Multifractal wavefunctions of charge carriers in graphene with folded deformations, ripples, or uniaxial flexural modes: Analogies to the quantum Hall effect under random pseudomagnetic fields

Abstract

The electronic behavior in graphene under arbitrary uniaxial deformations, such as foldings or flexural fields, is studied by including it in the Dirac equation pseudoelectromagnetic fields. General foldings are thus studied by showing that uniaxial deformations can be considered pseudomagnetic fields in the Coulomb gauge norm. This allows one to give an expression for the Fermi (zero) energy mode wavefunctions. For random deformations, contact is made with previous works on the quantum Hall effect under random magnetic fields, showing that the density of states has a power law behavior and that the zero energy mode wavefunctions are multifractal. This hints at an unusual electron velocity distribution. Also, it is shown that a strong Aharonov–Bohm pseudoeffect is produced. For more general nonuniaxial general flexural strain, it is not possible to use the Coulomb gauge. The results presented here helps to tailor-made graphene uniaxial deformations to achieve specific wavefunctions.