Majorana fermion induced power-law scaling in the violations of the Wiedemann-Franz law

Violation of the Wiedemann-Franz law in a 2D topological insulator due to Majorana bound states is studied via the Lorenz ratio in the single-particle picture. We study the scaling of the Lorenz ratio in the presence and absence of Majorana bound states with inelastic scattering modeled using a Buttiker voltage-temperature probe. We compare our results with that seen in a quantum dot junction in the Luttinger liquid picture operating in the topological Kondo regime. We explore the scaling of the Lorentz ratio in our setup when either phase and momentum relaxation or phase relaxation is present. This scaling differs from that predicted by the Luttinger liquid picture for both uncoupled and coupled Majorana cases.