Pseudomagnetic lens as a valley and chirality splitter in Dirac and Weyl materials

It is proposed that strain-induced pseudomagnetic fields in Dirac and Weyl materials could be used as valley and chirality sensitive lenses for beams of Weyl quasiparticles. The study of the (pseudo)magnetic lenses is performed by using the eikonal approximation for describing the Weyl quasiparticles propagation in magnetic and strain-induced pseudomagnetic fields. Analytical expressions for the locations of the principal foci and the focal lengths are obtained in the paraxial approximation in the models with uniform as well as nonuniform effective magnetic fields inside the lens. The results show that the left- and right-handed quasiparticles can be focused at different spatial locations when both magnetic and pseudomagnetic fields are applied. It is suggested that the use of magnetic and pseudomagnetic lenses could open new ways of producing and manipulating beams of chiral Weyl quasiparticles.

Figure 1

A schematic illustration of the experimental setup which allows for the magnetic and pseudomagnetic lensing of quasiparticles in Weyl materials. While the usual magnetic field $\mathbf{B}$ is produced by an electric current in the solenoid, the pseudomagnetic field ${\mathbf{B}}_5$ is created by twisting the crystal of a Weyl material.

Figure 2

Left panel: The focal length $f_{\lambda }$ for the quasiparticles of given chirality $\lambda$ as a function of the pseudomagnetic field. Right panel: The relative difference between the focal lengths with and without the Berry curvature effects $\mathrm{\Delta }{f}_{\lambda }/f_{\lambda }$ as a function of the pseudomagnetic field. While the red solid lines correspond to quasiparticles of both chiralities at $B=0$, the blue dashed and green dotted lines represent the right- and left-handed quasiparticles at $B={10}^{-4}{B}^{*}$, respectively. We set $\varepsilon =100\text{meV}$ and $L={10}^{-2}\text{cm}$.

Figure 3

A schematic illustration of the spatial separation of chiral quasiparticles inside a Dirac semimetal crystal that is a ${\mathbb{Z}}_2$ Weyl semimetal. While the red lines correspond to the right-handed quasiparticles, the blue lines represent the left-handed ones. The solid and dashed lines correspond to the different pairs of Weyl nodes.