Observation of sequential quantum oscillations induced by mini-Landau bands in a three-dimensional Dirac semiconductor

Abstract

Quantum oscillations, the oscillatory behavior of electrical and thermodynamic properties, are typically observed in metals and vanish in the quantum limit under strong magnetic fields1. Phenomena such as the fractional quantum Hall effect2, the Hofstadter butterfly3,4, and recent observations of quantum oscillations in exotic insulators are notable exceptions5-12. The narrow-gap Dirac semiconductor ZrTe5, a less exotic material without strong correlations or artificially engineered superlattices, nevertheless exhibits resistance oscillations in the quantum limit13 but can be interpreted within a simple Zeeman-effect-based picture14,15, which remains conventional quantum oscillations without exotic properties. Here, we report the observation of unexpected mini-oscillations superimposed on Zeeman-effect-induced main oscillations in the quantum limit. The subtracted mini-oscillations are periodic in 1/B with the highest frequency equal to 2.1% of the first Brillouin zone and have extremely heavy effective mass ~ 2me, which is unexpected in ZrTe5 given its ultralow carrier density. Additionally, the mini-oscillations exhibit sequential features that are synchronized with the main oscillations, suggesting an internal structure of the Landau bands. However, they appear incompatible with the Hofstadter butterfly due to the highly anisotropic/three-dimensional crystal structure. These sequential mini-oscillations correlate with the commensurability resonance effect with subunity fractions observed in angular magnetoresistance, relating to the formation of mini-Landau bands. Our results present solid experimental evidence of exotic quantum oscillations in the quantum limit beyond currently available mechanisms, and establish ZrTe5, a prototypical Dirac semiconductor, as a simple platform parallel to correlated insulators for exploring exotic oscillations.