The problem of Macroscopic Charge Quantization in the Coulomb Blockade

Based on the Ambegaokar-Eckern-SchOn 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 non-symmetrized 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.