Emergence of strain-induced moir\'e patterns and pseudo-magnetic field confined states in graphene

TL;DR

This paper investigates how strain-induced deformations in graphene create moiré patterns and localized pseudo-magnetic field states, revealing potential for designing quantum dot-like regions with unique electronic properties.

Contribution

It provides a detailed analysis of charge distribution evolution with multiple deformations and demonstrates the emergence of confined states due to pseudo-magnetic fields in strained graphene.

Findings

Moiré patterns become more pronounced with increased deformations.

Confined states are observed in regions with pseudo-magnetic fields.

Energy levels scale linearly with pseudo-field, differing from pseudo-Landau levels.

Abstract

Strain-inducing deformations in graphene alter charge distributions and provide a new method to design specific features in the band structure and transport properties. Novel approaches implement engineered substrates to induce specifically targeted strain profiles. Motivated by this technique, we study the evolution of charge distributions with an increasing number of out-of-plane deformations as an example of a finite size periodic substrate. We first analyze a system of two overlapping deformations and determine the quantitative relation between geometrical parameters and features in the local density of states. We extend the study to sets of 3 and 4 deformations in linear and two-dimensional arrays and observe the emergence of moir\'e patterns that are more pronounced for a hexagonal cell composed of 7 deformations. A comparison between the induced strain profile and spatial maps of the local density of states at different energies provides evidence for the existence of states confined by the pseudo-magnetic field in bounded regions, reminiscent of quantum dots structures. Due to the presence of these states, the energy level scaling to be observed by local probes should exhibit a linear dependence with the pseudo-field, in contrast to the expected scaling of pseudo-Landau levels.