Integer quantum Hall effects of Q-valley electrons in transition metal disulfides

In few-layer transition metal disulfides (TMDs), the conduction bands along the GK directions shift downward energetically in the presence of interlayer interactions, forming six Q valleys related by threefold rotational symmetry and time reversal symmetry. In even layers the extra inversion symmetry requires all states to be spin degenerate, whereas in odd layers the intrinsic inversion asymmetry dictates the states to be non-degenerate at each valley. Universally, the 12-fold (6-fold) degenerate Landau levels in even (odd) layers undergo spin (valley) Zeeman splitting at relatively high magnetic fields, yielding 6-fold (3-fold) degenerate Landau levels. Our theoretical analyses are in complete harmony with our experimental observations of the Shubnikov-de Hass oscillations in high-mobility low-density TMD devices. [Reference: Nature Communications 7, 12955 (2016).]