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Based on the Ambegaokar-Eckern-Schön approach [1] to the problem of Coulomb blockade we develop [2] 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 [3], is robustly integer quantized for any finite value of the tunneling conductance as the temperature goes to the absolute zero. This novel quantity is the sum of the average charge on the island and the term which is fundamentally related to the non-symmetrized (quantum) current noise in the single electron transistor. Our results allow us to establish similarity between the problem of Coulomb blockade in the single electron transistor on the one hand, and the theory of the integer quantum Hall effect on the other hand. The novel quantity is in all respects the same as the Hall conductance whereas the conductance of the single electron transistor is analogous to the longitudinal conductance. To summarize, the problem of Coulomb blockade in the single electron transistor is one more interesting example of the condensed matter system where the theta-angle concept, which previously arose in the theory of the quantum Hall effect, can be studied in details.
[1] V. Ambegaokar, U. Eckern, and G. Schön, Phys Rev. Lett. 48, 1745 (1982). [2] I. S. Burmistrov and A. M. M. Pruisken, "Coulomb blockade and superuniversality of the theta angle", cond-mat/0702400 [accepted for publication in Phys. Rev. Lett.] [3] K.A. Matveev, Sov. Phys. JETP 72, 892 (1991). |
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