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Volumn 112, Issue 3, 2014, Pages

Screening charged impurities and lifting the orbital degeneracy in graphene by populating landau levels

Author keywords

68.37.Ef; 71.70.Di; 73.22.Pr; 73.43. f

Indexed keywords


EID: 84894490721     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.112.036804     Document Type: Article
Times cited : (97)

References (29)
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    • Although STM explores only a small area of the sample, the gate-voltage dependence of the data in Fig. 3(a) reflects the available states in the entire sample including those that are outside the field of view of the STM. This is because the gate covers the entire sample and can populate all available states.
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    • These properties are readily understood by examining the local DOS, D s (E, r) = ∫ d 2 r D (E, r) / S, averaged over a finite-size region S around the impurity. Unlike the DOS averaged over the whole sample, D s (E, r), is manifestly particle-hole asymmetric within a given LL, which translates to the particle-hole asymmetry of the local screening.
    • These properties are readily understood by examining the local DOS, D s (E, r) = ∫ d 2 r D (E, r) / S, averaged over a finite-size region S around the impurity. Unlike the DOS averaged over the whole sample, D s (E, r), is manifestly particle-hole asymmetric within a given LL, which translates to the particle-hole asymmetry of the local screening.
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    • E 00 = (Z / κ) (e 2 / 4 π ε 0 l B) (π / 2) (1 / 2) [1 - E r f (a / l B)], where E r f (x) is the error function.
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    • This value is comparable to the zero-field RPA estimate by the authors of Ref. [26] for double layer graphene, κ g r = 1 + g l g s g v π r s / 8 ≈ 3.75, suggesting that when the LLs are almost empty, screening of positive charges in graphene is comparable to the zero-field case. Here, r s = 4 π e 2 / h v F (κ S i O 2 + 1) is the dimensionless Wigner-Seitz radius which measures the relative strength of the potential and kinetic energies in an interacting quantum Coulomb system with linear dispersion. We note that for single layer graphene, g l = 1, screening would be significantly weaker, κ g r ≈ 2.4.
    • This value is comparable to the zero-field RPA estimate by the authors of Ref. [26] for double layer graphene, κ g r = 1 + g l g s g v π r s / 8 ≈ 3.75, suggesting that when the LLs are almost empty, screening of positive charges in graphene is comparable to the zero-field case. Here, r s = 4 π e 2 / h v F (κ S i O 2 + 1) is the dimensionless Wigner-Seitz radius which measures the relative strength of the potential and kinetic energies in an interacting quantum Coulomb system with linear dispersion. We note that for single layer graphene, g l = 1, screening would be significantly weaker, κ g r ≈ 2.4.


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