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Coulomb excitations in AA- and AB-stacked bilayer graphites

Coulomb excitations in AA- and AB-stacked bilayer graphites. K.S.Novoselov, A.K.Geim, S.V.Morozov, D.Jiang, Y.zhang, S.V.Dubonos, I.V.Grigorieva Science 306, 666 (2004). Outline. Geometrical Structure Band structure ( tight-binding method) - Electronic excitations (RPA)

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Coulomb excitations in AA- and AB-stacked bilayer graphites

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  1. Coulomb excitations in AA- and AB-stacked bilayer graphites

  2. K.S.Novoselov, A.K.Geim, S.V.Morozov, D.Jiang, Y.zhang, S.V.Dubonos, I.V.GrigorievaScience 306, 666 (2004)

  3. Outline • Geometrical Structure • Band structure ( tight-binding method) • -Electronic excitations (RPA) • Low-frequency and High-frequency electronic excitations • Conclusion

  4. Geometrical structure (planar graphenes) armchair zigzag Ic~3.5Å

  5. Monolayer • Two linear energy bands intersect at EF • Zero-gap semiconductor (DOS=0 at EF) • Saddle point at M, which cause singularity (log. div.)

  6. AA Stacked • Two linear energy band are seperated by 21 • Carrier density increases

  7. AB Stacked • Two linear energy bands change into parabolic bands • There is some overlap between 1 and *1

  8. Dynamical Screening e e e e Vacuum Many-body system

  9. Effective potential e e e e 1 1 Ic e e 2 2

  10. Random Phase Approximation e (q,) (q,) e h 1 h 1 e (q,) 2 h 2

  11. Random Phase Approximation e h

  12. Dielectric function and Response function

  13. Response Function (monolayer) • * and * excitations • Square-root divergence structure for ImP is caused by excitation from kF to kF+q • ImP and ReP are related by K-K relation

  14. Response Function (AA) • 1 *1 and 1 1 excitations at 1sp=30bq/2 • 1 *2 , 2 *1 and 2 1 excitations at 3,2sp=2 130bq/2

  15. Response Function (AB) • ImP exhibits discontinuous structure due to band edge states

  16. Loss Function • Loss function characterizes the dynamics of the power dissipated in the medium due to an external perturbation

  17. Loss Function (AA) • Intensity of plasmon-1 declines as q↑ • Intensity of plasmon-2 increases as q↑ • Intensity of plasmon-3 increases and then decrease as q↑ • Loss spectra is isotropic and weak temperature dependence

  18. Loss Function (AB) • No plasmon mode • weak temperatue dependence

  19. Plasmon Dispersion • Three plasmon modes in AA-staced system • One is acoustic, the others are optical

  20. Response Function (AA and AB)

  21. Loss function (AA and AB)

  22. Plasmon Dispersion • Interlayer interaction raise and interlayer atomic interaction raise the -plasmon frequency

  23. Conclusion • Interlayer atomic interaction strongly affects the low energy states (near Fermi level) and hence the electronic excitations • Weak dependence on temperature and direction of transferred momentum • Three low-frequency plasmon modes in the AA-stacked system but not the AB-stacked system • AA- and AB-stacked system exhibit similar  plasmons • The bilayer graphites differ from the monolayer graphite in the existence of low-frequency plasmons and -plasmon frequency at small momentum

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