Electric carrier concentration in graphite: Dependence of electrical resistivity and magnetoresistance on defect concentration

Graphene is a two-dimensional carbon material with a honeycomb lattice and Dirac-like low-energy excitations. When Zeeman and spin-orbit interactions are neglected its Landau levels are four-fold degenerate, explaining the \(4 e^2/h\) separation between quantized Hall conductivity values seen in recent experiments. In this paper we derive a criterion for the occurrence of interaction-driven quantum Hall effects near intermediate integer values of \(e^2/h\) due to charge gaps in broken symmetry states.

Diffusion, coalescence, and reconstruction of vacancy defects in graphene layers are investigated by tight-binding molecular dynamics (TBMD) simulations and by first principles total energy calculations. It is observed in the TBMD simulations that two single vacancies coalesce into a 5-8-5 double vacancy at the temperature of 3000 K, and it is further reconstructed into a new defect structure, the 555-777 defect, by the Stone-Wales type transformation at higher temperatures. First principles calculations confirm that the 555-777 defect is energetically much more stable than two separated single vacancies, and the energy of the 555-777 defect is also slightly lower than that of the 5-8-5 double vacancy. In TBMD simulation, it is also found that the four single vacancies reconstruct into two collective 555-777 defects which is the unit for the hexagonal haeckelite structure proposed by Terrones et al. [Phys. Rev. Lett. 84, 1716 (2000)].