Thermoelectric quantum oscillations in ZrSiS

Abstract

Topological semimetals are systems in which conduction and valence bands cross each other and the crossings are protected by topological constraints. These materials provide intriguing tests for fundamental theories, while their unique physical properties promise a wide range of possible applications in low-power spintronics, optoelectronics, quantum computing and green energy harvesting. Here we report our study of the thermoelectric power of single-crystalline ZrSiS that is believed to be a topological nodal-line semimetal. We show that the thermoelectric power is an extremely sensitive probe of multiple quantum oscillations that are visible in ZrSiS at temperatures as high as 100 K. Two of these oscillations are shown to arise from three- and two-dimensional electronic bands, each with linear dispersion and the additional Berry phase predicted theoretically for materials with non-trivial topology. Our work not only provides further information on ZrSiS but also suggests a different route for studying other topological semimetals.

Figure 1. The temperature dependence of the a axis thermoelectric power for ZrSiS in zero magnetic field.

Inset shows the low temperature part of the same data and a linear fit through the origin.

Figure 2. The magnetic field dependence of the thermoelectric power in ZrSiS at T=1.7 K.

Panel (a) presents a broad view, whereas panels (b–d) show the same data on different scales chosen to expose distinct oscillation frequencies—the corresponding values of F (in Tesla) are indicated. The arrows mark a jump at B⁻¹=0.15 T⁻¹, as discussed in the text.

Figure 3. The FFT spectrum calculated for the thermoelectric power data at T=1.7 K.

Inset shows the low-frequency part, where peaks are attributed to F¹, F² and F³ frequencies as well as higher harmonics of F².

Figure 4. The magnetic field dependences of the thermoelectric power in ZrSiS at selected temperatures.

Upper panel (a) shows low temperature (T≤20 K) data (shifted vertically by 1.5 μV K⁻¹ for clarity), where high frequency oscillations were filtered out. ‘−’ and ‘+’ symbols mark Zeeman splitting. Bottom panel (b) shows the raw high-temperature data (T≥20 K).

Figure 5. The magnetic field dependence of the oscillatory part of the thermoelectric power in ZrSiS at high temperature.

Insets show the Landau-level index plot for F³ (upper one, 57 T) and F⁴ (bottom one, 240 T) together with parameters of the linear fits.

Figure 6. The magnetic field dependence of the filtered (low frequency) thermoelectric power data in ZrSiS at 1.7 K shown on different vertical scales.

The scale for panel (a) is −2 to 1.6μV/K and for panel (b) is 0.04 to 0.45μV/K. Inset shows the Landau level index plot for F¹ (8.5 T) together with parameters of the linear fit.

Figure 7. The temperature dependences of the peak heights obtained from the FFT.

The top panels (a–e) show FFT spectra calculated for various temperatures, the bottom panels (f–j) show the temperature dependence of the peak heights determined from the corresponding FFT plots. Solid red lines in the bottom panels are fits to equation (1).