Quantum Oscillations at Integer and Fractional Landau Level Indices in Single-Crystalline ZrTe₅

A three-dimensional (3D) Dirac semimetal (DS) is an analogue of graphene, but with linear energy dispersion in all (three) momentum directions. 3D DSs have been a fertile playground in discovering novel quantum particles, for example Weyl fermions, in solid state systems. Many 3D DSs were theoretically predicted and experimentally confirmed. We report here the results in exfoliated ZrTe 5 thin flakes from the studies of aberration-corrected scanning transmission electron microscopy and low temperature magneto-transport measurements. Several unique results were observed. First, a π Berry phase was obtained from the Landau fan diagram of the Shubnikov-de Haas oscillations in the longitudinal conductivity σ_xx. Second, the longitudinal resistivity ρ_xx shows a linear magnetic field dependence in the quantum limit regime. Most surprisingly, quantum oscillations were also observed at fractional Landau level indices N = 5/3 and 7/5, demonstrating strong electron-electron interaction effects in ZrTe₅.