Strain-gated nonlinear Hall effect in two-dimensional ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ van der Waals heterostructure

It is recently found that the Hall effect can survive in the presence of time-reversal symmetry but with inversion-symmetry breaking, which is known as the nonlinear Hall effect. So far, the studies concerning the nonlinear Hall effect are mainly focused on the homogeneous systems, while less attention has been paid to the van der Waals (vdW) heterostructure, which in fact naturally breaks the spatial inversion symmetry. In this study, we systematically study the nonlinear electric response in $1{\text{T}}^{\prime }$-phase ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ vdW heterostructure. Our results demonstrate that ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ vdW heterostructure owns a large Berry curvature dipole, which is comparable with those of homogeneous multilayers and much larger than that predicted for monolayers under the in-plane uniaxial strain. In addition, the nonlinear Hall response in vdW heterostructure is sensitive to the relative position between the Fermi energy and tilted Dirac cones, and can be effectively manipulated from positive to negative values by applying an out-of-plane strain. Further study indicates that this can be ascribed to the charge transfer within the vdW interlayer. Based on these findings, our work provides a fundamental understanding of the nature of strain-gated nonlinear Hall effect in vdW heterostructures, which may facilitate the design of novel high-frequency nanodevices.

Figure 1

(a) Top view of monolayer ${\mathrm{MSe}}_2$, where M stands for Mo or W element. The unit cell is indicated by the dashed red rectangle. (b) Side view of ${\mathrm{MoSe}}_2/{\mathrm{MoSe}}_2$ vdW heterostructure. The interlayer distance $d$ is defined as the average distance of Se atoms between the upper and lower layers. (c) First Brillouin zone of ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ vdW heterostructure.

Figure 2

(a) Orbit-projected band structures of ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ vdW heterostructure. The Fermi level is set to zero. The red, magenta, and blue colors represent Mo-$4d$, W-$5d$, and Se-$4p$ orbitals, respectively. (b) Band-decomposed charge densities for CBM, VBM, and VBM-1 bands at the $\mathrm{\Gamma }$-point. The isosurface value is set to $0.01\mathrm{e}/{\AA }^3$. (c) $k$-dependent distribution of Berry curvature at $E-E_f=-50$ meV after taking the logarithm as defined in Equation 5. Red and blue colors represent positive and negative contributions, respectively.

Figure 3

Band structures of ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ vdW heterostructure (a) with $-6$% compressive strain ($d=3.0$ Å), (b) without strain ($d=3.2$ Å), and (c) with 6% tensile strain ($d=3.4$ Å). The spin-orbit coupling is included and Fermi level is set to zero.

Figure 4

(a) Berry curvature dipole as a function of the energy with varying applied out-of-plane strains. (b) The nonlinear Hall current versus the applied electric field under various strains. (c) Schematic illustration of strain-gated nonlinear Hall effects in ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ vdW heterostructure. Here, $E_y$ is the driving electric field along $y$ direction, and $j_x$ is the induced nonlinear Hall current along $x$ direction, which can be switched by the out-of-plane strain (${\varepsilon }_z$).