  Quantum dots connected to larger systems containing a continuum of states
like charge reservoirs allow the theoretical study of many-body effects such as
the Coulomb blockade and the Kondo effect. Here, we analyze the nonequilibrium
Kondo effect and transport phenomena in a quantum dot coupled to pure monolayer
graphene electrodes under external magnetic fields for finite on-site Coulomb
interaction. The system is described by the pseudogap Anderson Hamiltonian. We
use the equation of motion technique to determine the retarded Green's function
of the quantum dot. An analytical formula for the Kondo temperature is derived
for electron and hole doping of the graphene leads. The Kondo temperature
vanishes in the vicinity of the particle-hole symmetry point and at the Dirac
point. In the case of particle-hole asymmetry, the Kondo temperature has a
finite value even at the Dirac point. The influence of the on-site Coulomb
interaction and the magnetic field on the transport properties of the system
shows a tendency similar to the previous results obtained for quantum dots
connected to metallic electrodes. Most remarkably, we find that the Kondo
resonance does not show up in the density of states and in the differential
conductance for zero chemical potential due to the linear energy dispersion of
graphene. An analytical method to calculate self-energies is also developed
which can be useful in the study of graphene-based systems. Our graphene-based
quantum dot system provides a platform for potential applications of
nanoelectronics. Furthermore, we also propose an experimental setup for
performing measurements in order to verify our model.
