We provide a theory of the electronic transport properties of a graphene layer
functionalized with molecular switches. Our considerations are motivated by
the spiropyran?merocyanine system which is non-polar in its ring-closed
spiropyran form and zwitterionic in its ring-open merocyanine form. The
reversible switching between these two isomers affects the carriers in
graphene through the associated change in the molecular dipole moment, turning
the graphene layer into a sensor of the molecular switching state. We present
results for both the quasiclassical (Boltzmann) and the quantum coherent
regimes of transport. Quite generally, we find a linear sensitivity of the
conductance on the molecular dipole moment whenever quantum interference
effects play an essential role which contrasts with a quadratic (and typically
weaker) dependence when quantum interference is absent
