Abstract
We present a brief pedagogical review of theoretical Green's function methods applicable to open quantum systems out of equilibrium, in general, and single molecule junctions, in particular. We briefly describe experimental advances in molecular electronics and then discuss different theoretical approaches. We then focus on Green's function methods. Two characteristic energy scales governing the physics are many-body interactions within the junctions and molecule-contact coupling. We, therefore, discuss weak interactions and weak coupling as two limits that can be conveniently treated within, respectively, the standard nonequilibrium Green's function (NEGF) method and its many-body flavors (pseudoparticle and Hubbard NEGF). We argue that the intermediate regime, where the two energy scales are comparable, can in many cases be efficiently treated within the recently introduced superperturbation dual fermion approach. Finally, we review approaches for going beyond these analytically accessible limits, as embodied by recent developments in numerically exact methods based on Green's functions.
Highlights
Since the first theoretical proposal to use single molecules as electronic devices[1] and the first experimental realization of a single molecule junction,[2,3] the field of molecular electronics has made tremendous progress
We argue that the intermediate regime, where the two energy scales are comparable, can in many cases be efficiently treated within the recently introduced superperturbation dual fermion approach
A variety of celebrated numerical wavefunction schemes have employed some variation of this idea to address transport problems, including the numerical renormalization group (NRG) method,[173,174] matrix product state (MPS) techniques,[175] multiconfiguration time-dependent Hartree (MCTDH) and its later[176–178] and more recent modifications.[179,180]
Summary
Since the first theoretical proposal to use single molecules as electronic devices[1] and the first experimental realization of a single molecule junction,[2,3] the field of molecular electronics has made tremendous progress. Surface enhanced Raman spectroscopy (SERS)[69,70,71,72] in junctions, besides providing (complementary to IETS) information on molecular vibrations, allows for estimating bias-induced heating of electronic and vibrational degrees of freedom.[73,74] Tip-enhanced Raman spectroscopy (TERS)[75,76] yields information on molecular structure.[77,78,79,80,81] optical emission in biased junctions was observed as bias-induced luminescence.[82,83,84,85,86,87] In this context, electroluminescence was employed to study energy transfer[88,89,90] and as a tool for molecular imaging with submolecular resolution.[91] It was employed for designing energetically efficient light emitting diodes.[92] Recently, strong light–matter interaction was measured in single molecule nanocavities.[89,93,94,95,96,97,98] While measurements in the strong coupling regime were performed in the absence of electron flux, extensions to current-carrying molecular junctions are expected soon Such developments will be an important step forward in the quest for optical control and characterization of molecular junctions.
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