In a topological Weyl semimetal [1], the correspondence between bulk Weyl nodes and surface Fermi-arc states gives rise to a unique nonlocal cyclotron motion via the electron tunnelings between the top and bottom Fermi-arc surface states as shown in Fig. 1, which is referred to as the Weyl-orbit effect (WOE) and exhibits an unusual thickness dependent quantum oscillations [2]. In our recent publication at npj Quantum Materials (https://rdcu.be/c31ub) [3], such an unusual thickness dependent Weyl-orbit quantum oscillation was demonstrated in untwinned Weyl metal thin films of SrRuO₃ (SRO) grown by oxide molecular beam epitaxy (MBE) facility at Institute of Physics, Academia Sinica, Taipei in Taiwan. The quantum oscillation measurements with fields up to 35 T were carried out at EMFL-Nijmegen in Netherlands in collaboration with Prof. S. Wiedmann’s group, and the rigorous band calculations were done by Prof. Wei-Cheng Lee’s group at SUNY Binghamton in USA. The high precision X-ray characterizations on SRO thin films were performed at the NSRRC, Hsinchu in Taiwan in collaboration with Director Chia-Hung Hsu‘s group.

By using adsorption-controlled growth technique [4], the high crystalline and untwinned SRO thin films were grown on miscut SrTiO₃ (001) substrates, which was confirmed by the high precision X-ray measurements. In order to avoid anisotropy-related effects, the electric bias currents for magnetotransport measurements in SRO thin films with different thicknesses were all applied along the same SRO orthorhombic [1-1 0] direction.  From rigorous angular and temperature dependent quantum oscillation measurements as shown in Fig. 2(a), we identified a small 2D like Fermi pocket with an oscillation frequency of F_s1 ~ 30 T and a light effective mass. In addition, a number of unusual features in the F_s1  quantum oscillations were observed. First, its oscillation amplitude attains a maximum for thickness ranging from 10 to 20 nm, and the phase of the oscillation also show systematic shift with the SRO film thickness. Secondly, when plotting the corresponding Landau fan diagram shown as star symbols in Fig. 2(b), an unusual large phase shift with an intercept of about -2, extrapolated from the high Landau index (n) regime, and a clear concave downward curvature were found. Those features turn out to agree well with the WOE theory with non-adiabatic corrections.           

On the other hand, according to the simulated curves due to WOE with different film thicknesses (ts) as demonstrated in Fig. 2(b), an optimum SRO thin film thickness of about 10-20 nm not only favors the WOE over other contributions from bulk Fermi pockets but also makes the Weyl-orbit quantum oscillations accessible at lower field regime, where the unusual large phase shift and also concave downward curvature in the Landau fan diagram can be better revealed in experiment. Our results may thus provide a practical guideline for identifying the intriguing WOE in a Weyl thin film system. 

 References:

[1] Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Y. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011).

[2] Potter, A. C., Kimchi, I. & Vishwanath, A. Quantum oscillations from surface Fermi arcs in Weyl and Dirac semimetals. Nat. Commun. 5, 5161 (2014).

[3] Kar, U., Singh, A.K., Hsu, YT. et al. The thickness dependence of quantum oscillations in ferromagnetic Weyl metal SrRuO₃. npj Quantum Mater. 8, 8 (2023). 

[4] Nair, H. P. et al. Synthesis science of SrRuO₃ and CaRuO₃ epitaxial films with high residual resistivity ratios. APL Mater. 6, 046101 (2018).