It is not unlikely that the tunneling transport through hBN is affected by impurity-or defectinduced mid-gap states, as predicted for an hBN/graphene heterostructure and evidenced by a slight p-doping in bulk hBN. Impurities usually average less than 10 18 cm -3 in good quality hBN, which can however be exceeded locally. Our own measurements of bulk hBN and hBN/graphite heterostructure by XPS and Raman spectroscopy, respectively, did not reveal any additional peaks or shoulders in the relevant spectral regions, suggesting that the defect/impurity concentrations are low (Supporting Fig. ). Furthermore, the dielectric breakdown measurements yielded a high dielectric strength of ~2 V nm -1 (Supporting Fig. ), in agreement with previous reports.