Violation of the Wiedemann-Franz law in the Topological Kondo model

Abstract

We study the thermal transport through a Majorana island connected to multiple external quantum wires. In the presence of a large charging energy, we find that the Wiedemann-Franz law is nontrivially violated at low temperature, contrarily to what happens for the overscreened Kondo effect and for nontopological junctions. For three wires, we find that the Lorenz ratio is rescaled by a universal factor 2/3 and we show that this behavior is due to the presence of localized Majorana modes on the island.

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

“…In doing so, we also argue how the reservoirs affect the scaling of the corrections to the fixed point values of the conductances and of the Lorenz ratio and how they may modify the phase diagram itself. Based on the results of this paper, in [55] we conclude that the emergence of MZMs and their action in inducing the topological Kondo effect becomes the effective mechanism triggering the (universal) breakdown of the WFL at the junction and that such phenomenon can be exploited for detection of the presence of MZMs at the junction. While standard charge transport experiments cannot presently distinguish MZMs from other effects unambiguously [57][58][59][60][61], our proposal provides a new experimental test, aimed at ruling out such ambiguities.…”

“…As we discuss in Section IV, at the DFP one finds vanishing conductance tensors. Turning on the boundary interaction, we perturbatively compute the expectation values of the currents by employing the Keldysh approach of Appendix E. As a result, we obtain for the electric and thermal conductance tensors [55]…”

“…This is due to the peculiar scattering dynamics at the junction, tightly related to the emergence of the MZMs at the central island and to the hybridization between the MZMs and the Klein factors used in the bosonization of the leads [32 and 81], which in turn washes out the effect of the Klein factors that destabilize the D N −1 FP in a junction of normal wires [2, 25, and 90]. These considerations eventually lead to the proposal of synoptically looking at the charge and at the thermal transport properties of the junction, as an alternative mean to characterize the MZMs at the island [55].…”

“…Importantly, in order to recover the breakdown of the WFL in a junction of normal wires, such as the ones studied in [2 and 6], we need to have an extremely strong bulk interaction in the wire. Alternatively, coupling the wires with emerging MZMs at the central island can effectively stabilize the breakdown of the WFL at relatively small interactions, or even with noninteracting leads [55]. The formalism we develop here, based on the Tomonaga-Luttinger liquid approach, allows us to make sharp predictions on the charge and thermal conductance tensors at the low-temperature fixed point (phase), as well as on their scaling dependence on the temperature in its vicinity.…”

“…The formalism we develop here, based on the Tomonaga-Luttinger liquid approach, allows us to make sharp predictions on the charge and thermal conductance tensors at the low-temperature fixed point (phase), as well as on their scaling dependence on the temperature in its vicinity. As an example, we extend the calculation in [55] for a junction providing a realization of the topological Kondo model (TKM) [27, 28, and 56].…”