Tunneling spectroscopy calculations of a Luttinger wire

We investigate the tunneling current between a one-dimensional (1D) wave guide and a metallic electrode. To be specific, we consider as an electrode a two-dimensional electron gas (2DEG) coupled to the 1D system over a finite length L by a thin tunnel barrier. Treating the 1D electrons within the Luttinger liquid model, we evaluate the tunneling current which flows through the barrier. Tunneling is assumed to be local (rather than being described by a constant matrix element in reciprocal space) and the spatial extent of the contact is taken into account. A characteristic maximum of the current for optimal barrier lengths is found. We calculate the finite-temperature spectral density of the 1D correlated electrons, which is needed to evaluate the current in the peak region