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Topological insulators represent a new quantum state of matter which ischaracterized by edge or surface states and an insulating band gap in the bulk.In a two dimensional (2D) system based on the HgTe quantum well (QW) ofcritical width random deviations of the well width from its average valueresult in local crossovers from zero gap 2D Dirac fermion system to either the2D topological insulator or the ordinary insulator, forming a complicatedin-plane network of helical channels along the zero-gap lines. We have studiedexperimentally the transport properties of the critical width HgTe quantumwells near the Dirac point, where the conductance is determined by apercolation along the zero-gap lines. The experimental results confirm thepresence of percolating conducting channels of a finite width. Our workestablishes the critical width HgTe QW as a promising platform for the study ofthe interplay between topology and localization.

Transport through the network of topological channels in HgTe based quantum well