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

We consider the electron transport in the capacitively coupled single-electron transistor with an ultrasmall Tomonaga-Luttinger liquid island. The charging effects, as well as the Tomonaga-Luttinger liquid nature, are treated by a self-consistent theory of the Coulomb blockade using the open boundary bosonization technique. Analytical expressions for conductance are derived in the limits of low and high voltages and temperatures, for bulk and edge island contact geometries, and for arbitrary environmental impedance. For an infinite system, we obtain the power law of the conductance with the exponent changed from the usual Tomonaga-Luttinger exponent due to the effects of the electromagnetic environment. For a finite system, we obtain expressions for the conductance as a function of voltage near the Coulomb blockade boundary and as a function of temperature for low temperatures; these expressions differ from the usual power-law behavior. The results show the potential for improving the accuracy of single-electron devices such as those used in electrical metrology.