Effects of vertex corrections on diagrammatic approximations applied to the study of transport through a quantum dot

In the present work, we calculate the conductance through a single quantum dot weakly coupled to metallic contacts. We use the spin-1/2 Anderson model to describe the quantum dot, while considering a finite Coulomb repulsion. We solve the interacting system using the noncrossing approximation (NCA) and the one-crossing approximation (OCA). We obtain the linear response conductance as a function of temperature and energy position of the localized level. From the comparison of both approximations we extract the role of the vertex corrections, which are introduced in the OCA calculations and neglected in the NCA scheme. As a function of the energy position, we observe that the diagrams omitted within the NCA are really important for appropriately describing transport phenomena in Kondo systems as well as in the mixed valence regime. On the other hand, as a function of temperature, the corrections introduced by the OCA partly recover the universal scaling properties known from numerical approaches such as the numerical renormalization group.

Figure 1

Sketch of the self-consistency OCA scheme for self-energies and vertex corrections of the auxiliary particles. The solid, wiggly, dashed, and curly lines stand for pseudofermion, empty boson, conduction electron, and doubly occupied boson propagators, respectively.

Figure 2

Physical spectral function of the QD for the symmetric case, $E_d=-U/2=-6$ and $D=20\Delta$. The insets show a zoom of the region near the Fermi energy $\omega =0$.

Figure 3

Conductance in the linear-response regime and occupation (dotted curve) of QD at high temperature, $T=0.8\Delta$, as a function of the energy position $E_d$. Parameters: $U=32$, $D=43$.

Figure 4

Conductance through the QD at low temperatures as a function of the energy position $E_d$. Parameters: $U=8$, $D=20$

Figure 5

Conductance as a function of $T/T_K$ for the symmetric Anderson model. Left panel: $E_d=6$, $U=12$, $D=20$. The solid, dashed, and dot-dashed lines stand for NRG, OCA, and NCA techniques respectively. Right panel: OCA conductance for the symmetric case, $U=12$, and far from this, $U=18$ (dot-dashed line).