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) Low-frequency and High-frequency electronic excitations Conclusion

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

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

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

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

Dynamical Screening ee e e VacuumMany-body system

Effective potential e e e 1 2 e e e 1 2 Ic

h e h e (q,  ) e h Random Phase Approximation

e h

Dielectric function and Response function

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

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

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

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

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

Loss Function (AB) No plasmon mode weak temperatue dependence

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

Response Function (AA and AB)

Loss function (AA and AB)

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

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