The electronic properties of hexagonal boron nitride (hBN) make it an ideal insulating or tunnel barrier in devices and heterostructures based on van der Waals crystals.  Of topical interest are the localised states due to defects and impurities in hBN which have potential for future applications in quantum information technology.    

Here we investigate the observation of sharp resonant peaks in the low temperature differential conductance of single-gated and double-gated transistors composed of a thin hBN tunnel barrier sandwiched between two graphene layers, which act as source and drain electrodes [1].  Our data and analysis show that each peak arises from electrons tunnelling resonantly through a localized state within the energy gap of the hBN barrier layer.  We compare the measurements with our modelling to determine the energy level positions of these states with respect to the valence band edge and the Dirac points of the graphene layers. Each state's spatial coordinate perpendicular to the hBN-graphene interfaces is also deduced from the data.   
  
A strong suppression of the tunnel conductance is observed in the presence of a quantising magnetic field applied perpendicular to the layers [2]. Analysis and modelling of the measured temperature and magnetic field dependences of the tunnel current suggest that the observed suppression of the differential conductance arises from e-e interactions which form a magnetically-induced Coulomb gap in the tunnelling density of states of the graphene layers at low temperatures. The presence of the localised state in the barrier, which acts as an electron “injector”, provides an technique to explore this many-body quantum phenomena in graphene-based devices and more generally can offer insights into the electronic properties of the layers of tunnel devices.  

[1] Greenaway et al., Communications Physics 1, 94 (2018)  
[2] Vdovin et al., Communications Physics 6, 159 (2023)