Theoretical Study On Single Molecule Electroluminescence Induced By A Scanning Tunneling Microscope Tip

Molecular electronics,as an important branch of nanoscience and even condensed matter physics,has made substantial progress.How to probe the quantum transport phenomena as well as to exploit its various applications at the single-molecule level constitutes the basic tasks of molecular electronics.In this context studying the optical response in current-carrying molecular junctions is important for understanding the light-matter interaction and the energy transport mechanisms in nanoscale.The combination of scanning tunneling microscope(STM)that has high spatial resolution and high sensitivity of photon detector makes it possible to detect or characterize single molecules by optical means.In STM-induced luminescence experiments,light emission from gap plasmon modes and from single molecules driven by the inelastic tunneling electrons are two important electroluminescence sources.Therefore,it is necessary to study the interplay between tunneling electrons,gap plasmons and molecular exciton in such STM junctions.Based on the nonequilibrium Green's function method with perturbation theory,we have carried out the following works.Firstly,we propose a general theoretical model to understand the single molecule emission spectrum in a STM junction from an energy transport point of view.It is found that the coherent interaction between molecular exciton and gap plasmons can give rise to a prominent Fano resonance,and manifests itself in light emission spectrum as an asymmetric line shape.We provide a unified account of several recent experimental observations by analyzing the dependence of the Fano line shape on the system parameters,such as the energy detuning and the coupling between molecular exciton and gap plasmons.More importantly,we can predict the evolution of the spectrum with the tip-molecule coupling,and the quenching of molecular exciton luminescence can be observed.Secondly,we simulate the light emission from C60 films driven by the tunneling electrons injected from a STM tip.Considering the electron-photon and exciton-plasmon interactions,we find that the light emission from gap plasmons and from exciton are independent,resulting in a bimodal-shaped light emission.The difference between the bimodal and Fano line shape is clarified.Meanwhile,the emission ratio between the two channelscan be adjusted by changing the tip-molecule coupling,the coupling dependence of excitonic and gap plasmonic emissions is consistent with a recent experiment.In particular,the stronger Purcell effect that is manifested by a significant enhancement of the spectrum in weak molecule-substrate coupling regime can be observed.On the other hand,the electronphonon coupling induced fluorescence enhancement and the light emission driven by GP can be obtained.Finally,we demonstrate that the molecular exciton and single harmonic oscillator(HO)are equivalent in equilibrium state,based on which the coupling between molecular exciton and gap plasmon can be described by the linear HO-HO coupling.In this case,we can observe the evolution of the spectral function of the GP from Fano-shaped to Rabi splitting.By considering the effect of nonequilibrium electron bath,the bias-dependent quantum cutoff can be observed in the spectrum.In nonequilibrium state,the molecular exciton can no longer be replaced by HO,and the HO-HO approximation describing the coupling between molecular exciton and gap plasmon is not valid.We can define the Green's functions of molecular exciton directly.There is a one-to-one correspondence between the Green's function of molecular exciton and the self-energies of photon due to coupling to the molecular orbitals.What's more,we can derive an effective formula that can describe the interaction between molecular exciton and gap plasmon in weak coupling regime.The results from the formula and the perturbation theory are consistent.