Regensburg 2016 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 16: Transport: Quantum Dots, Quantum Wires, Point Contacts

TT 16.9: Talk

Monday, March 7, 2016, 17:15–17:30, H21

Functional Renormalization Group Approach for Inhomogeneous One-Dimensional Fermi Systems with Finite-Ranged Interactions — •Lukas Weidinger, Florian Bauer, Jan Heyder, and Jan von Delft — LMU München, Arnold Sommerfeld Center for Theoretical Physics

We use the functional renormalization group (fRG) to study transport through quantum point contacts (QPCs) described by a one-dimensional lattice model with either on-site or finite-ranged interactions. In previous work on this model [Bauer2014], the so-called coupled-ladder approximation (CLA) was shown to admit a consistent fRG treatment for the case of a purely onsite interaction. We introduce an extended version of this scheme, called the extended coupled ladder approximation (eCLA), which includes a spatially extended feedback between the individual interaction channels, measured by a feedback length L. We applied a static version of this scheme to our QPC model, finding that for on-site interactions, this scheme converges to the third-order-truncated fRG when L is increased beyond the characteristic length l_x of the QPC. Additionally, it turns out that the enhanced feedback stabilizes the fRG flow. Furthermore, it allows us to also treat a finite-ranged interaction with a range of up to L sites. Studying our QPC model with a screened Coulomb interaction, we find that in certain parameter regimes (in particular interaction range ≳ l_x), the density shows the onset of crystaline features in the QPC region, accompanied by oscillatory behavior of the conductance as function of gate voltage.