# Klein collimation by rippled graphene superlattice

## TL;DR

This paper demonstrates how rippled graphene superlattices can be used to control electron momentum distribution and focusing without external fields, leveraging charge accumulation due to Klein penetration at flat-rippled junctions.

## Contribution

It introduces a novel method to manipulate electron trajectories in graphene using a superlattice of curved surfaces, enabling control without external fields.

## Key findings

- Charge accumulation occurs at rippled graphene due to Klein penetration.
- Electron momentum distribution can be selectively controlled by the superlattice.
- Electron focusing can be achieved by changing superlattice element properties.

## Abstract

The hybridization of $\sigma$ and $\pi$ orbitals of carbon atoms in graphene depends on the surface curvature. Considering a single junction between flat and rippled graphene subsystems, it is found an accumulation of charge in the rippled subsystem due to Klein penetration phenomenon that gives rise to n-p junction. Using this fact, we show that the momentum distribution of electrons in ballisitically propagating beam can be selective without a waveguide, or external electric, and/or magnetic fields in graphene strip under experimentally feasible one-dimensional periodic potential. Such a potential is created with the aid of superlattice that consists of periodically repeated graphene pieces withdifferent hybridizations of carbon orbits, produced by variation of the graphene surface curvature. The charge redistribution and selected transmission of electrons, caused by the superlattice, allows to control the electron focusing in the considered system by simply changing the element properties in the superlattice