Langevin approach for the shot noise calculation in single-electron tunneling

– The Langevin method for the calculation of the shot noise in correlated singleelectron tunneling is developed. Its equivalence to the existing Fokker-Plank-type approach is shown in the “orthodox” framework. The advantage of the Langevin method is a natural possibility to describe also the fluctuations in the high (“quantum”) frequency range. Correlated single-electron tunneling [1] has remained an attractive topic during last decade. Because in the systems of small-capacitance high-resistance tunnel junctions electrons tunnel almost as the classical particles, most experiments are well described within the framework of “orthodox” theory [1] based on the classical master equation. The shot noise in single-electron tunneling is due to the randomness of tunneling events (for general review on the shot noise in mesoscopic physics see ref. [2]). The basic theory of the shot noise in single-electron transistor has been developed in refs. [3,4] and independently in ref. [5]. Despite the classical description of the system, the current in this theory is treated as a kind of an operator because it is caused by tunneling events which change the charge state of the system. The shot noise in single-electron tunneling has been studied theoretically in a number of publications — see, e.g., refs. [6-12] (while there is only one experiment [13] so far). For example, the case of Andreev reflection has been considered in ref. [9]. The shot noise in single-electron transistor with discrete energy levels has been studied in ref. [10]. The shot noise theory has also been applied to single-electron systems other than single-electron transistors [11, 12]. Besides the noise in the “orthodox” frequency range ω ∼ W/eR (where W is a typical energy and R is a typical resistance), the noise in the “quantum” frequency range ω ∼ W/h̄ has been studied for a particular system [11] and the matching of two limits has been proven; however, an approach unifying both frequency ranges in one formalism has not been found. The existing formalism for the shot noise in single-electron tunneling is of the Fokker-Plank type and is based on the deterministic master equation. In the present letter we show that the alternative Langevin approach, in which the random term is introduced into the evolution equation, can also be applied (the method used is similar to that developed in ref. [14]).