Dynamic band structure and capacitance effects in scanning tunneling spectroscopy of bilayer graphene

Abstract

We develop a fully self-consistent model to describe scanning tunneling spectroscopy (STS) measurements of Bernalstacked bilayer graphene (BLG), and we compare the results of our model to experimental measurements. Our results show that the STS tip acts as a top gate that changes the BLG bandstructure and Fermi level, while simultaneously probing the voltage-dependent tunneling density of states (TDOS). These effects lead to differences between the TDOS and the local density of states (LDOS); in particular, we show that the bandgap of the BLG appears larger than expected in STS measurements, that an additional feature appears in the TDOS that is an artifact of the STS measurement, and that asymmetric charge distribution effects between the individual graphene layers are observable via STS. arXiv:1909.04280v2 [cond-mat.mtrl-sci]

Comprehensive Electrostatic Modeling of Exposed Quantum Dots in Graphene/Hexagonal Boron Nitride Heterostructures

“…We calculated the shape of the tip’s doping profile by using a standard Poisson solver; where the tip is modeled by a charged sphere with an 80 nm radius that is placed 7.5 away from a metal surface. The tip radius and distance to graphene that we used are both consistent with values found in the literature [ 18 , 35 , 36 ]. With this analysis we acquire the tip induced doping profile shown in Figure 4 b.…”

“…The tip radius and distance to graphene that we used are both consistent with values found in the literature [18,35,36]. With this analysis we acquire the tip induced doping profile shown in Figure 4b.…”

Direct Visualization of Native Defects in Graphite and Their Effect on the Electronic Properties of Bernal-Stacked Bilayer Graphene

“…Further asymmetry is produced by the gap closing at V G ≈ −52 V rather than V G = 0 V. This offset is attributed to the work function mismatch between the tip and the sample. 35,36 As a tentative explanation of feature (ii) (enhancement of small momentum transfer for low gate voltages), we first note the proximity of the gap edge in these cases (V G = +20 V, V G = −10 V, and V G = −20 V). However, the precise mechanisms behind this enhancement cannot be explained by pure band structure arguments, as we demonstrate in the Supporting Information (section VII) by showing computed joint density of states at various gate voltages.…”

“…This asymmetry is due to the polarization of the BLG sheet in the z direction upon application of the electric field induced by the gate and the STM tip. Further asymmetry is produced by the gap closing at V G ≈ −52 V rather than V G = 0 V. This offset is attributed to the work function mismatch between the tip and the sample. , …”

“…Figure b–h shows the simulated FFT for the same doping as in the experiments ( E F – E CNP indicated in Figure ), all on the same z -scale. The band gap induced by the perpendicular electric field produced by the backgate and the STM tip is considered in the simulation. − The method for determining the values used in the simulation for the band gap and for the electronic doping for each gate voltage is presented in section III of the Supporting Information. The T-matrix results presented in Figure b–h are obtained by averaging the signatures of dopants located on the four atomic sites of the BLG unit cell (A 1 , B 1 , A 2 , and B 2 ; see inset of Figure a) and only considering the density of states (DOS) in the top layer (similar to the situation for the STM experiment).…”