  Vibrations in materials and nanostructures at sufficiently high temperatures
result in anharmonic atomic displacements, which leads to new phenomena such as
thermal expansion and multiphonon scattering processes, with a profound impact
on temperature-dependent material properties including thermal conductivity,
phonon lifetimes, nonradiative electronic transitions, and phase transitions.
Nanoscale momentum-resolved vibrational spectroscopy, which has recently become
possible on monochromated scanning-transmission-electron microscopes, is a
unique method to probe the underpinnings of these phenomena. Here we report
momentum-resolved vibrational spectroscopy in hexagonal boron nitride at
temperatures of 300, 800, and 1300 K across three Brillouin zones (BZs) that
reveals temperature-dependent phonon energy shifts and demonstrates the
presence of strong Umklapp processes. Density-functional-theory calculations of
temperature-dependent phonon self-energies reproduce the observed energy shifts
and identify the contributing mechanisms.
