Thermoelectric transport through Majorana bound states and violation of Wiedemann-Franz law

Our work model a system composed by two current leads and a one-dimensional topological nanowire (NW) hosting Majorana bound states (MBS) at each edge and coupled between them with a strength $\varepsilon_{M}$. The NW is coupled symmetrically to the leads at temperature difference $\Delta T$. We study thermoelectric transport across the NW, for two different configurations: A) When only one MBS is connected to the leads and B) when both MBS are connected to the leads. We find a noticeable violation of the Wiedemann-Franz law, which leads to obtaining sizable values of thermoelectric efficiency, measured by the figure of merit, and also an $\varepsilon_{M}$-independent behavior of the Seebeck coefficient for configuration A. We believe our findings could lead to interesting thermoelectric-based Majorana detection devices.\\~ [1] M. Leijnse, New J. Phys. \textbf{16}, 015029 (2014).\\~ [2] R. L\'opez et al., Phys. Rev. B \textbf{89}, 205418 (2014).\\~ [3] J. P. Ramos-Andrade et al., Phys. Rev. B \textbf{94}, 155436 (2016).