Statistical theory of shot noise in quasi-one-dimensional field-effect transistors in the presence of electron-electron interaction

We present an expression for the shot noise power spectral density in quasi-one dimensional conductors electrostatically controlled by a gate electrode, which includes the effects of Coulomb interaction and of Pauli exclusion among charge carriers. In this sense, our expression extends the well known Landauer-B\"uttiker noise formula to include the effect of Coulomb interaction inducing fluctuations of the potential in the device region. Our approach is based on evaluating the statistical properties of the scattering matrix and on a second-quantization many-body description. From a quantitative point of view, statistical properties are obtained by means of Monte Carlo simulations on an ensemble of different configurations of injected states, requiring the solution of the Poisson-Schr\"odinger equation on a three-dimensional grid, with the nonequilibrium Green's functions formalism. In a series of examples, we show that failure to consider the effects of Coulomb interaction on noise leads to a gross overestimation of the noise spectrum of quasi-one-dimensional devices.