No abstract

The functional renormalization group (fRG) approach has the property that, in general, the flow equation for the two-particle vertex generates O(N 4 ) independent variables, where N is the number of interacting states (e.g. sites of a real-space discretization). In order to include the flow equation for the two-particle vertex one needs to make further approximations if N becomes too large. We present such an approximation scheme, called the coupled-ladder approximation, for the special case of an onsite interaction. Like the generic third-order-truncated fRG, the coupled-ladder approximation is exact to second order and is closely related to a simultaneous treatment of the random phase approximation in all channels, i.e. summing up parquet-type diagrams. The scheme is applied to a one-dimensional model describing a quantum point contact.

Quantum point contacts (QPCs) and quantum dots (QDs), two elementary building blocks of semiconducting nanodevices, both exhibit famously anomalous conductance features: the 0.7-anomaly in the former case, the Kondo effect in the latter. For both the 0.7-anomaly and the Kondo effect, the conductance shows a remarkably similar low-energy dependence on temperature T , source-drain voltage V sd and magnetic field B. In a recent publication [F. Bauer et al., Nature, 501, 73 (2013)], we argued that the reason for these similarities is that both a QPC and a Kondo QD (KQD) feature spin fluctuations that are induced by the sample geometry, confined in a small spatial regime, and enhanced by interactions. Here we further explore this notion experimentally and theoretically by studying the geometric crossover between a QD and a QPC, focussing on the B-field dependence of the conductance. We introduce a one-dimensional model with local interactions that reproduces the essential features of the experiments, including a smooth transition between a KQD and a QPC with 0.7-anomaly. We find that in both cases the anomalously strong negative magnetoconductance goes hand in hand with strongly enhanced local spin fluctuations. Our experimental observations include, in addition to the Kondo effect in a QD and the 0.7-anomaly in a QPC, Fano interference effects in a regime of coexistence between QD and QPC physics, and Fabry-Perot-type resonances on the conductance plateaus of a clean QPC. We argue that Fabry-Perot-type resonances occur generically if the electrostatic potential of the QPC generates a flatter-than-parabolic barrier top.