ar X iv : c on d - m at / 0 10 53 67 v 1 1 8 M ay 2 00 1 Many - Electron Systems with Constrained Current

A formulation for transport in an inhomogeneous, interacting electron gas is described. Electronic current is induced by a constraint condition imposed as a vector Lagrange multiplier. Constrained minimization of the total energy functional on the manifold of an arbitrary constant current leads to a many-electron Schrödinger equation with a complex, momentum-dependent potential. Constant current Hartree-Fock and Kohn-Sham approximations are formulated within the method and application to transport for quantum wires is developed. No appeal is made to near equilibrium conditions or other approximations allowing development of a general ab initio electronic transport formulation. In recent years, there has been considerable advances towards the development of accurate theoretical models to deal with electron transport through atomic and molecular wires [1]. This activity has been largely spurred on by development of experimental techniques to form atomic scale electrical contacts such as scanning tunneling microscopy [2] and mechanically controllable break junctions [3]. Measurement of current-voltage characteristics have been recently performed on a single benzene-1,4-dithiolate molecule [4], buckminsterfullerene [5], individual atoms [6], and DNA strands [7]. The mechanisms for charge transport through these low-dimensional structures remain largely unexplored and unexplained. Several approaches have been developed on the basis of the extended Hückel [8] and density functional theory within a Lippmann-Schwinger formalism [9] or nonequilibrium Green's functions [10]. In these approaches, the system is partitioned into three parts: molecular device (or wire) and two electron reservoirs. The interaction between contacts and wire represents the kernel for the Lippmann-Schwinger equation, and serves generally to define the non-interacting system for Green's function approaches. Recent studies indicate the exact nature of the molecule-contact bonding are critical in predicting the correct order of magnitude for the currents with applied bias revealing that accurate electronic structure methods must be incorporated into quantum transport methods for accurate predictions and analysis of current-voltage relationships. In this letter, we present a variational approach to charge transport in correlated electron systems. We begin by introducing a many-electron Schrödinger equation which provides exact wavefunctions on the manifold of a given current distribution. The many-electron Schrödinger equation is developed without any restrictions to the treatment of electron-electron correlations , whether as injected current or part of the molecular device. We next present specific approximations corresponding to the Hartree-Fock and configuration interaction treatments of 1