Detection of hole pockets in the candidate type-II Weyl semimetal MoTe$_2$ from Shubnikov-de Haas quantum oscillations

The bulk electronic structure of $T_d$-MoTe$_2$ features large hole Fermi pockets at the Brillouin zone center ($\Gamma$) and two electron Fermi surfaces along the $\Gamma-X$ direction. However, the large hole pockets, whose existence has important implications for the Weyl physics of $T_d$-MoTe$_2$, has never been conclusively detected in quantum oscillations. This raises doubt about the realizability of Majorana states in $T_d$-MoTe$_2$, because these exotic states rely on the existence of Weyl points, which originated from the same band structure predicted by density functional theory (DFT). Here, we report an unambiguous detection of these elusive hole pockets via Shubnikov-de Haas (SdH) quantum oscillations. At ambient pressure, the quantum oscillation frequencies for these pockets are 988 T and 1513 T, when the magnetic field is applied along the $c$-axis. The quasiparticle effective masses $m^*$ associated with these frequencies are 1.50 $m_e$ and 2.77 $m_e$, respectively, indicating the importance of Coulomb interactions in this system. We further measure the SdH oscillations under pressure. At 13 kbar, we detected a peak at 1798 T with $m^*$ = 2.86 $m_e$. Relative to the oscillation data at a lower pressure, the amplitude of this peak experienced an enhancement, which can be attributed to the reduced curvature of the hole pockets under pressure. Combining our experimental data with DFT + $U$ calculations, where $U$ is the Hubbard parameter, our results shed light on why these important hole pockets have not been detected until now.