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Time-Dependent Density-Functional TheoryConcepts and Applications$
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Carsten A. Ullrich

Print publication date: 2011

Print ISBN-13: 9780199563029

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199563029.001.0001

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Nanoscale transport and molecular junctions

Nanoscale transport and molecular junctions

(p.351) 15 Nanoscale transport and molecular junctions
Time-Dependent Density-Functional Theory

Carsten A. Ullrich

Oxford University Press

This chapter discusses the formal framework and applications of time-dependent density-functional theory (TDDFT) to nanoscale transport. It begins with a brief overview of the basic concepts of nanoscale transport, such as transmission coefficients, conductance, and the Landauer approach. An exact expression for the conductance is derived under the assumption of weak bias. The starting point is the linear current response equation. An exchange-correlation contribution to the resistivity is obtained, even if the transport is in the steady-state, zero-frequency regime. This contribution is shown to become significant for narrow junctions. Next, the finite-bias case is discussed. A TDDFT approach for time-dependent transport is formulated in which a finite scattering region is coupled to infinite leads. The steady-state transmission coefficient is expressed in terms of nonequilibrium Green's functions. The Coulomb blockade regime of transport is discussed. Lastly, the master equation approach and stochastic TDDFT for open systems are reviewed.

Keywords:   Landauer approach, nanoscale transport, molecular junctions, conductance, transmission coefficient, nonequilibrium Green's function, Coulomb blockade, master equation, open systems, dissipation

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