Thermoelectric properties of ballistic Normal-Weyl semimetal-Normal junction

Abstract

Weyl semimetals are a new class of topological materials possessing outstanding physical properties. We investigate the thermoelectric properties of a ballistic Weyl semimetal specimen connected to two normal contacts. We introduce a model to evaluate the thermoelectric coefficients of the junction and analyze its features along two distinct directions, one along the chiral axis of the Weyl semimetal and the other perpendicular to it. We demonstrate that the thermoelectric response of this junction depends on whether it is along the chiral axis of the Weyl semimetal or not. Electrical and thermal conductances of this junction reveal considerable dependence on the length and chemical potential of the Weyl semimetal layer. In particular, we observe that, decreasing the chemical potential in the normal contacts enhances the Seebeck coefficient and thermoelectric figure of merit of the junction to substantial values. Hence, we unveil that a ballistic junction of Weyl semimetal can serve as a fundamental segment for application in future thermoelectric devices for thermal energy harvesting.

Figure 1

Schematic representation of the considered junctions. (a) Junction is along the z axis and parallel to the line connecting two Weyl nodes (the chiral axis) of WSM in the momentum space. (b) It is along the x axis and perpendicular to the chiral axis of WSM.

Figure 2

Normalized electrical conductance (left panel) and normalized thermoelectrical conductance (right panel) as a function of the chemical potential of the normal leads. The other parameters are $\mathcal{M}=5$ eV nm${}^2$, $k_0=0.5$ nm${}^{-1}$, ${\mu }_W=-0.5$ eV, $L=30$ nm for figures (a) and (e), $\mathcal{M}=5$ eV nm${}^2$, $\gamma =1.0$ eV nm, ${\mu }_W=-0.5$ eV, $L=30$ nm for figures (b) and (f), $\mathcal{M}=5$ eV nm${}^2$, $\gamma =1.0$ eV nm, $k_0=0.5$ nm${}^{-1}$, $L=30$ nm for figures (c) and (e), $\mathcal{M}=5$ eV nm${}^2$, $\gamma =1.0$ eV nm, $k_0=0.5$ nm${}^{-1}$, ${\mu }_W=-0.5$ eV for figures (d) and (h).

Figure 3

Seebeck coefficient as a function of the chemical potential of the normal leads for different values of the junction parameters. All of the other parameters are same as Fig. 2.

Figure 4

Electrical conductance (left panel) and Seebeck coefficient (right panel) as a function of the length (figures (a,b,e,f)), and chemical potential of the WSM layer (figures (c,d,g,h)) in terms of different values of $k_0$ and $\gamma$. Here $\mathcal{M}=5$ eV nm${}^2$, $\mu =3.0$ meV and the values of the other parameters are considered as $k_0=0.5$ nm${}^{-1}$, ${\mu }_W=-0.5$ eV for figures (a) and (e), $\gamma =1.0$ eV nm, ${\mu }_W=-0.5$ eV for figures (b) and (f), $k_0=0.5$ nm${}^{-1}$, $L=30$ nm for figures (c) and (g), $\gamma =1.0$ eV nm, $L=30$ nm for figures (d) and (h).

Figure 5

The electronic contribution to the thermal conductance as a function of the chemical potential of the normal leads for different values of the junction parameters. All of the other parameters are same as Fig. 2.

Figure 6

Thermoelectric figure of merit as a function of the chemical potential of the normal leads for different values of the junction parameters. All of the other parameters are same as Fig. 2.

Figure 7

Normalized electrical conductance (left panel) and normalized thermoelectrical conductance (right panel) as a function of the chemical potential of the normal leads. All of the other parameters are same as Fig. 2.

Figure 8

Seebeck coefficient as a function of the chemical potential of the normal leads for different values of the junction parameters. All of the other parameters are same as Fig. 2.

Figure 9

Electrical conductance (left panel) and Seebeck coefficient (right panel) as a function of the length (figures (a,b,e,f)), and chemical potential of the WSM layer (figures (c,d,g,h)) in terms of different values of $k_0$ and $\gamma$. All of the other parameters are same as Fig. 4.

Figure 10

The electronic contribution to the thermal conductance as a function of the chemical potential of the normal leads for different values of the junction parameters. All of the other parameters are same as Fig. 2.

Figure 11

Thermoelectric figure of merit as a function of the chemical potential of the normal leads for different values of the junction parameters. All of the other parameters are same as Fig. 2.