Tunneling into a finite Luttinger liquid coupled to noisy capacitive leads

Tunneling spectroscopy of one-dimensional interacting wires can be profoundly sensitive to the boundary conditions of the wire. Here, we analyze the tunneling spectroscopy of a wire coupled to capacitive metallic leads. Strikingly, with increasing many-body interactions in the wire, the impact of the boundary noise becomes more prominent. This interplay allows for a smooth crossover from standard 1D tunneling signatures into a regime where the tunneling is dominated by the fluctuations at the leads. This regime is characterized by elevated zero-bias tunneling alongside a universal power-law decay at high energies. Furthermore, local tunneling measurements in this regime show a unique spatial-dependence that marks the formation of plasmonic standing waves in the wire. Our result offers a tunable method by which to control the boundary effects and measure the interaction strength (Luttinger parameter) within the wire.