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

We study features of thermoelectric transport through a one-dimensional topological system model hosting Majorana bound states (MBSs) at its ends. We describe the behavior of the Seebeck coefficient and the $ZT$ figure of merit for two configurations between the MBS and normal current leads. We find an important violation of the Wiedemann-Franz law in one of these geometries, leading to sizable values of the thermoelectric efficiency over a narrow window in chemical potential away from neutrality. These findings could lead to interesting thermoelectric-based MBS detection devices, via measurements of the Seebeck coefficient and figure of merit.

Figure 1

Model setup of a 1D topological superconductor nanowire hosting an MBS at both ends, connected to two metallic leads at different temperatures. (a) Each MBS is coupled to its nearest lead; (b) only one MBS is coupled to both leads simultaneously.

Figure 2

(a, c) Electrical and (b, d) thermal conductances, both as a function of the Fermi energy $\mu$. (a) and (b) correspond to model A in Fig. 1; (c) and (d), to model B.

Figure 3

Wiedemann-Franz law ratio, in units of the Lorenz number ${\ell }_0$, for (a) model A and (b) model B in Fig. 1. The horizontal dotted-dashed gray line corresponds to the universal maximum value of $4.19{\ell }_0$ [23].

Figure 4

Seebeck coefficient as a function of $\mu$ and ${\varepsilon }_M$. Upper and lower panels refer to model A and model B in Fig. 2, respectively. Note that $S$ in model B can be three orders of magnitude larger than in model A geometry.

Figure 5

$ZT$ as a function of $\mu$ and ${\varepsilon }_M$. Upper and lower panels refer to model A and model B in Fig. 2, respectively. Note the sizable $ZT$ in model B over the window $\mathrm{\Delta }\mu \sim 0.002\mathrm{\Gamma }\sim 20\mu \mathrm{eV}$.