Theory of the STM detection of Wigner molecules in spin-incoherent CNTs

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 one 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.