Quantum Oscillations at Integer and Fractional Landau Level Indices in ZrTe5*

A three-dimensional (3D) Dirac semimetal (DS) is an analogue of graphene, but with linear energy dispersion in all (three) momentum directions. We report here the results in exfoliated ZrTe$_{\mathrm{5}}$ thin flakes from the studies of scanning transmission electron microscopy and low temperature magneto-transport measurements. Several unique results were observed. First, a $\pi $ Berry phase was obtained from the Landau fan diagram. Second, the longitudinal resistivity shows linear magnetic field dependence. 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 ZrTe$_{\mathrm{5}}$.