Figure 2: Quantum oscillations in odd-layer TMDCs.
(a – d) Quantum oscillations in 9L MoS2. (a) Resistance R as a function of B field at + 40 V (orange line), +60 V (blue line) and +70 V (black line) gate voltages. The inset shows the sample image. (b) After subtracting the baselines of R ∼ B curves in a, ΔR curves plotted as a function of 1/B yields an oscillation period 1/BF, which decreases with increasing gate voltages. The filling factors are labelled for the oscillations valleys. The degeneracy of 6 arises from the degeneracy between the 3 Q and 3 Q’ valleys; the spin degeneracy within each Q or Q’ valley is already lifted by the broken inversion symmetry. At relatively high magnetic fields, an LL sextet can be lifted into two LL triplets caused by the valley Zeeman effect. (c) The total carrier density n obtained from the Hall measurements as a function of BF/Φ0 (black dots) for different gate voltages. The best fit (red line) indicates a LL degeneracy of ∼3.0±0.1. (d) LL filling factors as a function of 1/B at different gate voltages. The linear fit yields a zero berry phase. (e,f) Quantum oscillations in 3L WS2. (e) R plotted as a function of B at the carrier density of 7.5 × 1012 cm−2 (f) ΔR curves plotted as a function of 1/B. The LL degeneracy evolves from 6 at low-B fields to 3 at high-B fields. (g) The onset of QH states in 3L MoS2. Magnetoresistance resistance R (blue line) and Hall resistance Rxy (orange line) as a function of B field at 2 K. The QH states are shown by at least three almost quantized plateaus in Rxy at ν=36, 39 and 42.
