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Quantum transport of Dirac fermions in HgTe gapless quantum wells

We study transport properties of HgTe quantum wells with critical well thickness, where the band gap is closed, and the low energy spectrum is described by a single Dirac cone. In this work, we examined both macroscopic and micron-sized (mesocopic) samples. In micron-sized samples, we observe a magnetic field induced, quantized resistance ($\sim h/2e^{2}$) at Landau filling factor $ν=0$, corresponding to the formation of helical edge states centered at the charge neutrality point (CNP). In macroscopic samples, the resistance near zero Landau level (LL) reveals strong oscillations, which we attribute to scattering between the edge $ν=0$ state and bulk $ν\neq 0$ hole LL. We provide a model taking an empirical approach to construct a LL diagram based on a reservoir scenario, formed by the heavy holes.