Coulomb Blockade and Superuniversality of the $\theta$ Angle

Based on the Ambegaokar-Eckern-Schön approach to the Coulomb blockade, we develop a complete quantum theory of the single electron transistor. We identify a previously unrecognized physical observable in the problem that, unlike the usual average charge on the island, is robustly quantized for any finite value of the tunneling conductance as the temperature goes to absolute zero. This novel quantity is fundamentally related to the nonsymmetrized current noise of the system. Our results display all of the superuniversal topological features of the $\theta$ angle concept that previously arose in the theory of the quantum Hall effect.

Figure 1

Unified scaling diagram of the Coulomb blockade in terms of the SET conductance $g^{\prime }$ and the quasiparticle charge $q^{\prime }$. The arrows indicate the scaling toward $T=0$ (see text).