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Authors  I.S. Burmistrov, A.M.M. Pruisken  Title  Macroscopic charge quantization in singleelectron devices 
Journal  Physical Review B 
Volume  81 
Year  2010 
Issue  8 
Pages  085428 
ISSN  10980121 
Faculty  Faculty of Science 
Institute/dept.  FNWI: Institute for Theoretical Physics (ITF) 
Abstract  In a recent paper by the authors [I. S. Burmistrov and A. M. M. Pruisken, Phys. Rev. Lett. 101, 056801 (2008)] it was shown that singleelectron devices (singleelectron transistor or SET) display “macroscopic charge quantization” which is completely analogous to the quantum Hall effect observed on very different electron systems. In this investigation we present more detail on these findings. Based on the AmbegaokarEckernSchön (AES) theory of the Coulomb blockade we introduce a general response theory that probes the sensitivity of SET to changes in the boundary conditions. This response theory defines a set of physical observables and we establish the contact with the standard results obtained from ordinary linearresponse theory. The response parameters generally define the renormalization behavior of the SET in the entire regime from weak coupling with large values of the tunneling conductance all the way down to the strongcoupling phase where the system displays the Coulomb blockade. We introduce a general criterion for charge quantization that is analogous to the Thouless criterion for Anderson localization. We present the results of detailed computations on the weakcoupling side of the theory, i.e., both perturbative and nonperturbative (instantons). Based on an effective theory in terms of quantum spins we study the quantum critical behavior of the AES model on the strongcoupling side. Consequently, a unifying scaling diagram of the SET is obtained. This diagram displays all the super universal topological features of the θ angle concept that previously arose in the theory of the quantum Hall effect. 
Document type  Article 
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