  It is straightforward to calculate the conductance of a quantum device once
all its scattering centers are fully specified. However, to do this in reverse,
i.e., to find information about the composition of scatterers in a device from
its conductance, is an elusive task. This is particularly more challenging in
the presence of disorder. Here we propose a procedure in which valuable
compositional information can be extracted from the seemingly noisy spectral
conductance of a two-terminal disordered quantum device. In particular, we put
forward an inversion methodology that can identify the nature and respective
concentration of randomly-distributed impurities by analyzing energy-dependent
conductance fingerprints. Results are shown for graphene nanoribbons as a case
in point using both tight-binding and density functional theory simulations,
indicating that this inversion technique is general, robust and can be employed
to extract structural and compositional information of disordered mesoscopic
devices from standard conductance measurements.
