Kekul\'e Induced Valley Birefringence and Skew Scattering in Graphene

TL;DR

This paper explores how Kekulé bond textures in graphene induce valley birefringence and skew scattering, revealing optical-like effects and valley Hall phenomena through scattering analysis.

Contribution

It introduces a scattering approach to characterize Kekulé-induced valley birefringence and demonstrates the emergence of valley Hall effects in graphene.

Findings

Caustics with two cusps depend on Kekulé interaction strength

Non-zero skew cross section indicates asymmetric scattering at low carrier density

Valley polarization leads to opposite deflections, demonstrating valley Hall effect

Abstract

In graphene, a Kekul\'e-Y bond texture modifies the electronic band structure generating two concentric Dirac cones with different Fermi velocities lying in the {\Gamma}-point in reciprocal space. The energy dispersion results in different group velocities for each isospin component at a given energy. This energy spectrum combined with the negative refraction index in p-n junctions, allows the emergence of an electronic analog of optical birefringence in graphene. We characterize the valley birefringence produced by a circularly symmetric Kekul\'e patterned and gated region using the scattering approach. We found caustics with two cusps separated in space by a distance dependent on the Kekul\'e interaction and that provides a measure of its strength. Then, at low carrier concentration we find a non-vanishing skew cross section, showing the asymmetry in the scattering of electrons around the axis of the incoming flux. This effect is associated with the appearance of the valley Hall effect as electrons with opposite valley polarization are deflected towards opposite directions.