Electron transport through a quantum dot in the Coulomb blockade regime: Nonequilibrium Green’s function based model

We explore electron transport through a quantum dot coupled to the source and drain charge reservoirs. We trace the transition from the Coulomb blockade regime to Kondo regime in the electron transport through the dot occurring when we gradually strengthen the coupling of the dot to the charge reservoirs. The current-voltage $\left(I\text{−}V\right)$ characteristics are calculated using the equations of motion approach within the nonequilibrium Green’s function formalism beyond the Hartree-Fock approximation. We show that within the Coulomb blockade regime the $I\text{−}V$ characteristics for the quantum dot containing a single spin-degenerated level with the energy $E_0$ include two steps whose locations are determined by the values of $E_0$ and the energy of Coulomb interaction of electrons in the dot $U$. The heights of the steps are related as 2:1 which is consistent with the results obtained by means of the transition rate equations.

Figure 1

(Color online) Average occupation numbers in the quantum dot as a function of the voltage applied across the junction. The curves are plotted assuming $U=0.5\text{eV}$, $kT=0.00026\text{eV}$, $E_0\left(V_g\right)=-0.2\text{eV}$, and $\tau =0.01\text{eV}$ (solid line), 0.02 eV (dashed-dotted line), and 0.04 eV (dashed line).

Figure 2

(Color online) Current through a junction within the Coulomb blockade regime. The curves are plotted assuming $U=0.5\text{eV}$, $kT=0.00026\text{eV}$, $E_0\left(V_g\right)=-0.2\text{eV}$, ${\tau }_0=0.04\text{eV}$, and $\tau =0.01\text{eV}$ (solid line), 0.02 eV (dashed-dotted line), and 0.04 eV (dashed line). The factor ${\tau }_0^2/{\tau }^2$ is introduced to bring all $I\text{−}V$ curves to the same scale. The ratio of heights of the two steps revealed in the curves equals 2:1.

Figure 3

(Color online) The equilibrium $\left(V=0\right)$ electron density of states in the quantum dot. The curves are plotted for $\tau =0.2\text{eV}$ (solid line), 0.1 eV (dashed line), and 0.06 eV (dashed-dotted line). The remaining parameters are the same as those in Fig. 1.

Figure 4

(Color online) Splitting of the Kondo peak in the electron density of states with increasing bias. The curves are plotted for $\text{eV}=0$ (solid line); 0.02 eV (dashed line), 0.04 eV (dashed-dotted line), and 0.06 eV (dotted line). The coupling strength $\tau =0.2\text{eV}$. The remaining parameters are taken as in Figs. 1, 2.