The Renormalization Group Approach – From Fermi Liquids to Quantum Dots

N. Dupuis

Bengt L. Friman, K. Hebeler, A. Schwenk

V. S. Protsenko, A. A. Katanin

We propose a version of the functional renormalization-group (fRG) approach, which is, due to including Litim-type cutoff and switching off (or reducing) the magnetic field during fRG flow, capable of describing a singular Fermi-liquid (SFL) phase, formed due to the presence of local moments in quantum dot structures. The proposed scheme allows one to describe the first-order quantum phase transition from the ``singular'' to the ``regular'' paramagnetic phase with applied gate voltage to parallel quantum dots, symmetrically coupled to leads, and shows sizable spin splitting of electronic states in the SFL phase in the limit of vanishing magnetic field $H\ensuremath{\rightarrow}0$; the calculated conductance shows good agreement with the results of the numerical renormalization group. Using the proposed fRG approach with the counterterm, we also show that for asymmetric coupling of the leads to the dots the SFL behavior similar to that for the symmetric case persists, but with occupation numbers, effective energy levels, and conductance changing continuously through the quantum phase transition into the SFL phase.

Joelson F. Silva, Luis G. G. V. Dias da Silva, E. Vernek

The prospect of using semiconductor quantum dots as an experimental tool to distinguish Majorana zero modes (MZMs) from other zero-energy excitations such as Kondo resonances has brought up the fundamental question of whether topological superconductivity and the Kondo effect can coexist in these systems. Here, we study the Kondo effect in a quantum dot coupled to a metallic contact and to a pair of MZMs. We consider a situation in which the MZMs are spin polarized in opposite directions. By using numerical renormalization group calculations and scaling analysis of the renormalization group equations, we show that the Kondo effect takes place at low temperatures, regardless of the coupling to the MZMs. Interestingly, we find that the Kondo singlet essentially decouples from the MZMs such that the residual impurity entropy can show local non-Fermi-liquid properties characteristic of the single Majorana excitations. This offers the possibility of tuning between Fermi-liquid and non-Fermi-liquid regimes simply by changing the quantum-dot-MZM couplings.

Walter Hofstetter

Tom Lancaster, Stephen J. Blundell