The recent discover of Weyl semimetals has shown that topological effects can play a significant role in the behavior of gapless systems. However, correlation effects in known Weyl semimetals did not seem to play a significant role in most materials. Here I will show that the charge density wave compound (TaSe_2)_4I is a Weyl semimetal with strong correlations due to electron-phonon coupling. I will show how the topological charge of the Weyl nodes leaves its mark on the behavior of the collective phase mode of the charge density wave, which was verified in nonlinear transport experiments. Taking inspiration from this system, I will explore how charge-density wave order in Weyl and Dirac systems can lead to new realizations of higher-order topological phases through a series of simple examples. I will argue that the sliding mode in topological charge-density wave materials offers a new experimental avenue to probe the response of these systems.
Recordings of Condensed Matter Seminar events can be found on mediaspace: https://mediaspace.illinois.edu/channel/Condensed%2BMatter%2BSeminar%2BTalks%2BFall%2B2020/178724052
