  Graphene is an attractive electrode material to contact nanostructures down
to the molecular scale since it can be gated electrostatically. Gating can be
used to control the doping and the energy level alignment in the nanojunction,
thereby influencing its conductance. Here we investigate the impact of
electrostatic gating in nanojunctions between graphene electrodes operating at
finite bias. Using first principles quantum transport simulations, we show that
the voltage drop across \emph{symmetric} junctions changes dramatically and
controllably in gated systems compared to non-gated junctions. In particular,
for \emph{p}-type(\emph{n}-type) carriers the voltage drop is located close to
the electrode with positive(negative) polarity, i.e. the potential of the
junction is pinned to the negative(positive) electrode. We trace this behaviour
back to the vanishing density of states of graphene in the proximity of the
Dirac point. Due to the electrostatic gating, each electrode exposes different
density of states in the bias window between the two different electrode Fermi
energies, thereby leading to a non-symmetry in the voltage drop across the
device. This selective pinning is found to be independent of device length when
carriers are induced either by the gate or dopant atoms, indicating a general
effect for electronic circuitry based on graphene electrodes. We envision this
could be used to control the spatial distribution of Joule heating in graphene
nanostructures, and possibly the chemical reaction rate around high potential
gradients.
