Abstract
We present a density functional theory (DFT) for steady-state nonequilibrium quantum systems such as molecular junctions under a finite bias. Based on the steady-state nonequilibrium statistics that maps nonequilibrium to an effective equilibrium, we show that ground-state DFT (GS-DFT) is not applicable in this case and two densities, the total electron density and the density of current-carrying electrons, are needed to uniquely determine the properties of the corresponding nonequilibrium system. A self-consistent mean-field approach based on two densities is then derived. The theory is implemented into SIESTA computational package and applied to study nonequilibrium electronic/transport properties of a realistic carbon-nanotube (CNT)/Benzene junction. Results obtained from our steady-state DFT (SS-DFT) are compared with those of conventional GS-DFT based transport calculations. We show that SS-DFT yields energetically more stable nonequilibrium steady state, predicts significantly lower electric current, and is able to produce correct electronic structures in local equilibrium under a limiting case.
Highlights
Due to highly reduced dimensions, the properties of molecular devices are often strongly size-dependent and very sensitive to their chemical environment
Without rigorous proof, we suggested that additional degrees of freedom besides the total electron density are needed to determine the properties of a nonequilibrium quantum system[16]
We prove that with given two densities, the total electron density and the density of current-carrying electrons, the Hamiltonian of an effective equilibrium system is uniquely determined, and in turn the steady-state properties of the corresponding nonequilibrium system are determined, confirming that GS-density functional theory (DFT) is in principle incorrect for nonequilibrium systems
Summary
Due to highly reduced dimensions, the properties of molecular devices are often strongly size-dependent and very sensitive to their chemical environment. It has been shown that the mean-field equation from density functional theory (DFT) with SBCs can be solved either by plane-wave based methods[11] or by non-equilibrium Green’s functions’ (NEGF) techniques[12]. In this paper, starting from the Hershfield’s nonequilibrium quantum statistics[19], we derive a density functional theory for the steady-state (SS) properties of molecular junctions under a finite bias. We prove that with given two densities, the total electron density and the density of current-carrying electrons, the Hamiltonian of an effective equilibrium system (that can be mapped to the desired steady-state nonequilibrum junction) is uniquely determined, and in turn the steady-state properties of the corresponding nonequilibrium system are determined, confirming that GS-DFT is in principle incorrect for nonequilibrium systems.
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