  The linear conductance of a carbon nanotube quantum dot in the Wigner
molecule regime, coupled to two scanning tunnel microscope tips is inspected.
Considering the high temperature regime, the nanotube quantum dot is described
by means of the spin-incoherent Luttinger liquid picture. The linear
conductance exhibits spatial oscillations induced by the presence of the
correlated, molecular electron state. A power-law scaling of the electron
density and of the conductance as a function of the interaction parameter are
found. They confirm local transport as a sensitive tool to investigate the
Wigner molecule. The double-tip setup allows to explore different transport
regimes with different shapes of the spatial modulation, all bringing
information about the Wigner molecule.
