctuations shows a characteristic sinusoidal modulation. Right: This encodes the phase differences by which atoms of the two carbon sublattices (red/blue) are displaced out-of-plane. These observations are necessary consequences, but do not a direct measure of the topological character of the band-crossing.
Using the ID28 spectrometer at the European Synchrotron Radiation Facility (ESRF), we carefully mapped the intensities of phonon excitations around a Dirac-like band crossing around 67 meV. Since a weak van-der-Waals coupling between the graphene sheets breaks the inversion symmetry of the honeycomb layers, the “Dirac-like points” in graphite must necessarily be gapped.
Nevertheless, measurements and simulations show that the structure factor still resembles what had previously been considered proof of non-trivial topology. As such, our main finding is an important “caveat”: Modulations in x-ray (or neutron) scattering intensities that have been taken as a direct measure of phonon (or magnon) topological winding numbers may, in fact, survive even if the material is, like graphite, not strictly topological.
