Tuning the Effective Fine Structure Constant in Graphene: Opposing Effects of Dielectric Screening on Short- and Long-Range Potential Scattering

Abstract

We reduce the dimensionless interaction strength α in graphene by adding a water overlayer in ultra-high vacuum, thereby increasing dielectric screening. The mobility limited by long-range impurity scattering is increased over 30 percent, due to the background dielectric constant enhancement leading to reduced interaction of electrons with charged impurities. However, the carrier-densityindependent conductivity due to short range impurities is decreased by almost 40 percent, due to reduced screening of the impurity potential by conduction electrons. The minimum conductivity is nearly unchanged, due to canceling contributions from the electron/hole puddle density and longrange impurity mobility. Experimental data are compared with theoretical predictions with excellent agreement. PACS numbers:Most theoretical and experimental work on graphene has focused on its gapless, linear electronic energy dispersion E = v F k. One important consequence of this linear spectrum is that the dimensionless coupling constant α (or equivalently r s , defined here as the ratio between the graphene Coulomb potential energy and kinetic energy) is a carrier-density independent constant [1, 2], and as a result, the Coulomb potential of charged impurities in graphene is renormalized by screening, but strictly maintains its long-range character. Thus there is a clear dichotomy between long-range and short-range scattering in graphene, with the former giving rise to a conductivity linear [2,3] in carrier density (constant mobility), and the latter having a constant conductivity independent of carrier density. Charged impurity scattering necessarily dominates at low carrier density, and the minimum conductivity at charge neutrality is determined by the charged impurity scattering and the self-consistent electron and hole puddles of the screened impurity potential [3,4,5,6].Apart from the linear spectrum, an additional striking aspect of graphene, setting it apart from all other twodimensional electron systems, is that the electrons are confined to a plane of atomic thickness. This fact has a number of ramifications which are only beginning to be explored [7]. One such consequence is that graphene's properties may be tuned enormously by changing the surrounding environment. Here we provide a clear demonstration of this by reducing the dimensionless coupling constant α in graphene by more than 30 percent through the addition of a dielectric layer (ice) on top of the graphene sheet. Upon addition of the ice layer, the mobility limited by long-range scattering by charged impurities increases by 31 percent, while the conductivity limited by short-range scatterers decreases by 38 percent. The minimum conductivity value remains nearly unchanged. The FIG. 1:Schematic illustrating dielectric screening in graphene. The dielectric environment controls in the interaction strength parameterized by the coupling constant α.opposing effects of reducing α on short-and long-range scattering are easily understood theoretically. The major effect on long-range...

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