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

Violation of the Wiedemann-Franz (WF) law in a 2D topological insulator due to Majorana bound states (MBS) 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 MBS with inelastic scattering modeled using a B\"uttiker 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 find that the scaling of the Lorenz ratio in our setup corresponds to the scaling in the Luttinger-liquid setup only when both phase and momentum relaxation occur, but not when only phase relaxation occurs. This suggests that the interplay between the presence of Majorana bound states and the type of inelastic scattering process, can have a significant impact on the violation of the Wiedemann-Franz law in 2D topological insulators.