Nonequilibrium charge-Kondo transport through negative-$U$ molecules

Low-temperature transport through molecules with effectively negative charging energy $U$ exhibits a charge-Kondo effect. We explore this regime analytically by establishing an exact mapping between the negative-$U$ and the positive-$U$ Anderson models, which is suitable for the description of nonequilibrium transport. We employ this mapping to demonstrate the intimate relation between nonequilibrium transport in the spin-Kondo and charge-Kondo regimes, and derive analytical expressions for the nonlinear current-voltage characteristics as well as the shot noise in the latter regime. Applying the mapping in the opposite direction, we elucidate the finding of super-Poissonian noise in the positive-$U$ Anderson model at high temperatures, by relating the correlations between spin flips to pair-tunneling processes at negative $U$.

Figure 1

(Color online) Illustration of the mapping between the negative-$U$ model (a) and the conventional Anderson model (b) with additional local Zeeman field $B^{\prime }$. All level energies are given as energies per particle.[20] The horizontal dashed line marks the zero-bias Fermi energy of the leads. The one-particle energy ${\epsilon }_d$ is required for adding a single electron to the neutral molecule.

Figure 2

(Color online) Fano factor as a function of bias and gate voltage for a symmetric junction with ${\Gamma }_L={\Gamma }_R=k_{B}T$, and with $U=-2\times {10}^3{k}_{B}T$. Super-Poissonian noise reflects the bunching of electrons in pair-tunneling processes.

Figure 3

(Color online) Relation between (a) the unidirectional pair-tunneling process for negative $U$ and (b) the inelastic spin-flip in the conventional Anderson model with local Zeeman field, as obtained by the PHLR transformation. The phase space available for the spin-up electron in the initial state is marked in red (dark gray).

Figure 4

(Color online) Elementary processes for the transitions $\mid 0⟩\to \mid 2⟩$ and $\mid 0⟩\to \mid 0⟩$. The label “$\times 2$” signals an additional factor of 2 due to two incoherent spin contributions. The diagrams for the processes corresponding to the transitions $\mid 2⟩\to \mid 0⟩$ and $\mid 2⟩\to \mid 2⟩$ are obtained by reversing the direction of all arrows.

Figure 5

(Color online) Fano factor as a function of gate voltage at finite bias $(eV=50\times {10}^{-3}\mid U\mid )$ for different magnitudes of junction asymmetry ${\Gamma }_L∕{\Gamma }_R$. The dominance of mixed pair-tunneling processes for asymmetric junctions reduces the super-Poissonian noise and leads to Fano factors below 1.