Partial positive refraction in asymmetric Veselago lenses of uniaxially strained graphene

TL;DR

This paper investigates how uniaxial strain in graphene creates asymmetric Veselago lenses with partial positive refraction, revealing novel electron optical behaviors and potential applications in strain-tunable devices.

Contribution

It introduces a new type of asymmetric Veselago lens in strained graphene, demonstrating unique refraction and tunneling properties caused by strain-induced symmetry breaking.

Findings

Partial positive refraction enables tunable electron focusing.

Klein tunneling occurs along a strain-independent straight line.

Strain affects Fabry-Pérot interference asymmetry.

Abstract

Asymmetric Veselago lenses (AVLs) can be created from ballistic $p$-$n$ and $n$-$p$-$n$ homojunctions of uniaxially strained graphene. This atypical converging electron flow emerges by applying uniaxial tension out of the device's symmetry axes. A part of electron flow needs to be positively refracted for focusing in an asymmetric spot, whose location is tunable with the strain. In AVLs, Klein tunneling is angularly shifted regards to the normal incidence. This perfect transmission occurs at the straight line that connects the point source and focus, which is unaffected by variation of the Fermi level and barrier's width. Moreover, the mirror symmetry breaking by the strain also causes the asymmetry in Fabry-P\'erot interference. The novel electron optical laws allow to evidence that reflected and refracted electrons in AVLs lie on the same straight line with opposite group velocities and pseudo-spins. Unlike isotropic graphene, electrons under normal incidence present backscattering, angles of reflection and refraction different to zero. The average particle transmission is higher (lower) than isotropic case when the tensile strain is increased near (far away) the normal direction. These results may be useful for designing strain-bendable probing tips in scanning tunneling microscopes.