Multi-particle scattering and breakdown of the Wiedemann-Franz law at a junction of N interacting quantum wires

Abstract

We analyze the charge and thermal transport at a junction of interacting quantum wires close to equilibrium. Within the framework of Tomonaga-Luttinger liquids, we compute the thermal conductance for a wide class of boundary conditions and detail the physical processes leading to the breakdown of the Wiedemann-Franz law at the junction. We show how connecting external reservoirs to the quantum wires affects the conductance tensors close to the various fixed points of the phase diagram of the junction. We therefore distinguish two types of violation of the Wiedemann-Franz law: a "trivial" one, independent of the junction dynamics and arising from the breakdown of the Fermi-liquid picture in the wire, and a junction-related counterpart, arising from multi-particle scattering processes at the junction.

Finite-temperature corrections to the Lorenz ratio at the N = 3 topological Kondo fixed point

“…The splitting matrix ρ is defined so that, denoting respectively with φ R,a (x) and with φ L,a (x) the right-and the left-handed components of the field φ a (x), one has φ R,a (0) = 3 b=1 ρ a,b φ L,b (0). Given ρ and letting G a,b and K a,b respectively being the charge and the heat conductance tensor elements at the junction, one finds [20,21] T G a,b = 2 3g L 0 . We therefore identify a "bulk" renormalization of L 0 by the nonuniversal factor g −1 , which is typical of a the WFL in a spinless Luttinger liquid [27,28].…”

“…This is purely determined by the junction dynamics and, in particular, by the onset of multi-particle scattering processes at the TKFP. Probing this renormalization should provide a remarkable piece of evidence of the presence of localized MMs at the junction, which are deemed to be the main mechanism stabilizing the TKFP [20,21,17].…”

“…As a reference calculation, we briefly review the derivation of the finite-T corrections at the DFP in a perturbative expansion in J K [20,21]. At the DFP, the boundary interaction in Eq.…”

“…A striking possibility of recovering a stable SFP with an expected robust, and universal, violation of the WFL in a weakly interacting, or even noninteracting (in the bulk) junction of quantum wires, has been recently put forward in [20,21]. Specifically, it has been shown that the WFL breaks down in a robust and predictable way in a junction of N = 3 spinless quantum wires connected to a superconducting island in its charging regime hosting a set of Majorana modes (MMs).…”

“…This requires the knowledge of the leading, finite-T corrections to the conductances near by the TKFP. In order to compute them, we employ the formalism developed in [20,21] and as a result, beside recovering the main temperature dependence, we provide the explicit corrections of the conductances at the TKFP on the bulk interaction in the leads.…”