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Link to original content: https://pubmed.ncbi.nlm.nih.gov/30723283
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. 2019 Feb 5;10(1):611.
doi: 10.1038/s41467-019-08629-9.

Intrinsic valley Hall transport in atomically thin MoS2

Zefei Wu  1 , Benjamin T Zhou  2 , Xiangbin Cai  2 , Patrick Cheung  3 , Gui-Bin Liu  4 , Meizhen Huang  2 , Jiangxiazi Lin  2 , Tianyi Han  2 , Liheng An  2 , Yuanwei Wang  2 , Shuigang Xu  2 , Gen Long  2 , Chun Cheng  5 , Kam Tuen Law  2 , Fan Zhang  6 , Ning Wang  7
Affiliations

Intrinsic valley Hall transport in atomically thin MoS2

Zefei Wu et al. Nat Commun. .

Abstract

Electrons hopping in two-dimensional honeycomb lattices possess a valley degree of freedom in addition to charge and spin. In the absence of inversion symmetry, these systems were predicted to exhibit opposite Hall effects for electrons from different valleys. Such valley Hall effects have been achieved only by extrinsic means, such as substrate coupling, dual gating, and light illuminating. Here we report the first observation of intrinsic valley Hall transport without any extrinsic symmetry breaking in the non-centrosymmetric monolayer and trilayer MoS2, evidenced by considerable nonlocal resistance that scales cubically with local resistance. Such a hallmark survives even at room temperature with a valley diffusion length at micron scale. By contrast, no valley Hall signal is observed in the centrosymmetric bilayer MoS2. Our work elucidates the topological origin of valley Hall effects and marks a significant step towards the purely electrical control of valley degree of freedom in topological valleytronics.

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Conflict of interest statement

The authors declare no competing interests.

Figures

Fig. 1
Fig. 1
Valley Hall transport induced nonlocal resistance in monolayer MoS2. a Top view and side view of the crystal structure of 2H-MoS2; an odd- (even-) layer is inversion asymmetric (symmetric). b Schematic of the h-BN encapsulated MoS2 field-effect transistor. c High-resolution bright-field STEM image showing details of the edge-contacted monolayer MoS2 device structure (scale bar 10 nm). The expanded region shows that the BN-MoS2-BN interface is pristine and free of impurities down to the atomic scale (scale bar 3 nm). d Schematic of the nonlocal resistance measurement and the VHE-mediated nonlocal transport. The applied charge current in the left circuit generates a pure valley current in the transverse direction via a VHE. This valley current induces opposite chemical potential gradients for the two valleys over the inter-valley scattering length, which, in turn, generates a voltage drop measured by probes 3 and 4 in the right circuit via an inverse VHE. e Nonlocal resistance RNL (upper panel) and the classical ohmic contribution RCL (lower panel) as functions of gate voltage Vg at varied temperatures. Inset: optical image of a typical monolayer MoS2 device (scale bar 2 μm). A MoS2 Hall bar is sandwiched between the top and bottom h-BN flakes
Fig. 2
Fig. 2
Local and nonlocal resistances of monolayer MoS2. a, b Semilog plots of RL and RNL as a function of Vg measured at varied temperatures. Inset of b: optical micrograph of our typical h-BN/MoS2/h-BN device with multi-terminal Hall Bar configurations. Scale bar: 5 μm. c Scaling relations between ln RL and ln RNL at Vg ranging from −50 V to −60 V. When the electron density is relatively high, i.e., RL and RNL are small, RNL is linearly proportional to RL. When the electron density is relatively low, a crossover from linear to cubic scaling is observed. The critical density nc = 4 × 1011 cm−2, with the gate voltage Vg = −57 V. d Crossover phenomenon by considering classical diffusion (RNL ∝ RL) and valley Hall transport (RNL ∝ RL3). The experimental data (solid circles, Vg = −60 V) clearly show two different regimes which are fitted by two linear curves (orange dashed line with slope 1 and blue dashed line with slope 3). The critical temperature is around 160 K~200 K, as marked by the blue arrow. e RNL plotted as a function of Vg at low temperatures. The ohmic contribution, calculated according to RL and device geometry, is deducted from the measured RNL at different temperatures. f 1/RNL (orange circles) and 1/RL (blue circles) in log scale plotted as functions of 1/T at Vg = −60 V. Three distinct transport regimes were observed: the thermal activation (TA) transport, nearest neighbor hopping (NNH) transport, and the variable range hopping (VRH) transport. g Semilog plot of RNL as a function of L at n = 2 × 1011 cm−2 (orange squares). Nonlocal signal decays exponentially with increasing L. The dashed line yields a valley diffusion length of ∼1 μm
Fig. 3
Fig. 3
Local and nonlocal resistances of bilayer and trilayer MoS2. a, b, e, f Gate-dependence of RL and RNL at different temperatures in bilayer a, b and trilayer e, f samples. c, g Scaling relation between ln RL and ln RNL is obtained at different temperatures in bilayer c and trilayer g samples. For the trilayer case, RNL scales linearly with RL in the high electron density regime, whereas the cubic scaling law RNL ∝ RL3 is observed in the low electron density regime (nc = 4 × 1011 cm−2 or Vg = −18.4 V). d lnRL v.s. lnRNL for bilayer MoS2. In the full range of gate voltages, RNL scales linearly with RL, and the experimental data (black dots, Vg = −60 V) is fitted by a linear curve (red solid line). h lnRL v.s. lnRNL for trilayer MoS2. The experimental data (black dots, Vg = −20 V) clearly show two different regimes which are fitted by two linear curves (red solid line with slope 1 and blue solid line with slope 3). Evidently, a crossover exists from linear (RNL ∝ RL) to cubic scaling behaviors (RNL ∝ RL3)
Fig. 4
Fig. 4
Band structures and Berry curvatures of atomically thin MoS2. a–c Band structure of (a) monolayer, (b) bilayer, and (c) trilayer MoS2. The conduction band edges lie at the K-valleys in the monolayer but at the Q-valleys in the bilayer and trilayer. Insets of a–c: The Fermi levels only cross the lowest sub-bands, which are spin degenerate in b but spin split in a and c. d–f Berry curvatures of d monolayer, e bilayer, and f trilayer MoS2. The blue curves are the total curvatures of all occupied states below the Fermi levels (~2 meV from the conduction band bottom), whereas the orange curves are the total curvatures of all valence-band states. The red arrow in f points out a tiny bump at a Q-valley. Insets of d–f 2D mapping of Berry curvatures in the 2D Brillouin zone (white dashed lines)
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