  Layered van-der-Waals materials with hexagonal symmetry offer an extra degree
of freedom to their electrons, the so called valley index or valley pseudospin.
This quantity behaves conceptually like the electron spin and the term
valleytronics has been coined. In this context, the group of semiconducting
transition-metal dichalcogenides (TMDC) are particularly appealing, due to
large spin-orbit interactions and a direct bandgap at the K points of the
hexagonal Brillouin zone. In this work, we present investigations of excitonic
transitions in mono- and multilayer WSe$_2$ and MoSe$_2$ materials by
time-resolved Faraday ellipticity (TRFE) with in-plane magnetic fields,
$B_{\parallel}$, of up to 9 T. In monolayer samples, the measured TRFE time
traces are almost independent of $B_{\parallel}$, which confirms a close to
zero in-plane exciton $g$ factor $g_\parallel$, consistent with
first-principles calculations. In stark contrast, we observe pronounced
temporal oscillations in multilayer samples for $B_{\parallel}>0$. Remarkably,
the extracted in-plane $g_\parallel$ are very close to reported out-of-plane
exciton $g$ factors of the materials, namely $|g_{\parallel 1s}|=3.1\pm 0.2$
and $2.5\pm0.2$ for the 1s A excitons in WSe$_2$ and MoSe$_2$ multilayers,
respectively. Our first-principles calculations nicely confirm the presence of
a non-zero $g_{\parallel}$ for the multilayer samples. We propose that the
oscillatory TRFE signal in the multilayer samples is caused by pseudospin
quantum beats of excitons, which is a manifestation of spin- and pseudospin
layer locking in the multilayer samples. Our results demonstrate ultrafast
pseudospin rotations in the GHz- to THz frequency range, which pave the way
towards ultrafast pseudospin manipulation in multilayer TMDC samples.

Mesoscale and Nanoscale Physics