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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 even-layer TMDC.(a–d) Quantum oscillations in 6L WS2. (a) Resistance R as a function of B field at + 50 V (orange line), +60 V (blue line) and +70 V (black line) gate voltages. The inset shows the sample image. (b) ΔR plotted as a function of 1/B field yields an oscillation period 1/BF. The filling factors are labelled for the oscillation valleys. A twelve-fold LL degeneracy at low fields and six-fold LL degeneracy at high fields is observed, caused by the spin Zeeman splitting within each valley. (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 ∼11.8±0.1. (d) LL filling factors as a function of 1/B for different gate voltages. The linear fit yields a zero Berry phase (the fitting results are in the range of −0.1 to+0.3 π) (e,f) Quantum oscillations in 6L MoS2. (e) R plotted as a function of B at the carrier density of 4.32 × 1012 cm−2 (f) ΔR curves plotted as a function of 1/B. The LL degeneracies derive from 12 at low-B fields to 6 at high-B fields. (g,h) Quantum oscillations of 10L WS2 show a LL degeneracy of 12. The negative magnetoresistance implies the existence of disorders, which might be the reason for the absence of the sixfold LLs at high-B fields.
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f3: Quantum oscillations in even-layer TMDC.(a–d) Quantum oscillations in 6L WS2. (a) Resistance R as a function of B field at + 50 V (orange line), +60 V (blue line) and +70 V (black line) gate voltages. The inset shows the sample image. (b) ΔR plotted as a function of 1/B field yields an oscillation period 1/BF. The filling factors are labelled for the oscillation valleys. A twelve-fold LL degeneracy at low fields and six-fold LL degeneracy at high fields is observed, caused by the spin Zeeman splitting within each valley. (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 ∼11.8±0.1. (d) LL filling factors as a function of 1/B for different gate voltages. The linear fit yields a zero Berry phase (the fitting results are in the range of −0.1 to+0.3 π) (e,f) Quantum oscillations in 6L MoS2. (e) R plotted as a function of B at the carrier density of 4.32 × 1012 cm−2 (f) ΔR curves plotted as a function of 1/B. The LL degeneracies derive from 12 at low-B fields to 6 at high-B fields. (g,h) Quantum oscillations of 10L WS2 show a LL degeneracy of 12. The negative magnetoresistance implies the existence of disorders, which might be the reason for the absence of the sixfold LLs at high-B fields.

Mentions: The SdH oscillations in the representative 6L WS2 device emerge when B field is greater than 2.5 T (Fig. 3a). Although the gate voltages applied (Vg=50–70 V) to the 6L WS2 device are similar to those applied (Vg=40, 60 and 70 V) to the 9L MoS2 device, the period of SdH oscillations appears twice larger in the 6L WS2 device (Fig. 3b). Given that the experimentally accessible carrier density is low, the Fermi energy crosses only the lowest spin-degenerate sub-band at the Q/Q' valleys in our calculated band structure of 6L WS2. The single sub-band nature is also evidenced by the unique period in the SdH oscillations (Fig. 3b). The linear fit of n versus BF/Φ0 (Fig. 3c) indicates a LL degeneracy of ∼11.8±0.1; the linear fit of the LL filling factors versus the SdH valley positions (Fig. 3d) yields a zero Berry phase. At a large field of 6.5 T, the secondary SdH valleys and doubling of the oscillation frequency are clearly visible because of the spin Zeeman splitting of LL duodectets into LL sextets (see Supplementary Fig. 4). The disappearance of secondary SdH valleys at around 10 K further indicates that the Lande factor is gL∼2.2 (Supplementary Table 1). Under similar experimental conditions, the presence of SdH valleys, as a result of the complete filling of a LL duodectet or sextet, has been repeatedly observed; for example, in a 6L MoS2 device (g=12/6 at low-/high-B fields in Fig. 3e,f), in a 10L WS2 device (g=12 in Fig. 3g,h) and in a 10L MoS2 (g=6 in Supplementary Fig. 5). Clearly, in contrast to odd-layer MoS2 devices (for example, 3L and 9L MoS2), even-layer MoS2 devices exhibit doubled LL degeneracies (see for example the data of 6L MoS2 in Fig. 3). We note that a tilted magnetic field will be helpful to further exploration of the TMDC QH effect and better determination of the physical parameters.


Even – odd layer-dependent magnetotransport of high-mobility Q-valley electrons in transition metal disulfides
Quantum oscillations in even-layer TMDC.(a–d) Quantum oscillations in 6L WS2. (a) Resistance R as a function of B field at + 50 V (orange line), +60 V (blue line) and +70 V (black line) gate voltages. The inset shows the sample image. (b) ΔR plotted as a function of 1/B field yields an oscillation period 1/BF. The filling factors are labelled for the oscillation valleys. A twelve-fold LL degeneracy at low fields and six-fold LL degeneracy at high fields is observed, caused by the spin Zeeman splitting within each valley. (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 ∼11.8±0.1. (d) LL filling factors as a function of 1/B for different gate voltages. The linear fit yields a zero Berry phase (the fitting results are in the range of −0.1 to+0.3 π) (e,f) Quantum oscillations in 6L MoS2. (e) R plotted as a function of B at the carrier density of 4.32 × 1012 cm−2 (f) ΔR curves plotted as a function of 1/B. The LL degeneracies derive from 12 at low-B fields to 6 at high-B fields. (g,h) Quantum oscillations of 10L WS2 show a LL degeneracy of 12. The negative magnetoresistance implies the existence of disorders, which might be the reason for the absence of the sixfold LLs at high-B fields.
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f3: Quantum oscillations in even-layer TMDC.(a–d) Quantum oscillations in 6L WS2. (a) Resistance R as a function of B field at + 50 V (orange line), +60 V (blue line) and +70 V (black line) gate voltages. The inset shows the sample image. (b) ΔR plotted as a function of 1/B field yields an oscillation period 1/BF. The filling factors are labelled for the oscillation valleys. A twelve-fold LL degeneracy at low fields and six-fold LL degeneracy at high fields is observed, caused by the spin Zeeman splitting within each valley. (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 ∼11.8±0.1. (d) LL filling factors as a function of 1/B for different gate voltages. The linear fit yields a zero Berry phase (the fitting results are in the range of −0.1 to+0.3 π) (e,f) Quantum oscillations in 6L MoS2. (e) R plotted as a function of B at the carrier density of 4.32 × 1012 cm−2 (f) ΔR curves plotted as a function of 1/B. The LL degeneracies derive from 12 at low-B fields to 6 at high-B fields. (g,h) Quantum oscillations of 10L WS2 show a LL degeneracy of 12. The negative magnetoresistance implies the existence of disorders, which might be the reason for the absence of the sixfold LLs at high-B fields.
Mentions: The SdH oscillations in the representative 6L WS2 device emerge when B field is greater than 2.5 T (Fig. 3a). Although the gate voltages applied (Vg=50–70 V) to the 6L WS2 device are similar to those applied (Vg=40, 60 and 70 V) to the 9L MoS2 device, the period of SdH oscillations appears twice larger in the 6L WS2 device (Fig. 3b). Given that the experimentally accessible carrier density is low, the Fermi energy crosses only the lowest spin-degenerate sub-band at the Q/Q' valleys in our calculated band structure of 6L WS2. The single sub-band nature is also evidenced by the unique period in the SdH oscillations (Fig. 3b). The linear fit of n versus BF/Φ0 (Fig. 3c) indicates a LL degeneracy of ∼11.8±0.1; the linear fit of the LL filling factors versus the SdH valley positions (Fig. 3d) yields a zero Berry phase. At a large field of 6.5 T, the secondary SdH valleys and doubling of the oscillation frequency are clearly visible because of the spin Zeeman splitting of LL duodectets into LL sextets (see Supplementary Fig. 4). The disappearance of secondary SdH valleys at around 10 K further indicates that the Lande factor is gL∼2.2 (Supplementary Table 1). Under similar experimental conditions, the presence of SdH valleys, as a result of the complete filling of a LL duodectet or sextet, has been repeatedly observed; for example, in a 6L MoS2 device (g=12/6 at low-/high-B fields in Fig. 3e,f), in a 10L WS2 device (g=12 in Fig. 3g,h) and in a 10L MoS2 (g=6 in Supplementary Fig. 5). Clearly, in contrast to odd-layer MoS2 devices (for example, 3L and 9L MoS2), even-layer MoS2 devices exhibit doubled LL degeneracies (see for example the data of 6L MoS2 in Fig. 3). We note that a tilted magnetic field will be helpful to further exploration of the TMDC QH effect and better determination of the physical parameters.

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