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We analyzed the effects of a spin voltage as well as a conventionally appliedvoltage in a QD system with a different number of quantum states in the dotregion in presence of Coulombic interaction between the quantum dot and twoleads. We extended the NEGF treatment developed for noninteracting leads ontothe case of four quantum states $m =\{\sigma,\lambda\}=\{\pm,\pm\}$ interactingwith leads. Our derivation is based on the equation-of-motion technique andLangreth's theorem. For a Coulombic repulsion between the contacts and QD weobtain an expression for the current through QD for the four quantum states. Todetermine the parameters of the model Hamiltonian we used our previouscalculations [1] of the electronic properties of a symmetrical nanotube QD(5,5)/(10,0)\_1/(5,5) in a tight binding model, where \_1 denotes the length ofthe middle QD segment of a (10,0) zigzag nanotube. We calculated the density ofelectronic states with spin up and down for the case of a single QD withoutpseudospin states for an infinite Coulomb repulsion, in good agreement with thecalculations of Yuan Li, et al. [2]. Our calculation showed that the positionof the conductance peaks nearest to zero is not affected by the strength of theQD-lead Coulombic interaction parameters. We also demonstrated that thisinteraction shifts the density of states to higher energies. The interplaybetween the Kondo effect and the bias is highly temperature-dependent andbecomes significant only at low temperatures. Lastly, we found that theexistence of four quantum states $m=\{\sigma,\lambda\}$ leads to abrupt changesin the density of states. In this case the values of the current areapproximately ten times lower than for QD with only two quantum states $m=\{\sigma\}=\{\pm\}$. However, in the case of a conventional bias the currentamplitudes in both cases are approximately the same.

Nanotube Quantum Dot Transport With Spin-Orbit Coupling and Interacting Leads