Polarization charge around impurities in two-dimensional anisotropic Dirac systems

Introducing quasiparticle anisotropy in graphene via uniaxial strain has a profound effect on the polarization charge density induced by external impurities, both Coulomb and short range. In particular, the charge distribution induced by a Coulomb impurity exhibits a power-law tail modulated by a strain-dependent admixture of angular harmonics. The appearance of distributed charge is in sharp contrast to the response in pristine or isotropic graphene, where for subcritical impurities the polarization charge is fully localized at the impurity position. It is also interesting to note that our results are obtained strictly at zero chemical potential, and the behavior is distinct from the familiar Friedel oscillations observed at finite chemical potential. We find that over a wide range of strain, the $d$-wave symmetry is dominant. The presence of Dirac cone tilt, relevant to some two-dimensional materials beyond graphene, can also substantially affect the induced charge distribution. Finally, we consider impurities with short-range potentials and study the effect of strain on the charge response. Our results were obtained in the continuum via perturbation theory valid for weak (subcritical) potentials and are supported by numerical lattice simulations based on density functional theory.