Gate-Training Effects and Enhanced Transparency in HgTe Quantum Spin Hall Edge Channels

HgTe quantum wells are the most intensively studied 2D topological insulators. The key property of these systems is the existence of helical edge channels, which has been investigated in detail in various experiments. However, the experimental observation of quantized conductance in these edge channels is limited to only very small sample dimensions (in the range of a few $\mu$m), which is not yet entirely understood. In this talk I will first discuss the influence of the size of the band gap to this limitation. One finds that an enlarged band gap does not result in a more stable quantization, as one would naively expect. We suggest that this the approach of gating affects our devices i.e. potential fluctuations prevent the sample from the bulk insulating state homogeneously. I will show that the non-quantized conductance in large samples can be influenced by hysteretic gate training and thus smoothening the potential landscape in the quantum well. On a 58 $\mu$m long pair of edge channels, this leads to a yet unseen conductance of 1.6 $e^2$/h, almost reaching the theoretically predicted value of 2 $e^2$/h.