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.

Nearly massless Dirac fermions and strong Zeeman splitting in the nodal-line semimetal ZrSiS probed by de Haas–van Alphen quantum oscillations

“…2b) Table 1, which is clearly nontrivial. This is consistent with the previous SdH [50 -51, 53] and thermoelectric [56] quantum oscillation studies from which non-trivial Berry phase for the high frequency band has also been obtained by fitting the oscillation patterns or by using the LL fan diagram (i.e. the LL index n as a function of the inverse of magnetic field 1/B n ).…”

“…2a). We note similar low and high frequencies have also been observed in previous SdH [50][51][52][53] and thermoelectric oscillation studies [56]. As will be discussed later, both the low and high frequency oscillations originate from the Fermi surface (FS) comprised of the nodal-line bands, The extreme FS cross section areas A F estimated using the Onsager relation F = (Φ 0 /2π 2 )A F (Φ 0 = h/2e is the magnetic flux quantum) are ~0.08 and 2.3nm -2 , respectively, for the Fermi surface pocket associated with F α and F β .…”

“…Of course, the fit made below 1T covers limited data points, which may give rise to larger uncertainty for the fitted Berry phase. The nontrivial Berry phase for the low frequency (8.4T) band obtained from our dHvA oscillation studies is in contrast with that obtained from the thermoelectric oscillations, in which the intercept of the LL index plot is nearly zero [56]. Such inconsistency may be caused by the fact that the integer LL index was assigned when DOS(E F ) reaches a minimum in our work but maximum (i.e., maximum thermopower) in Ref.…”

“…This discrepancy might be due to the limited magnetic field range (B ≤ 7T) in our experiments. Indeed, though only two oscillation frequencies were probed in our dHvA experiments and several other previous low field SdH studies (B ≤ 9T) [50][51], the recent thermoelectric [56] and high field (B ≤ 33T) SdH [53] experiments have revealed additional frequency around 600T, which is attributed to the electron pocket [53].…”

“…Such inconsistency may be caused by the fact that the integer LL index was assigned when DOS(E F ) reaches a minimum in our work but maximum (i.e., maximum thermopower) in Ref. [56].…”