Nonvertical Transitions Research Articles

Modification of transition pathways in polarized resonance Raman spectroscopy for carbon nanotubes by highly confined near-field light

We observed a modification of transition pathways in polarized resonance Raman spectroscopy during tip-enhanced Raman spectroscopy (TERS) analysis of metallic carbon nanotubes (CNTs). At a spatial resolution reaching up to the sub-nanometer regime, the signal intensity of the typical D-band is observed to be even higher than the intensity of the G-band all over the probed CNTs in TERS imaging. The measured D-band is attributed to the non-vertical transitions of electrons in k-space that are facilitated by highly confined near-field light at the tip–sample junction of our scanning tunneling microscope based TERS system. The D-band signal was observed even when the CNTs were excited by light polarized perpendicular to the tube axis that corresponds to electronic excitations between different cutting line numbers of a CNT. By combining the electron pathways brought about by both the near-field light and its polarization, we found a unique optical transition of electrons of CNTs in near-field Raman spectroscopy.

Multichannel High-Order Harmonic Generation from Fractal Bands in Fibonacci Quasicrystals.

High-order harmonic generation (HHG) in solids was expected to be efficient due to their high density. However, the strict transition laws in crystals restrict the number of HHG channels. Quasicrystals with fractal band structures could solve this problem and produce multichannel HHG emissions, which has been rarely studied. We simulate the Fibonacci quasicrystal (FQ) HHG for the first time and investigate the electron dynamics on the attosecond timescale. Our results reveal that (i)the acceleration theorem is approximately applicable in FQ, which provides us a valuable tool to analyze the electron trajectories. (ii)Fractal bands lead to more excitation channels, analogous to the forbidden nonvertical electron transitions in crystals. (iii)The broken symmetry results in more frequent backscattering of electrons. (iv)Compared with crystals, multichannel HHG in FQ has a higher yield and wider spectral range. Our results pave the way to understand and control the HHG in quasicrystals and shed light on a potential shorter and stronger attosecond light source based on compact solids.

Non-vertical optical transition in near-field enhanced spectroscopy of graphene

We theoretically investigate the optical transition of an electron in graphene that is excited by near-field around a conical Au tip. The interaction between the near-field and the electron is calculated by tight-binding method. In the case of near-field, the wavevector of the electron changes by the optical absorption from the valence band to the conduction band. We show that the change of the wavevector is inversely proportional to the localization width of the near-field, which is given as a function of the distance between the tip and graphene. We calculate the near-field absorption probability as a function of k in the Brillouin zone.

Microscopic theory of optical absorption in graphene enhanced by lattices of plasmonic nanoparticles

We present a microscopic description of plasmon-enhanced optical absorption in graphene, which is based on perturbation theory. We consider the interaction of graphene with a lattice of plasmonic nanoparticles, as was previously realized experimentally. By using tight-binding wave functions for the electronic states of graphene and the dipole approximation for the plasmon, we obtain analytic expressions for the coupling matrix element and enhanced optical absorption. The plasmonic nanostructure induces nonvertical optical transitions in the band structure of graphene with selection rules for the momentum transfer that depend on the periodicity of the plasmonic lattice. The plasmon-mediated optical absorption leads to an anisotropic carrier population around the $K$ point in phase space, which depends on the polarization pattern of the plasmonic near field in the graphene plane. Using Fourier optics, we draw a connection to a macroscopic approach, which is independent from graphene-specific parameters. Each Fourier component of the plasmonic near field corresponds to the momentum transfer of an optical transition. Both approaches lead to the same expression for the integrated optical absorption enhancement, which is relevant for the photocurrent enhancement in graphene-based optoelectronic devices.

Control of semiconductor emitter frequency by increasing polariton momenta

Light emission and absorption is fundamentally a joint property of both an emitter and its optical environment. Nevertheless, because of the much smaller momenta of photons compared with electrons at similar energies, the optical environment typically modifies only the emission/absorption rates, leaving the emitter transition frequencies practically an intrinsic property. We show here that surface polaritons, exemplified by graphene plasmons, but also valid for other types of polariton, enable substantial and tunable control of the transition frequencies of a nearby quantum well, demonstrating a sharp break with the emitter-centric view. Central to this result is the large momenta of surface polaritons that can approach the momenta of electrons and impart a pronounced non-local behaviour to the quantum well. This work facilitates non-vertical optical transitions in solids and empowers ongoing efforts to access such transitions in indirect-bandgap materials, such as silicon, as well as enriching the study of non-locality in photonics.

(Invited) Prospects for Wavelength-Tunable Photodetectors with Carbon Nanomaterials

Dynamic wavelength tunability has long been the holy grail of photodetector technology. Because of their atomic thickness and unique properties, carbon nanomaterials such as carbon nanotubes and graphene open up new paradigms to realize this concept, but so far this has been elusive experimentally. In this presentation, I will discuss the value behind tunable photodetectors, and present detailed quantum transport modeling of photocurrent in realistic devices, including full simulations of the electromagnetic fields. Our work shows that wavelength tunability is possible by dynamically changing the gate voltage, and we reveal the phenomena that govern the behavior of this type of device and show significant departure from the simple expectations based on vertical optical transitions. We find strong focusing of the electromagnetic fields at the contact edges over the same length scale as the band-bending. Both of these spatially-varying potentials lead to an enhancement of non-vertical optical transitions, which dominate even the absence of phonon or impurity scattering. We also show that the vanishing density of states near the Dirac point leads to contact blocking and a gate-dependent modulation of the photocurrent. We further highlight the challenges in realizing this technology by studying the impact of charge fluctuations on optical absorption.

Dynamic Wavelength-Tunable Photodetector Using Subwavelength Graphene Field-Effect Transistors

Dynamic wavelength tunability has long been the holy grail of photodetector technology. Because of its atomic thickness and unique properties, graphene opens up new paradigms to realize this concept, but so far this has been elusive experimentally. Here we employ detailed quantum transport modeling of photocurrent in graphene field-effect transistors (including realistic electromagnetic fields) to show that wavelength tunability is possible by dynamically changing the gate voltage. We reveal the phenomena that govern the behavior of this type of device and show significant departure from the simple expectations based on vertical transitions. We find strong focusing of the electromagnetic fields at the contact edges over the same length scale as the band-bending. Both of these spatially-varying potentials lead to an enhancement of non-vertical optical transitions, which dominate even in the absence of phonon or impurity scattering. We also show that the vanishing density of states near the Dirac point leads to contact blocking and a gate-dependent modulation of the photocurrent. Several of the effects discussed here should be applicable to a broad range of one- and two-dimensional materials and devices.

UV–Vis spectroscopy and density functional study of solvent effect on the charge transfer band of the n → σ* complexes of 2-Methylpyridine and 2-Chloropyridine with molecular iodine

UV–Vis spectroscopy has established that Pyridine substitutes form n→σ* charge transfer (CT) complexes with molecular Iodine. This study is a combined approach of purely experimental UV–Vis spectroscopy, Multiple linear regression theory and Computational chemistry to analyze the effect of solvent upon the charge transfer band of 2-Methylpyridine-I2 and 2-Chloropyridine-I2 complexes. Regression analysis verifies the dependence of the CT band upon different solvent parameters. Dielectric constant and refractive index are considered among the bulk solvent parameters and Hansen, Kamlet and Catalan parameters are taken into consideration at the molecular level. Density Functional Theory results explain well the blue shift of the CT bands in polar medium as an outcome of stronger donor acceptor interaction. A logarithmic relation between the bond length of the bridging atoms of the donor and the acceptor with the dielectric constant of the medium is established. Tauc plot and TDDFT study indicates a non-vertical electronic transition in the complexes. Buckingham and Lippert Mataga equations are applied to check the Polarizability effect on the CT band.

Plasmons dispersion and nonvertical interband transitions in single crystal Bi2Se3investigated by electron energy-loss spectroscopy

Plasmons dispersion and nonvertical interband transitions in Bi${}_{2}$Se${}_{3}$ single crystals were investigated by electron energy-loss spectroscopy in conjunction with (scanning) transmission electron microscopy [(S)TEM-EELS]. Both volume plasmons (\ensuremath{\pi} plasmon at 7 eV and \ensuremath{\pi} + \ensuremath{\sigma} plasmon at 17 eV) and surface plasmons (\ensuremath{\sim}5.5 and 10 eV) were demonstrated in STEM-EELS spectra and the corresponding spectral imaging in real space. In further EELS experiments in reciprocal space, the momentum-dependent spectra reveal very different dispersion behavior between \ensuremath{\pi} and \ensuremath{\pi} + \ensuremath{\sigma} plasmons, with \ensuremath{\pi} + \ensuremath{\sigma} plasmons showing a typical quadratic dependence, whereas the \ensuremath{\pi} plasmon exhibited a linear dispersion analogous to what was reported for graphene. Furthermore, a low energy excitation 0.7--1.6 eV was also observed which is attributed to direct nonvertical interband transitions along the \ensuremath{\Gamma}$F$ direction.

Electronic Excitations of Simple Cyanine Dyes: Reconciling Density Functional and Wave Function Methods.

The simplest cyanine dye series [H2N(CH)nNH2](+) with n = 1, 3, 5, 7, and 9 appears to be a challenge for all theoretical excited-state methods since the experimental spectra are difficult to predict and the observed deviations cannot be easily explained with standard arguments. We compute here the lowest vertical excitation energies of these dyes using a variety of approaches, namely, complete active space second-order perturbation theory (CASPT2), quantum Monte Carlo methods (QMC), coupled cluster linear response up to third approximate order (CC3), and various flavors of time-dependent density functional theory (TDDFT), including the recently proposed perturbative correction scheme (B2PLYP). In our calculations, all parameters such as basis set, active space, and geometry dependence are carefully analyzed. We find that all wave function methods give reasonably close excitation energies, with CASPT2 yielding the lowest values, and that the B2PLYP scheme gives excitations in satisfactory agreement with CC3 and DMC, significantly improving on the generalized gradient and hybrid approximations. Finally, to resolve the remaining discrepancy between predicted excitation energies and experimental absorption spectra, we also investigate the effect of excited-state relaxation. Our results indicate that a direct comparison of the experimental absorption maxima and the theoretical vertical excitations is not possible due to the presence of nonvertical transitions. The apparent agreement of earlier CASPT2 calculations with experiments was an artifact of the choice of active space and the use of an older definition of the zero-order Hamiltonian.

Polarization dependence of radial breathing mode peaks in resonant Raman spectra of vertically aligned single-walled carbon nanotubes

Polarization-dependent resonance Raman spectra of a vertically aligned single-walled carbon nanotube (SWNT) array were measured such that the polarization of the scattered light was selected either parallel or perpendicular to that of the incident light. For the parallel configuration, radial breathing mode (RBM) peaks exhibited two different polarization angle dependencies. One group (dominated by a peak at $203\text{ }{\text{cm}}^{\ensuremath{-}1}$) had a maximum scattering intensity for incident light parallel to the alignment direction whereas the other group (dominated by a peak at $181\text{ }{\text{cm}}^{\ensuremath{-}1}$) had maximum intensity for excitation perpendicular to the alignment direction. This anomalous behavior has been attributed to resonance with nonvertical transitions due to perpendicularly polarized excitation [Y. Murakami et al., Phys. Rev. B 71, 085403 (2005)]. Here we systematically measure the polarization-dependent Raman spectra and compare to theoretical expectations for the two different configurations. The $203\text{ }{\text{cm}}^{\ensuremath{-}1}$ group peaks are found to behave as expected for parallel-polarized dipole excitation, however the $181\text{ }{\text{cm}}^{\ensuremath{-}1}$ group peaks deviate significantly from the prediction assuming perpendicularly polarized excitation. The $181\text{ }{\text{cm}}^{\ensuremath{-}1}$ group peak intensities were found to be both environment and morphology dependent, indicative of isolated SWNTs. Therefore, the sound interpretation of these results is that the apparently anomalous polarization dependence is not due to perpendicular RBM excitation but rather the parallel excitation of isolated SWNTs suspended within the array.

On the nature of the π → π* ionic excited states: The V state of ethene as a prototype

This article addresses an analysis of the physical effects required for the correct description of the ionic pi --> pi* excited states in the frame of ab initio quantum chemistry, using the ionic V state of the ethene molecule as an example. The importance of the dynamic sigma polarization (absent in methods where the sigma skeleton is treated at a mean-field level) has been recognized by many authors in the past. In this article a new physical effect is described, i.e. the spatial contraction of the pi and pi* molecular orbitals (or of the local p atomic orbitals) originated from the reduction of the ionicity due to the dynamic sigma polarization. Such an effect is a second-order effect (it appears only as a consequence of the dynamic sigma polarization) but it cannot be ignored. Many of the difficulties found in the past in the calculation of the vertical excitation energy of the ionic states are attributed to an incomplete description of this contraction, while the few successes have been obtained when it has been fortuitously introduced by ad hoc procedures or when it is described in a brute force approach. Various strategies are proposed to allow for the spatial contraction of the p atomic orbitals. If this effect is considered at the orbital optimization step, it is shown that for the V state of ethene no Rydberg/valence mixing occurs and a simple perturbation correction (to the second order in the energy) on the pi --> pi* singly excited configuration gives stable results with respect to the computational parameters and in good agreement with the experimental findings and with the best theoretical calculations. Moreover, our results confirm the indication of Müller et al. (J Chem Phys 1999, 110, 7176) that the transition to the V state of ethene conforms to the Franck-Condon principle and that it is not necessary to appeal to a nonvertical transition to interpret the experimental data. The strategy reported in this article for ethene can be in principle generalized to the pi --> pi* ionic excited states of other molecules.

Vertical and nonvertical transitions in triple-ionization-induced dissociation of diatomic molecules

In this paper, we study triple-ionization-induced dissociation in ${\mathrm{N}}_{2}$ and ${\mathrm{O}}_{2}$ for laser polarization aligning either parallel or perpendicular along the molecular axis. For the first time, we demonstrate that vertical or nonvertical transition can be turned on and off by simply switching the laser polarization between being perpendicular and parallel to the molecular axis. We also show that the dependence of kinetic energy release on intensity can be used to distinguish vertical from nonvertical transition in triple-ionization-induced dissociation.

Joint density of states of nanostructures: an application to porous silicon

In this work the electronic interband transitions in porous silicon are studied. The calculation is performed using a supercell model with a tight-binding Hamiltonian, where an atomic-orbital sp3s* basis set is used. The pores are modelled as empty columns, digged in a crystalline silicon structure, and then passivated with hydrogen atoms. The effects of disorder in porous silicon are considered by introducing a random perturbative potential into the Hamiltonian, which produces non-vertical interband transitions in the reciprocal space. Such transitions occur in an interval inversely proportional to the electronic localization length. Finally, a comparative analysis of the optical absorption coefficient is performed by means of vertical, non-vertical transition, and the joint density of states (JDOS). (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Electronic structures of double perovskitesSr2(Mn1−xFex)MoO6: LSDA +U studies

Electronic structures of double perovskitesSr2(Mn1−xFex)MoO6 (x = 0.0, 0.5, 1.0) have beenstudied by using the LSDA +U method, where the on-site Coulomb interactionU oflocalized d electrons has been considered in the local-spin density approximation. The band structureof Sr2MnMoO6 with antiferromagnetic structure is found to be semiconducting with a gap of 0.5 eV, which isin good agreement with recent optical absorption results. The optical absorption correspondingto this optical threshold is found to be a non-vertical transition, which can occur only if anon-zero momentum such as from phonons participates in the transition. With the increase ofx, the band becomes half-metallic and ferrimagnetic. These semiconductor–metal andmagnetic structure transitions can be rationalized by different characteristics of chargetransfers between Fe–Mo and Mn–Mo via intermediate O 2p orbitals. The down-spin Mot2g states cross theFermi energy (EF) in the presence of Fe ions. With the increase ofx, more statescross over EF, which explains the high conductivity in the compound with largex observed in experiment.

Ultrafast non-Franck–Condon transitions via a two-pulse scheme

In molecular electronic transitions, an ultrashort laser pulse creates a nuclear wave packet at rest on the excited-state potential energy surface via a perfect vertical transition. In a bound excited-state potential, this wave packet will reach another turning point due to the natural (field-free) dynamics. We show, using a two-pulse scheme where a strong infrared (IR) field is combined with a weak-field ultrashort ultraviolet (UV) pulse, that it is possible to reach that turning point (i.e. induce a non-vertical transition) faster than the time associated with the natural dynamics of the molecule in the excited electronic state.

Instantaneous nonvertical electronic transitions with shaped femtosecond laser pulses: Is it possible?

In molecular electronic transitions, a vertical transition can be induced by an ultrashort laser pulse. That is, a replica of the initial nuclear state—times the transition dipole moment of the electronic transition—can be created instantaneously (on the time scale of nuclear motion) in the excited electronic state. Now, applying pulse shaping via the modulation of the phases of each spectral component of an ultrashort pulse, it is tempting to ask whether it is also possible to induce instantaneous nonvertical transitions to bound electronic states, provided that the phases of each spectral component of the pulse are set to appropriate values at the discrete frequencies corresponding to the energy levels of the potential. We analyze the problem in the weak-field limit, and show that such a phase requirement cannot be encoded into an ultrashort pulse. This result is equivalent to the statement that it is not possible to move matter faster than the time associated with the natural (field-free) dynamics of the system.

Semiclassical estimation of Franck–Condon factors and transition rates for vertical and nonvertical transitions

We develop a systematic way for estimating multidimensional Franck–Condon factors and transition rates for vertical and nonvertical transitions. By analyzing the phase-space overlap integral, we find the most probable positions and momenta of the nuclei immediately after the electronic transition. We find the transition rate by treating the dominant region in phase space as a funnel for the transition and by calculating the flow of probability through this funnel. We use the Wigner representation and its semiclassical limit and find that the transition occurs through a point(s) on the final surface of constant energy where the initial Wigner function is maximal. This dominant contribution is estimated analytically. Results are illustrated for Harmonic, Morse and Poeschl–Teller oscillators.

Ultrafast dynamics in the excited state of green fluorescent protein (wt) studied by frequency-resolved femtosecond pump-probe spectroscopy

The time and frequency resolved optical response of wild-type green fluorescent protein (wt-GFP) has been measured at room temperature following 30 fs, 400 nm photo-excitation. In the wavelength range covering the stationary fluorescence spectrum of the protein, the stimulated emission rises on a time scale of roughly 20 ps due to excited-state proton-transfer (ESPT). The rise can be described phenomenologically by a sum of two exponentials. A long-time isosbestic behavior on the blue edge of the stationary emission implies a barrier for ESPT which is significantly larger than thermal excitations. In addition, an instantaneous component to the stimulated emission appears within the time resolution of our experiment. This observation is indicative of non-vertical cross-well transitions that prepare the proton-transferred configuration of the excited state directly from the equilibrium geometry of the ground-state neutral species during photo-excitation. Finally, transient absorptions around 500 nm and 650 nm can be observed, which are attributed to transitions from different protonated forms of the excited-state of GFP to higher lying electronic configurations, Sn. The entire optical response of GFP is quantitatively simulated using a dynamic model that includes: (i) an energy-dependent rate coefficient for ESPT, (ii) intra- and intermolecular transfer of excess vibrational energy (IVR and VET), and (iii) an additional non-radiative decay pathway for the initially prepared Franck–Condon state leading to internal conversion via motion along a torsional coordinate. In particular, the nonexponential nature of the ESPT originates from overlapping time scales of reactive and non-reactive elementary processes following optical excitation.

Temperature dependence of photoluminescence of ann-i-p-iGaAs superlattice

Both the photoluminescence peaks corresponding to the vertical transitions and the nonvertical transitions in an n-i-p-i GaAs superlattice are clearly observed. The redshifts of the two peaks with increasing temperature are: discussed in terms of the temperature-dependent carrier separation effect.