Thermoelectric response of nodal-line semimetals: Probing the Fermi surface topology

We investigate the low-temperature thermoelectric properties of three-dimensional nodal-line semimetals within the semiclassical Boltzmann formalism. Considering short-range interaction between electrons and scattering agents, we calculate the anisotropic relaxation times and then obtain the charge conductivity and thermopower along the radial and the axial directions with respect to the nodal-line plane. Increasing the carrier concentration, a sharp change in the thermopower signals topological transition in the shape of the Fermi surface from a torus into an ellipsoid. An adequate treatment of the energy and direction dependence of the relaxation time is necessary for the observation of the topological transition of the Fermi surface in the thermoelectric properties.

Figure 1

Sketches of the Fermi surface of a three-dimensional nodal-line semimetal at two different Fermi energies ${\varepsilon }_{\mathrm{F}}<{\varepsilon }_0$ (a) and ${\varepsilon }_{\mathrm{F}}>{\varepsilon }_0$ (b). (c) The low energy dispersions of electrons in a three-dimensional nodal-line semimetal (in units of ${\varepsilon }_0$) versus $k_x/k_0$, for $k_y=k_z=0$.

Figure 2

The zero temperature static charge conductivities versus the Fermi energy ${\varepsilon }_{\mathrm{F}}$ along the axial (solid blue) and axial (dashed red) directions (in units of ${\sigma }_0$ and $2{\lambda }^2{\sigma }_0$, respectively), obtained within the constant relaxation time approximation.

Figure 3

The Fermi energy dependance of the radial (solid blue) and axial (dashed red) thermopowers (in units of $S_0$) obtained using the constant relaxation time. Inset: The ratio between radial and axial thermopowers $S_{xx}/S_{zz}$ versus the Fermi energy.

Figure 4

The dependence of radial (solid blue) and axial (dashed red) conductivities (in units of ${\sigma }_0$ and $2{\lambda }^2{\sigma }_0$, respectively) on the Fermi energy ${\varepsilon }_{\mathrm{F}}$ at zero temperature obtained from the anisotropic relaxation time.

Figure 5

The Fermi energy dependence of the radial (solid blue) and axial (solid red) thermopowers (in units of $S_0$) obtained from the anisotropic relaxation time. Dashed lines show the same results obtained from the numerical solution of Eq. (8) at $k_{\mathrm{B}}T=0.01{\varepsilon }_0$. Inset: The ratio between radial and axial thermopowers $S_{xx}/S_{zz}$ versus the Fermi energy.