Path-integral simulations with fermionic and bosonic reservoirs: Transport and dissipation in molecular electronic junctions

Abstract

We expand iterative numerically-exact influence functional path-integral tools and present a method capable of following the nonequilibrium time evolution of subsystems coupled to multiple bosonic and fermionic reservoirs simultaneously. Using this method, we study the real-time dynamics of charge transfer and vibrational mode excitation in an electron conducting molecular junction. We focus on nonequilibrium vibrational effects, particularly, the development of vibrational instability in a current-rectifying junction. Our simulations are performed by assuming large molecular vibrational anharmonicity (or low temperature). This allows us to truncate the molecular vibrational mode to include only a two-state system. Exact numerical results are compared to perturbative Master equation calculations demonstrating an excellent agreement in the weak electron-phonon coupling regime. Significant deviations take place only at strong coupling. Our simulations allow us to quantify the contribution of different transport mechanisms, coherent dynamics and inelastic transport, in the overall charge current. This is done by studying two model variants: The first admits inelastic electron transmission only, while the second one allows for both coherent and incoherent pathways.

Inelastic effects in molecular transport junctions: The probe technique at high bias

“…Energy exchange between conducting electrons and the nuclei can locally heat the junction 4-8 , as was demonstrated experimentally in Refs. [9][10][11] , and drive vibrational instabilities [12][13][14][15][16] , even rupturing the junction 17 . These complex many-body effects can be captured within seemingly simple models: The Anderson-Holstein model describes molecular junctions with a single electronic site coupled to a dominant vibrational mode 18 .…”

Effects of vibrational anharmonicity on molecular electronic conduction and thermoelectric efficiency

“…We assume that the molecular orbitals do not shift with bias. This effect could be implemented easily to materialize a strong diode behavior 18,19 .…”

“…In this setup, electrons in the junction couple to a highly anharmonic impurity mode, which consists of only two states, replacing the full harmonic manifold. Based on this model, we had examined the role of mode harmonicity/anharmonicity on vibrational heating, cooling, and instability, under high voltage biases 18,19 , then analyzed the impact of mode anharmonicity on current blockade physics 40 . Moreover, in Refs.…”

“…Theoretical descriptions of single-molecule electronic junctions essentially assume that molecular vibrations are harmonic, as in the celebrated Anderson-Holstein (AH) model 15,16 , the phonon-assisted donor-acceptor (DA) charge transfer model [17][18][19][20][21] , or in multi-electronic state constructions 22,23 . The harmonic approximation is valid when atomic displacements are rather limited.…”

Reconciling perturbative approaches in phonon-assisted transport junctions

“…These effects can be captured within simple models: The celebrated Anderson-Holstein model includes a single electronic site embedded between metals, further coupled to a single vibration, or a harmonic bath [13][14][15][16][17][18][19][20][21][22][23][24][25][26] . A different class of problems, relevant as well to photovoltaic devices 27 , concerns donor-acceptor type molecular systems, with two electronic sites coupled to molecular vibrations 11,[28][29][30][31][32][33][34] . Experimentally, inelastic electron tunnelling spectroscopy can identify molecular vibrations participating in the transport process [35][36][37] .…”