Superlattices and Microstructures, Vol. 11, NO. 2, 1992 205 CORRELATION FUNCTIONS AND QUANTIZED NOISE IN MESOSCOPIC SYSTEMS Tilmann Kuhn, Lino Reggiani, and Luca Varani Dipartimento di Fisica, Universitd di Modena Via Campi 213/A, 41100 Modena, Italy (Received 19 May 1991) We present a theoretical calculation of the current correlation functions and the associated noise spectra of a quasi one-dimensional system terminated by ideal contacts. The shape of the correlation functions is directly related to the micro- scopic carrier dynamics. When applying a voltage we find: In the classical limit the low-frequency noise spectrum recovers the well-known shot noise formula at high voltages. In the degenerate limit it is suppressed due to quantum-mechanical correlations. The extension of the theory to a multi-subband system shows that in the presence of an applied voltage the step height of the low-frequency spectral density is reduced to one half of its equilibrium value. 1. Introduction Electronic noise in mesoscopic systems in the ab- sence of dissipation is of physical interest due to its di- rect relation to fundamental constants. In particular, noise spectra at low-frequencies have been investigated recently in several theoretical [l-3] and experimental (4-71 papers. The aim of this contribution is to present a theoretical analysis of the noise spectrum under equi- librium and nonequilibrium conditions in the full fre- quency range, or equivalently, to analyze the full time dependence of the current correlation function. As a matter of fact, the shape of the correlation function can be directly related to characteristic times of the carrier transport [3]. Therefore, a study of the full time depen- dence of fluctuations in mesoscopic systems can provide additional insight into the microscopic dynamics. 2. Theory We consider a two-terminal device of length L, terminated by ideal contacts. The cross-section is as- sumed to be so small that the electronic states in the transverse directions are quantized and can be de- scribed by a quantum number 0. In the stationary state, the current noise in this system is determined by the correlation function CI(t) of current fluctuations under the condition of a constant voltage applied at the contacts: Cr(t) = +(O)I(t) + I(t - (I)2 (1) with where j&z, t) is the current operator in subband a and brackets indicate averages with respect to the ap- propriate statistical operator. Equation (2) follows from a quantum generalization of the Ramo-Shockley theorem (81. The current spectral density is then ob- tained from the Wiener-Khintchine theorem according to J +m S1(w)= 2 dl eiYtCr(t) (3) The current operator jzTaTz, t) can be expressed in terms of the Wigner operator gp in subband r~ which, by definition, is given by g&z,l) = -J& Jdrfeikzt . !tj&(% + ;, t)*,,,(z - fJ) (4) according to j,?, = $Idkkg,(k,z,t). Here, Sz,, (9, ,) denote the field creation (annihilation) opera- tors’in subband a with spin s and m is a scalar effec- tive mass. With these definitions, the current correla- tion function can be expressed in terms of the “ Wigner correlation function” 6fPa as Cl(t) = (-$)2 c pkdk’ a,0 __- 0749-6036/92/020205 + 05 $02.00/O 0 1992 Academic Press Limited