Non-adiabatic corrections to electric current in molecular junctions due to nuclear motion at the molecule-electrode interfaces

Abstract

We present quantum electron transport theory that incorporates dynamical effects of motion of atoms on electrode-molecule interfaces in the calculations of the electric current. The theory is based on non-equilibrium Green's functions. We separate time scales in the Green's functions as fast relative time and slow central time. The derivative with respect to the central time serves as a small parameter in the theory. We solve the real-time Kadanoff-Baym equations for molecular Green's functions using Wigner representation and keep terms up to the second order with respect to the central time derivatives. Molecular Green's functions and consequently the electric current are expressed as functions of molecular junction coordinates as well as velocities and accelerations of molecule-electrode interface nuclei. We apply the theory to model a molecular system and study the effects of non-adiabatic nuclear motion on molecular junction conductivity.

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.…”