Nonequilibrium Green’s function theory for nonadiabatic effects in quantum electron transport

Abstract

We develop nonequilibribrium Green's function based transport theory, which includes effects of nonadiabatic nuclear motion in the calculation of the electric current in molecular junctions. Our approach is based on the separation of slow and fast timescales in the equations of motion for the Green's functions by means of the Wigner representation. Time derivatives with respect to central time serves as a small parameter in the perturbative expansion enabling the computation of nonadiabatic corrections to molecular Green's functions. Consequently, we produce series of analytic expressions for non-adiabatic electronic Green's functions (up to the second order in the central time derivatives); which depend not solely on instantaneous molecular geometry but likewise on nuclear velocities and accelerations. Extended formula for electric current is derived which accounts for the non-adiabatic corrections. This theory is concisely illustrated by the calculations on a model molecular junction.

Current-induced atomic motion, structural instabilities, and negative temperatures on molecule-electrode interfaces in electronic junctions

“…Therefore the small parameter in our theory is Ω Γ . The solution described below follows closely the ideas of previous authors 36,[56][57][58][59]63 . The exponential operators in Eqs.…”

Non-equilibrium Green’s function theory for non-adiabatic effects in quantum transport: Inclusion of electron-electron interactions

“…In the case of U = 0 (corresponding to the absence of electron-electron interaction) the nuclear motion plays destructive role at resonance but slightly increases conductance in the offresonance regimes, a result that agrees with calculation in our previous work. 66,67 Contrary to the non-interacting case, non-adiabatic effects contribute constructively at resonance in the presence of electron-electron interactions in the system. Finally, we observe that the conduction profile width becomes wider with increasing values of U.…”

“…Different models have been developed to tackle this problem in a wide range of theoretical formalisms: master equations, [36][37][38][39][40][41][42][43][44][45][46] path integral, 47 scattering theory, [48][49][50][51] non-equilibrium Green's functions, [52][53][54][55][56][57][58][59] and multilayer multiconfiguration time-dependent Hartree theory. 19,[60][61][62] These approaches (apart from several recent works [23][24][25][26][63][64][65][66][67] ) have almost universally assumed that nuclear vibrations are harmonic in nature, effectively describing systems that deviate slightly from their zero-current and equilibrium geometry. In addition, it is common to treat either the electron-vibration or moleculeelectrode couplings as the small parameter relative to other energy scales in the system.…”

“…24,26,33 The scope of current theoretical work with simultaneous modeling electronic correlations and nuclear dynamics is, at present, limited and all these considering nuclear motion as harmonic vibrations around equilibrium geometry. [78][79][80] Recently, several authors have used gradient expansions, 81 a technique reaching back to work of Kadanoff and Baym, 82 in their theoretical approaches, 24,26,[63][64][65][66][67]83,84 where classically described nuclei are treated as a slow disturbance in non-equilibrium Green's functions. Our previous works expanded on this methodology, where we developed a transport theory in the non-equilibrium Green's function formalism that takes into account the non-adiabatic effects of nuclear motion.…”

“…Our previous works expanded on this methodology, where we developed a transport theory in the non-equilibrium Green's function formalism that takes into account the non-adiabatic effects of nuclear motion. 66,67 The theory allowed for the computation of non-adiabatic effects associated with nuclear motion in the central region and at the molecule-electrode interface.…”