Modified correlation entropy of a gated nanowire system described by a numerically determined non‐equilibrium many‐body statistical operator

Abstract

A numerical correlation measure of the interacting electrons in a semiconductor nanowire‐based field‐effect transistor (NWFET) is presented, which solely quantifies correlation whether the preparation of the system is pure or mixed, in contrast to the single‐particle‐reduced entropy, which depends on the degree of correlation and mixture as well. This numerical measure, which is termed modified correlation entropy ΔS, is based on the concept of von Neumann entropy, whose calculation is dependent on the non‐equilibrium many‐body statistical operator of the system. Therefore, we present a numerical approach to construct such a non‐equilibrium many‐body statistical operator trueρˆrel for relevant quasi‐bound electronic states in a NWFET. As a constraint for trueρˆrel, we assume that the single‐particle density matrix ρ1 is a given quantity, resulting from a non‐equilibrium Green's function (NEGF) calculation for the NWFET for a given set of applied voltages. The eigenbasis of trueρˆrel is assumed to be identical to the eigenbasis of the projected many‐body Hamiltonian trueHˆrel within a relevant Fock subspace of the quasi‐bound subsystem. As for the eigenvalues wN of trueρˆrel, we furthermore assume that wN have a generalized Boltzmann form, parameterized by effective electrochemical potentials of natural orbitals and a given temperature. Once trueρˆrel is obtained, we calculate and compare the modified entropy ΔS, the single‐particle‐reduced entropy S1 and the von Neumann entropy S for two different transport regimes of the NWFET.