Universal Fano factor and anomalous $I\text{−}V$ characteristics in weakly interacting quantum dots

We study interaction effects in quantum dots coupled to perfectly conducting leads via barriers of arbitrary transparencies and embedded in an electromagnetic environment characterized by a fixed external impedance. Combining a recently proposed renormalization group equation for the semiclassical regime of this system with an extended version of circuit theory, we study the Fano factor and the $I\text{−}V$ characteristics in the low-temperature and low-energy regime. The Fano factor exhibits a sequence of universal plateaus as a function of the transparencies of the barriers. We also show that a recently discovered quantum transition, at intermediate values of the barrier’s transparencies, leads to an anomalous transport regime characterized by a Fano factor that is the harmonic average of its values in adjacent plateaus. Our result extends a previous classification scheme for mesoscopic conductors.

Figure 1

Diagram illustrating the transport regimes as a function of the tunnel probabilities. The solid lines represent the transition lines $\zeta ={\zeta }_0$ and $\zeta =1$. The region above and below these solid lines are gapped phases, while the region in between is the gapless Fabry-Perot phase. The dashed line represents the particular case $T_1=T_2$, whereas the dotted lines are guides to the eye at $T_1=0.5$ and $T_2=0.5$.

Figure 2

Fano factor $F$ and its derivative, $dF∕d\zeta$, as a function of $\zeta$ for $T_1=0.4$. The dotted lines are numerical estimates for the transition lines, $\zeta =1$ and $\zeta ={\zeta }_0\simeq 2.33$, and for the critical value $F_c={\alpha }_c∕2\simeq 0.67$ for $\epsilon ⪡1$.