Quantum Hall effect near the charge neutrality point in two-dimensional electron-hole system

We study the transport properties of $HgTe$-based quantum wells containing simultaneously electrons and holes in magnetic field B. At the charge neutrality point (CNP) with nearly equal electron and hole densities, the resistance is found to increase very strongly with B while the Hall resistivity turns to zero. This behavior results in a wide plateau in the Hall conductivity $\sigma_{xy}\approx 0$ and in a minimum of diagonal conductivity $\sigma_{xx}$ at $\nu=\nu_p-\nu_n=0$, where $\nu_n$ and $\nu_p$ are the electron and hole Landau filling factors. We suggest that the transport at the CNP point is determined by electron-hole "snake states" propagating along the $\nu=0$ lines. Our observations are qualitatively similar to the quantum Hall effect in graphene as well as to the transport in random magnetic field with zero mean value.