Dirac electrons in graphene and topological insulators

The lecture is devoted to extraordinary electronic properties of graphene and topological insulators.
As it is known graphite consists of graphene layers coupled by weak van der Waals forces. But inside graphene layers the binding is very high. This gives the possibility to write by graphitic rods by splitting off graphite flakes. Recently the wonderful discovery was done by A. Geym, K. Navoselov et al. — single graphite monolayer, graphene, with only one atom thick was experimentally obtained. Its electronic properties were studied rather in detail now. Graphene is essentially harder than steel, its thermoconductivity is much greater than that for copper. But what is the most wonderful that is its electronic properties. The energy gap between valence and conductivity bands is identically equal to zero, effective masses both electrons and holes are also equal to zero. As the result, electrons and holes are described by Dirac equation but with zero mass. Thus physics of graphene is a bridge to high energy physics of elementary particles. Electrons in graphene penetrate with probability equals to one through any high potential barrier and backscattering for slowly varying potential barriers is impossible. This changes the effect of impurities in cardinal way, particularly the weak localization become to be impossible. The last fact leads to some peculiarities in creation of nanodevices based on graphene. Graphene has great potential for creation new nanoelectronic, nanophotonic and nanoelectromechnical systems.
We studied the structure of two graphene layers independently gated. We predicted the existence of coherent phase and superfluidity in such a graphene bilayer originated from pairing of spatially separated electrons and holes. Bose condensation and Kosterlitz-Thouless transition were predicted for bilayer graphene in strong normal magnetic field. The systems considered give the possibility to create nondissipative nanoelements for information transfer operating even at room temperatures. Analysis of nanoelements based on graphene by generalized density functional approach for system with “ultrarelativistic” electronic spectra will be discussed. Possible superconductivity of strongly doped graphene is analyzed. Possible NEMS based on graphene are analyzed.
Topological insulators is the new state of matter that was recently began to study both theoretically and experimentally. 3D (strong) topological insulators have insulating bulk and topologically protected helical states on the surface that can be described by Dirac-like equation for massless particles analogously to electrons in graphene. Similarity and distinctions between chiral Dirac electrons in graphene and on the surface of topological insulator will be discussed. Collective excitations of Dirac electrons in topological insulator, graphene and graphene based structures are considered. Properties of new quasiparticles, dyons — coupled electrons and magnetic monopole — like polarization originated from magnetoelectric effect in topological insulators will be discussed.

References

1. K. Geim, K. S. Novoselov, “The rise of graphene”, Nature Materials, 6 (2007), 183–191        
2. M. I. Katsnelson, “Graphene: carbon in two dimensions”, Materials Today, 10:1-2 (2007), 20–27      
3. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, A. K. Geim, “The electronic properties of graphene”, Rev. Mod. Phys., 81:1 (2009), 109–162        
4. Yu. E. Lozovik, A. A. Sokolik, “Electron-hole pair condensation in graphene bilayer”, JETP Lett., 87:1 (2008), 55–59          ; Physics-Uspekhi, 51:7 (2008), 727–748      ; “Multi-band pairing of ultrarelativistic electrons and holes in graphene bilayer”, Phys. Lett. A, 374:2 (2009), 326–330          ; “Ultrarelativistic electron-hole pairing in graphene bilayer”, Eur. Phys. J. B, 73:2 (2010), 195–206        ; “Phonon-mediated electron pairing in graphene”, Phys. Lett. A, 374:27 (2010), 2785–2791          
5. Yu. E. Lozovik, S. Ogarkov, A. A. Sokolik, “Electron–electron and electron–hole pairing in graphene structures”, Philosophical Transactions of the Royal Society A, 368:1932, Special Issue on “Graphene” (2010), 5417–5429