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Even – odd layer-dependent magnetotransport of high-mobility Q-valley electrons in transition metal disulfides

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ABSTRACT

In few-layer transition metal dichalcogenides (TMDCs), the conduction bands along the ΓK 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 Kramers degenerate; whereas in odd layers, the intrinsic inversion asymmetry dictates the Q valleys to be spin-valley coupled. Here we report the transport characterization of prominent Shubnikov-de Hass (SdH) oscillations and the observation of the onset of quantum Hall plateaus for the Q-valley electrons in few-layer TMDCs. Universally in the SdH oscillations, we observe a valley Zeeman effect in all odd-layer TMDC devices and a spin Zeeman effect in all even-layer TMDC devices, which provide a crucial information for understanding the unique properties of multi-valley band structures of few-layer TMDCs.

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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.
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f2: 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.

Mentions: In the representative 9L MoS2 device, the Shubnikov-de Hass (SdH) oscillations in the longitudinal resistance R appear at perpendicular magnetic fields B>4 T (Fig. 2a). This property is the hallmark of the high quality and homogeneity of our BN-MoS2-BN devices. Pronounced SdH oscillations are observed at relatively high gate voltages, where μH is sufficiently high. Quantitatively, at the low magnetic field range, the SdH oscillations in the longitudinal resistance R of a single sub-band in two-dimensional electron gas can be described by the Lifshitz–Kosevich formula29:


Even – odd layer-dependent magnetotransport of high-mobility Q-valley electrons in transition metal disulfides
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.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5036047&req=5

f2: 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.
Mentions: In the representative 9L MoS2 device, the Shubnikov-de Hass (SdH) oscillations in the longitudinal resistance R appear at perpendicular magnetic fields B>4 T (Fig. 2a). This property is the hallmark of the high quality and homogeneity of our BN-MoS2-BN devices. Pronounced SdH oscillations are observed at relatively high gate voltages, where μH is sufficiently high. Quantitatively, at the low magnetic field range, the SdH oscillations in the longitudinal resistance R of a single sub-band in two-dimensional electron gas can be described by the Lifshitz–Kosevich formula29:

View Article: PubMed Central - PubMed

ABSTRACT

In few-layer transition metal dichalcogenides (TMDCs), the conduction bands along the ΓK 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 Kramers degenerate; whereas in odd layers, the intrinsic inversion asymmetry dictates the Q valleys to be spin-valley coupled. Here we report the transport characterization of prominent Shubnikov-de Hass (SdH) oscillations and the observation of the onset of quantum Hall plateaus for the Q-valley electrons in few-layer TMDCs. Universally in the SdH oscillations, we observe a valley Zeeman effect in all odd-layer TMDC devices and a spin Zeeman effect in all even-layer TMDC devices, which provide a crucial information for understanding the unique properties of multi-valley band structures of few-layer TMDCs.

No MeSH data available.


Related in: MedlinePlus