Online

Wilson, Noah

Physics

2016

MS

Graphene, the world's first truly two-dimensional material, is unique for having an electronic structure described by an effective Lorentz invariant theory. One important consequence is that the ratio or Coulomb energy to kinetic energy is a constant, depending only on conditions within the lattice rather than on the average charge density as in a typical Galilean invariant material. Given this unusual property, a natural question would be how do phenomena, such as screening of a Coulomb impurity, happen in graphene? Moreover, how does the addition of uniaxial strain enhance or diminish this behavior? Here I discuss our work to calculate the charge density distribution in a lattice of strained graphene under the effect of an external Coulomb impurity. Graphene can have its band structure significantly altered by the application of uniaxial strain. Two cases are here explored: relatively weak strain at some finite chemical potential, and extreme strain with zero chemical potential. In the first system, the strain induces elliptic Dirac cones, engendering some inherent directionality to graphene's electronic properties that did not exist before. This anisotropy manifests itself in the polarization function, and so too in the screening charge density. A finite chemical potential in this case is necessary for any screening to take place in graphene since, without it, there are no electron states near the Fermi level to polarize. Both in the strained and unstrained case, decaying oscillations known as Friedel oscillations are observed. The result of strain is a multifaceted anisotropy of the charge distribution: the amplitude, frequency, and the position of the first peak in the oscillations are each varied depending on the direction one observes. In the second system, extreme strain in graphene leads to a merging of Dirac cones, yielding a transition to a new energy spectrum. This band structure is unusual in that it becomes quadratic along the direction of strain while remaining linear along the perpendicular. We evaluate the screening response to a Coulomb impurity in this case at zero chemical potential, and yet long-range distribution tails are still observed. The result is a very exotic charge distribution, in which the radial distribution of charge and the angular distribution are highly coupled, and at various distances, both screening and anti-screening regions are observed around the impurity. The anti-screening regions are local, and the net induced charge density still satisfies the accepted model of screening.