Nanotube quantum dot transport with spin–orbit coupling and interacting leads

Abstract

To date the impact of spin bias on the Kondo effect in nanotube quantum dots (QDs) is scarcely explored, especially in the case of significant Coulomb interaction between quantum dots and electric contact leads. Recent rapid experimental progress in nanotechnology opens new possibilities to study spin-bias-induced transport phenomena. Thus, of great interest are theoretical investigations of these transport properties in comparison with the case of a conventionally applied voltage for nanotube QDs interacting with contact leads. Such an investigation was carried out in this work where we analyzed the effects of a spin voltage as well as a conventionally applied voltage in a QD system with a different number of quantum states in the dot region in the presence of Coulombic interaction between the quantum dot and two leads. The transport is described within the Keldysh non-equilibrium Green's function (NEGF) framework. We extended the NEGF treatment developed for noninteracting leads onto the case of four quantum states m={σ,λ}={±,±} (two spins and two energy subbands, which are the cases for a nanotube QD) interacting with leads. Our derivation is based on the equation-of-motion technique and Langreth's theorem. For a Coulombic repulsion between the contacts and QD we obtain an expression for the current through QD for the four quantum states. To determine the parameters of the model Hamiltonian we used our previous calculations (Ogloblya and Prylutskyy, 2010 [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 of the middle QD segment of a (10,0) zigzag nanotube. We calculated the density of electronic states with spin up and down for the case of a single QD without pseudospin states for an infinite Coulomb repulsion, in good agreement with the calculations of Li et al. (2011 [2]). Our calculation showed that the position of the conductance peaks nearest to zero is not affected by the strength of the QD–lead Coulombic interaction parameters. We also demonstrated that this interaction shifts the density of states to higher energies. The interplay between the Kondo effect and the bias is highly temperature-dependent and becomes significant only at low temperatures. Lastly, we found that the existence of four quantum states m={σ,λ}={±,±} leads to abrupt changes in the density of states. In this case the values of the current are approximately 10 times lower than for QD with only two quantum states m={σ}={±}. However, in the case of a conventional bias the current amplitudes in both cases are approximately the same.