Tuning the supercritical effective charge in gapless graphene via Fermi velocity modifying through the mechanical stretching

We present a theoretical study of the stretched graphene containing the Coulomb impurity. The cases of uniaxial armchair/zigzag and biaxial symmetry stretching are considered. For the uniaxial stretching, we found the gap opening with the non-monotonic dependence between the gap value and the strain. For the biaxial stretching, we observe a monotonic decreasing of Fermi velocity without the gap opening. Non-relativistic ab initio calculations of graphene electronic structure are combined with the analytical solution of relativistic Dirac equation. We found that the sheet stretching could provide a smooth fitting of Fermi velocity and, therefore, the smooth transformation of subcritical Coulomb impurity to the supercritical one. [Display omitted] •The electronic properties of stretched graphene are investigated.•Uniaxial stretching opens a band gap in graphene, in contrast to the biaxial one.•Biaxial graphene stretching can provide a smooth fitting of Fermi velocity.•Stretching allows tuning a supercritical effective charge in gapless graphene.