Fizika Nizkikh Temperatur: Volume 44, Number 11 (November 2018), p. 1417-1455 ( to contents , go back )
Electronic properties of graphene with point defects (Review Article)
Y.V. Skrypnyk1 and V.M. Loktev1,2
1Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine 14-b Metrolohichna Str., Kyiv 03143, Ukraine
2National Technical University of Ukraine “KPI”, 37 Peremohy Ave., Kyiv 03056, Ukraine
Received Lule 9, 2018, published online September 26, 2018
An attempt has been made to study consecutively the electronic spectrum of graphene, containing defects (such as adsorbed atoms, substitutional atoms, vacancies), which can be adequately described by the Lifshitz model. For this purpose, the known Hamiltonian of the given model is chosen in the case of two-dimensional relativistic electrons, and criteria for the appearance of an impurity resonance near the Dirac point are provided. Then, the theory of the concentration band structure transformation in graphene is presented, from which it follows that when a specific value of the impurity concentration is reached, a transport gap develops in the vicinity of the impurity resonance energy. In passing, the question on the possibility (or impossibility) to localize Dirac quasiparticles in such a spatially disordered system is analyzed. On this ground, it becomes possible to explain and describe the recently observed phenomenon in the impure graphene — the metal-insulator transition, which turns out to be a direct consequence of the Fermi level’s entering inside the transport gap domain. The concept of local spectrum rearrangement, which can also unfold with increasing the concentration of defects, is intro-duced and justified for graphene. We formulate the physical rea-sons why the minimum position in the low-temperature conduc-tivity dependence on the Fermi energy of electrons in graphene does correspond to the impurity resonance energy, but not to the Dirac point, as it was claimed in a number of theoretical and ex-perimental studies. At that, the mentioned minimum value, as it became apparent, is not a universal value, but depends on the concentration of defects. Analytical approach to impurity effects is accompanied by numerical modeling of the system under consideration, by which means a complete correspondence between these two approaches is established. In particular, the general scenario of the spectrum rearrangement, the localization of elec-tronic states, as well as effects that are of a local nature, are confirmed.
Key words: impurity, resonance state, spectrum rearrangement, Anderson transition, mobility edge, localization, graphene.