Tunable $\Gamma -K$ Valley Populations in Hole-Doped Trilayer WSe${}_2$

Abstract

We present a combined experimental and theoretical study of valley populations in the valence bands of trilayer WSe${}_2$. Shubnikov$-$de Haas oscillations show that trilayer holes populate two distinct subbands associated with the $K$ and $\Gamma$ valleys, with effective masses 0.5$m_e$ and $1.2m_e$, respectively; $m_e$ is the bare electron mass. At a fixed total hole density, an applied transverse electric field transfers holes from $\Gamma$ orbitals to $K$ orbitals. We are able to explain this behavior in terms of the larger layer polarizability of the $K$ orbital subband.

5 pages, 4 figures, includes supplementary material