We found that the electron transitions of the molecule occur via the excitation channels resulting from the learn more exciton-plasmon coupling. The results also show that the vibrational excitations assist the occurrence of the upconverted luminescence. Figure 1 Schematic diagram of mechanism for occurrence of the upconverted luminescence. Horizontal lines in each parabola denote vibrational
sublevels where |g〉 and |e〉 denote the electronic ground and excited states, respectively. The electronic excitation and de-excitation of the molecule are induced by the absorption and emission of the surface plasmon, respectively. These electron transitions are accompanied by the vibrational excitations, and the vibrational excitations assist the occurrence of the upconverted luminescence.
Methods We consider a model which includes the electronic ground (excited) state of the molecule |g〉 (|e〉). The electron on the molecule interacts with the molecular vibrations and the surface plasmons. The Hamiltonian of the system is (1) where and c m (m = e, g) are creation and annihilation operators for an electron with energy ϵ m in state |m〉. Operators b † and b are boson creation and annihilation operators for a molecular vibrational mode with energy ; a † and a are for a surface plasmon mode with energy , and and b β are for a phonon mode in the thermal phonon bath, with Q b = b + b † and . The energy parameters M, V, and U β correspond to the coupling between electronic and vibrational degrees of freedom on the molecule (electron-vibration coupling), the exciton-plasmon Clomifene coupling, and the coupling between the molecular buy AZD1480 vibrational mode and a phonon mode in the thermal phonon bath. By applying the canonical (Lang-Firsov) transformation , H becomes (2) where X = exp[-λ(b † - b)], and . The luminescence spectra of the molecule are expressed in terms of Green’s function of the molecular exciton on the Keldysh contour , which is defined as (3) where 〈⋯ 〉 H and denote statistical average in representations by system evolution for H and , respectively. τ is the
Keldysh contour time variable, and T C is the time ordering along the Keldysh contour. By assuming the condition of stationary current, the distribution function N pl of the surface plasmons excited by inelastic tunneling between the tip and the Dibutyryl-cAMP substrate is given by (4) where T pl is a coefficient related to the current amplitude due to the inelastic tunneling . We calculate L according to the calculation scheme previously reported by us . The spectral function and the luminescence spectra of the molecule are defined by the relations, (5) (6) where L r and L < are the retarded and lesser projection of L. The parameters are given so that they correspond to the experiment on the STM-LE from TPP molecules on the gold surface : , , and .