Nonlocal Coulomb drag in Weyl semimetals

Nonlocality is one of the most striking signatures of the topological nature of Weyl semimetals. We propose to probe the nonlocality in these materials via a measurement of a magnetic-field-dependent Coulomb drag between two sheets of graphene which are separated by a three-dimensional slab of Weyl semimetal. We predict a mechanism of Coulomb drag, based on cyclotron orbits that are split between opposite surfaces of the semimetal. In the absence of impurity scattering between different Weyl nodes, this mechanism does not decay with the thickness of the semimetal.

Figure 1

(a) Drag setup: two layers of graphene (red) are placed above and below a 3D Weyl semimetal. The graphene layers and the Weyl semimetal are separated by insulating layers (brown). The graphene layers are coupled to the Weyl metal only via the local Coulomb interaction. Current is pushed on the top layer while the voltage on the bottom layer is measured. (b) A sketch of the relevant length scales in the problem. $L$ is the thickness of the WSM, $d_s$ is the extent of the surface states, and $d$ is the thickness of the layer at which the drag coupling is nonzero. We denote the layers at which the surface states exist by ${\mathcal{L}}_1$ and ${\mathcal{L}}_2$.

Figure 2

The ratio of $R_D$ in the presence of nonlocality ($\mathrm{\Gamma }\ne 0$) and $R_D$ in the absence of nonlocality ($\mathrm{\Gamma }=0$). Here, $L=100$ nm, $d_s=3$ nm, $d=2$ nm, $r_0=5\mathrm{\Omega }$, ${\rho }_d=0.5\mathrm{\Omega }$, and $\xi =100$. For $\mathrm{\Gamma }=0$ the drag coefficient is $R_D=2\times {10}^{-5}\mathrm{\Omega }$ and for $\mathrm{\Gamma }=1/2$ it is $R_D=0.75\mathrm{\Omega }$.

Figure 3

(a) $R_D^{xx}$ as a function of $\mathrm{\Gamma }$ for three different values of $\varphi$. (b) The ratio $\mathrm{\Phi }$ as a function of $\mathrm{\Gamma }$ for $\varphi =0.2$. In both (a) and (b), $L=100$ nm, $d_s=d=1$ nm, $r_0=5\mathrm{\Omega }$, ${\rho }_d=0.1\mathrm{\Omega }$, and $\xi =60$. For $\mathrm{\Gamma }\ll 1$, both $R_D^{xy}$ and $R_D^{xx}$ are small. As $\mathrm{\Gamma }$ increases towards half, $R_D^{xx}$ increases dramatically while $R_D^{xy}$ remain almost unchanged.