Joint CM seminar

[Cond.Matt. & Stat.Mech.Section]

JOINT ICTP/SISSA CONDENSED MATTER SEMINARS



Seminar Room - ICTP Leonardo Building   (first floor)





Wednesday, 11 November -     4:00 p.m.



Veronica BISTI   ( Institute of Solid State Physics, Chernogolovka )



"Excitations in bilayer graphene in high magnetic field"



Abstract



The charge-density excitations in bilayer graphene at the filling- 
factor  <<1 at small momenta are considered in the frame of the  
Hartree-Fock  approximation. The presence of small asymmetry of  
graphene layers is included. The dependence of the magnetoplasmon  
energy on the bilayer ground state is shown. The energy splitting  
proportional to square root of H for the symmetric case with half- 
filled zero-energy levels is found both for bilayer and monolayer  
graphene.

Recent experimental progress has allowed the fabrication and study of  
monolayer and bilayer graphene.  The electronic band structure of  
these objects is gapless and has a chirality. The monolayer has Dirac- 
type spectrum with linear dispersion and chirality exhibiting Berry  
phase \pi. In magnetic field there is zero-energy Landay level,  
fourfold degenerate due to two spins and two valleys. The bilayer  
graphene is the unique object which combines the parabolic dispersion  
law of quasiparticles with their chirality exhibiting Berry phase   
2\pi. In magnetic field there is a double-degenerate zero-energy  
Landay level incorporating two different orbital states with the same  
energy. Taking into account spin and valley degeneracies, the zero- 
energy Landau level is eightfold degenerate. For the bilayer with  
small asymmetry there are  four weakly split  two-fold levels, close  
to zero. This one-electron structure was confirmed in experiments on  
integer quantized Hall effect and Shubnikov-de Haas oscillations.These  
properties are understood in terms of non-interacting electrons. The  
electron-electron interaction is an important problem in the study of  
cyclotron resonance in monolayer, bilayer and multilayer graphene .

The charge-density excitations  at small momenta are considered in the  
frame of the Hartree-Fock approximation. The case of filling-factor  
<<1  is considered. This filling-factor means the absence of free  
carriers due to doping. The presence of small asymmetry of graphene  
layers is included. Without magnetic field, the asymmetry gives rise  
to the gap in the spectrum; in the presence of the field, the  
asymmetry splits the eightfold degenerate zero-energy Landau level  
into two fourfold levels. The energy of the magnetoplasmon excitations  
is considered and the strong  dependence of the energy on the form of  
the bilayer ground state is shown.  In asymmetric bilayer taking into  
account spin we have four transitions with equal energies. Energy  
splitting due to asymmetry is absent, only additional shift takes  
place. In the case of symmetric ground state with half-filled 0 and 1  
for each valley and spin there are two combined transitions splitted  
in energy.  This splitting for combined electron-hole transitions from  
half-filled level is not specific to bilayer graphene. For monolayer  
graphene with filling-factor $\nu=0$ the value of splitting is  
practically the same as for bilayer graphene. If this splitting would  
be observed it would be the evidence of Coulomb interaction in   
graphene.