Numerical determination of a non-equilibrium many-body statistical operator for quasi-bound electrons in a gated nanowire system

We present a numerical approach to construct a non-equilibrium many-body statistical operator \(\hat{\rho}_\mathrm{rel}\) for an adaptive subspace of relevant quasi-bound electronic states in a semiconductor nanowire-based field-effect transistor (NWFET). As a constraint for \(\hat{\rho}_\mathrm{rel...

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Bibliographic Details
Published in:arXiv.org 2014-06
Main Authors: Castelo, J M, Indlekofer, K M
Format: Article
Language:English
Subjects:
Covariance
Eigenvalues
Eigenvectors
Electron density
Electron states
Equilibrium
Field effect transistors
Green's functions
Mathematical analysis
Nanowires
Operators (mathematics)
Orbitals
Particle density (concentration)
Semiconductor devices
Subspaces
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Summary:We present a numerical approach to construct a non-equilibrium many-body statistical operator \(\hat{\rho}_\mathrm{rel}\) for an adaptive subspace of relevant quasi-bound electronic states in a semiconductor nanowire-based field-effect transistor (NWFET). As a constraint for \(\hat{\rho}_\mathrm{rel}\), we assume that the single-particle density matrix \(\rho_1\) is a given quantity, resulting from a non-equilibrium Green's function (NEGF) calculation for the NWFET for a given set of applied voltages. Two different orthonormal (ON) eigenbases for \(\hat{\rho}_\mathrm{rel}\) are considered: (A) a Slater determinant basis of natural orbitals (eigenstates of \(\rho_1\)) and (B) the eigenbasis of the projected many-body Hamiltonian \(\hat{H}_\mathrm{rel}\) within a relevant Fock subspace of the system. As for the eigenvalues \(w_n\) of \(\hat{\rho}_\mathrm{rel}\), we furthermore assume that \(w_n\) have a generalized Boltzmann form, parameterized by effective electrochemical potentials of natural orbitals and a given temperature. From the determined \(\hat{\rho}_\mathrm{rel}\), in turn, one can calculate expectation values for any many-body observable within the relevant subspace. As an example, we analyze the electron density and the covariance of the density-density correlation function for representative electronic preparations of the NWFET.
ISSN:2331-8422