Conductance of the capacitively coupled single-electron transistor with a Tomonaga-Luttinger liquid island in the Coulomb blockade regime

We consider transport properties of the capacitively coupled single-electron transistor with a one-dimensional island. We describe the island using the Tomonaga-Luttinger liquid model, and obtain the analytic expressions for the conductance in the limits of low and high voltages and temperatures, and for arbitrary electromagnetic environment. The results show potential for applications of such nanoscale devices in electrical metrology.