Analytic Solution for the Density of States of the Disordered Quasi-One-Dimensional Electron Gas in a Quantum Wire

A theory is presented of the density of states (DOS) over the entire energy spectrum of the disordered quasi-one-dimensional electron gas (1DEG) in a quantum wire. The disorder is caused by Gaussian random fields of any origin, especially those of short range. The solution is derived by means of a 1D version of the path-integral technique within the approximation based on a non-local harmonic modeled action. A simple analytic expression for the 1D DOS and different variational equations for the curvature of the trial well are then obtained, where the autocorrelation function of the random field plays the key role as the input function for disorder interaction. This enables us, for the first time, to examine in detail the effect from disorder of various origins on the DOS of 1DEG's in quantum wires of arbitrary geometry as well as to incorporate the many-body screening by 1DEG's. The theory is verified by reproducing the well-known asymptotics of the white-noise energy spectrum given by earlier theories. Numerical calculations have been carried out with inclusion of the local-field correction due to exchange and correlation in the 1DEG for a modulation-doped cylindrical quantum wire from GaAs/Al x Ga 1- x As.

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