Electron-Phonon Interacation in Quantum Dots: A Solvable Model

The relaxation of electrons in quantum dots via phonon emission is hindered by the discrete nature of the dot levels (phonon bottleneck). In order to clarify the issue theoretically we consider a system of $N$ discrete fermionic states (dot levels) coupled to an unlimited number of bosonic modes with the same energy (dispersionless phonons). In analogy to the Gram-Schmidt orthogonalization procedure, we perform a unitary transformation into new bosonic modes. Since only $N(N+1)/2$ of them couple to the fermions, a numerically exact treatment is possible. The formalism is applied to a GaAs quantum dot with only two electronic levels. If close to resonance with the phonon energy, the electronic transition shows a splitting due to quantum mechanical level repulsion. This is driven mainly by one bosonic mode, whereas the other two provide further polaronic renormalizations. The numerically exact results for the electron spectral function compare favourably with an analytic solution based on degenerate perturbation theory in the basis of shifted oscillator states. In contrast, the widely used selfconsistent first-order Born approximation proves insufficient in describing the rich spectral features.Comment: 8 pages, 4 figure

On the validity of the Franck-Condon principle in the optical spectroscopy: optical conductivity of the Fr\"{o}hlich polaron

The optical absorption of the Fr\"{o}hlich polaron model is obtained by an approximation-free Diagrammatic Monte Carlo method and compared with two new approximate approaches that treat lattice relaxation effects in different ways. We show that: i) a strong coupling expansion, based on the the Franck-Condon principle, well describes the optical conductivity for large coupling strengths ($\alpha >10$); ii) a Memory Function Formalism with phonon broadened levels reproduces the optical response for weak coupling strengths ($\alpha <6$) taking the dynamic lattice relaxation into account. In the coupling regime $6<\alpha<10$ the optical conductivity is a rapidly changing superposition of both Franck-Condon and dynamic contributions.Comment: accepted for publication in PR

A Study Of A New Class Of Discrete Nonlinear Schroedinger Equations

A new class of 1D discrete nonlinear Schr${\ddot{\rm{o}}}$dinger Hamiltonians with tunable nonlinerities is introduced, which includes the integrable Ablowitz-Ladik system as a limit. A new subset of equations, which are derived from these Hamiltonians using a generalized definition of Poisson brackets, and collectively refered to as the N-AL equation, is studied. The symmetry properties of the equation are discussed. These equations are shown to possess propagating localized solutions, having the continuous translational symmetry of the one-soliton solution of the Ablowitz-Ladik nonlinear Schr${\ddot{\rm{o}}}$dinger equation. The N-AL systems are shown to be suitable to study the combined effect of the dynamical imbalance of nonlinearity and dispersion and the Peierls-Nabarro potential, arising from the lattice discreteness, on the propagating solitary wave like profiles. A perturbative analysis shows that the N-AL systems can have discrete breather solutions, due to the presence of saddle center bifurcations in phase portraits. The unstaggered localized states are shown to have positive effective mass. On the other hand, large width but small amplitude staggered localized states have negative effective mass. The collison dynamics of two colliding solitary wave profiles are studied numerically. Notwithstanding colliding solitary wave profiles are seen to exhibit nontrivial nonsolitonic interactions, certain universal features are observed in the collison dynamics. Future scopes of this work and possible applications of the N-AL systems are discussed.Comment: 17 pages, 15 figures, revtex4, xmgr, gn

Effects of Lattice and Molecular Phonons on Photoinduced Neutral-to-Ionic Transition Dynamics in Tetrathiafulvalene-pp-Chloranil

For electronic states and photoinduced charge dynamics near the neutral-ionic transition in the mixed-stack charge-transfer complex tetrathiafulvalene-$p$-chloranil (TTF-CA), we review the effects of Peierls coupling to lattice phonons modulating transfer integrals and Holstein couplings to molecular vibrations modulating site energies. The former stabilizes the ionic phase and reduces discontinuities in the phase transition, while the latter stabilizes the neutral phase and enhances the discontinuities. To reproduce the experimentally observed ionicity, optical conductivity and photoinduced charge dynamics, both couplings are quantitatively important. In particular, strong Holstein couplings to form the highly-stabilized neutral phase are necessary for the ionic phase to be a Mott insulator with large ionicity. A comparison with the observed photoinduced charge dynamics indicates the presence of strings of lattice dimerization in the neutral phase above the transition temperature.Comment: 9 pages, 7 figures, accepted for publication in J. Phys. Soc. Jp

The Yellow Excitonic Series of Cu2O Revisited by Lyman Spectroscopy

We report on the observation of the yellow exciton Lyman series up to the fourth term in Cu2O by time-resolved mid-infrared spectroscopy. The dependence of the oscillator strength on the principal quantum number n can be well reproduced using the hydrogenic model including an AC dielectric constant, and precise information on the electronic structure of the 1s exciton state can be obtained. A Bohr radius a_{1s}=7.9 A and a 1s-2p transition dipole moment \mu_{1s-2p}= 4.2 eA were found

Polaron Effective Mass, Band Distortion, and Self-Trapping in the Holstein Molecular Crystal Model

We present polaron effective masses and selected polaron band structures of the Holstein molecular crystal model in 1-D as computed by the Global-Local variational method over a wide range of parameters. These results are augmented and supported by leading orders of both weak- and strong-coupling perturbation theory. The description of the polaron effective mass and polaron band distortion that emerges from this work is comprehensive, spanning weak, intermediate, and strong electron-phonon coupling, and non-adiabatic, weakly adiabatic, and strongly adiabatic regimes. Using the effective mass as the primary criterion, the self-trapping transition is precisely defined and located. Using related band-shape criteria at the Brillouin zone edge, the onset of band narrowing is also precisely defined and located. These two lines divide the polaron parameter space into three regimes of distinct polaron structure, essentially constituting a polaron phase diagram. Though the self-trapping transition is thusly shown to be a broad and smooth phenomenon at finite parameter values, consistency with notion of self-trapping as a critical phenomenon in the adiabatic limit is demonstrated. Generalizations to higher dimensions are considered, and resolutions of apparent conflicts with well-known expectations of adiabatic theory are suggested.Comment: 28 pages, 15 figure

Ab initio Green's function formalism for band structures

Using the Green's function formalism, an ab initio theory for band structures of crystals is derived starting from the Hartree-Fock approximation. It is based on the algebraic diagrammatic construction scheme for the self-energy which is formulated for crystal orbitals (CO-ADC). In this approach, the poles of the Green's function are determined by solving a suitable Hermitian eigenvalue problem. The method is not only applicable to the outer valence and conduction bands, it is also stable for inner valence bands where strong electron correlations are effective. The key to the proposed scheme is to evaluate the self-energy in terms of Wannier orbitals before transforming it to a crystal momentum representation. Exploiting the fact that electron correlations are mainly local, one can truncate the lattice summations by an appropriate configuration selection scheme. This yields a flat configuration space; i.e., its size scales only linearly with the number of atoms per unit cell for large systems and, under certain conditions, the computational effort to determine band structures also scales linearly. As a first application of the new formalism, a lithium fluoride crystal has been chosen. A minimal basis set description is studied, and a satisfactory agreement with previous theoretical and experimental results for the fundamental band gap and the width of the F 2p valence band complex is obtained.Comment: 20 pages, 3 figures, 1 table, RevTeX4, new section on lithium fluorid

Theory of optical spectra of polar quantum wells: Temperature effects

Theoretical and numerical calculations of the optical absorption spectra of excitons interacting with longitudinal-optical phonons in quasi-2D polar semiconductors are presented. In II-VI semiconductor quantum wells, exciton binding energy can be tuned on- and off-resonance with the longitudinal-optical phonon energy by varying the quantum well width. A comprehensive picture of this tunning effect on the temperature-dependent exciton absorption spectrum is derived, using the exciton Green's function formalism at finite temperature. The effective exciton-phonon interaction is included in the Bethe-Salpeter equation. Numerical results are illustrated for ZnSe-based quantum wells. At low temperatures, both a single exciton peak as well as a continuum resonance state are found in the optical absorption spectra. By contrast, at high enough temperatures, a splitting of the exciton line due to the real phonon absorption processes is predicted. Possible previous experimental observations of this splitting are discussed.Comment: 10 pages, 9 figures, to appear in Phys. Rev. B. Permanent address: [email protected]

Ultrahigh Bandwidth Spin Noise Spectroscopy: Detection of Large g-Factor Fluctuations in Highly n-Doped GaAs

We advance all optical spin noise spectroscopy (SNS) in semiconductors to detection bandwidths of several hundred gigahertz by employing an ingenious scheme of pulse trains from ultrafast laser oscillators as an optical probe. The ultrafast SNS technique avoids the need for optical pumping and enables nearly perturbation free measurements of extremely short spin dephasing times. We employ the technique to highly n-doped bulk GaAs where magnetic field dependent measurements show unexpected large g-factor fluctuations. Calculations suggest that such large g-factor fluctuations do not necessarily result from extrinsic sample variations but are intrinsically present in every doped semiconductor due to the stochastic nature of the dopant distribution.Comment: 5 pages, 3 figure