Screening Charged Impurities and Lifting the Orbital Degeneracy in Graphene by Populating Landau Levels

Abstract

We report the observation of an isolated charged impurity in graphene and present direct evidence of the close connection between the screening properties of a 2D electron system and the influence of the impurity on its electronic environment. Using scanning tunneling microscopy and Landau level spectroscopy, we demonstrate that in the presence of a magnetic field the strength of the impurity can be tuned by controlling the occupation of Landau-level states with a gate voltage. At low occupation the impurity is screened, becoming essentially invisible. Screening diminishes as states are filled until, for fully occupied Landau levels, the unscreened impurity significantly perturbs the spectrum in its vicinity. In this regime we report the first observation of Landau-level splitting into discrete states due to lifting the orbital degeneracy.

Local potential fluctuation of topological surface states in Bi1.5Sb0.5Te1.7Se1.3 observed by Landau level spectroscopy

“…At this point, we are unsure if the fluctuation in v F is from the noise caused by the small amplitude of highindex LL peaks 21 or by a physical origin such as the effect from the local charge states. 26 The error estimation from the zeroth LL peak width D % 20 meV shows that the measured fluctuation in E D from À60 to 40 meV is much larger than D, while the fluctuation in v F is comparable to the expected error of D/ͱ(2ehB) $ 2 Â 10 5 m/s. Although the exact determination would require the measurement at higher magnetic fields with increased LL amplitude and energy spacing, we note that local potential fluctuation should only shift the position of Fermi level, not the slope of band dispersion, 4 and it is more likely that the spatial variation of v F is coming from the measurement error.…”

Bound states of charges on top of graphene in a magnetic field

“…This has been calculated [19,37,38] and demonstrated experimentally [19] for one Coulomb impurity. Below we consider several impurities.…”

“…For example, α ≈ 1 on SiO 2 substrate [19] and α ≈ 0.4 on SiC. In dimensionless units, the equation to solve is [37] […”

“…When a magnetic field is applied, the ordinary screening is significantly suppressed [18,19] and electrons become localized. * S.Slizovskiy@lboro.ac.uk…”

Spin relaxation in disordered graphene: Interplay between puddles and defect-induced magnetism

“…37 and 38. However, it is expected that changes in the impurity environment lead to a different screening of the impurity 67 , and hence different U values. In Fig.…”