Electron localization in periodically strained graphene

Pseudo-magnetic field (PMF) in deformed graphene has been proposed as a promising and flexible method to quantum-confine electronic states and create gaps in the local density of states. Motivated by this perspective, we numerically analyze various different configurations leading to electronic localization and band flattening in periodically strained graphene. In particular, we highlight the existence of a fine structure in the pseudo-Landau levels confined in large-PMF regions, the emergence of states confined to PMF nodes as well as of snake-like orbits. In our paper, we further analyze the importance of the relative rotation and asymmetry of the strain lattice with respect to the atomic lattice and show how it can be used to modulate the PMF periodicity and to create localized orbits far from the strain points. Possible implementations and applications of the simulated structures are discussed.