In this paper, the commensurability conditions, which originated from the unique topology of two-dimensional systems, are applied to determine the quantum Hall effect hierarchy in the case of a monolayer graphene. The fundamental difference in a definition of a typical semiconductor and a monolayer graphene filling factor is pointed out. The calculations… (More)
This chapter is devoted to the recent theoretical results on the optical quantum control over charges confined in quantum dots under influence of phonons. We show that lattice relaxation processes lead to decoherence of the confined carrier states. The theoretical approach leading to a uniform, compact description of the phonon impact on carrier dynamics,… (More)
The commensurability condition is applied to determine the hierarchy of fractional fillings of Landau levels in monolayer and in bilayer graphene. The filling rates for fractional quantum Hall effect (FQHE) in graphene are found in the first three Landau levels in one-to-one agreement with the experimental data. The presence of even denominator filling… (More)
A short overview of the technology and physics of semiconductor quantum dots is given. Different methods of creation of quantum dots and mechanisms of carrier confinements are described. The fundamental properties of these systems are discussed including current attempts for applications in new ultra-small opto-electronic semiconductor devices.