Hitoshi Sumi

Urbach-Martienseen Rule and Exciton Trapped Momentarily by Lattice Vibrations

Theory for the Urbach-Martienssen (U-M) rule on the low energy tail of the fundamental absorption edge of insulators is proposed. The exciton propagator solved for an adiabatic lattice is averaged for lattice vibrations at finite temperature, and the self-energy of exciton is obtained. It describes two characters of exciton in the lattice; the one is the mobile nature of exciton in the undeformed lattice, and the other is the localized nature of exciton trapped momentarily by the lattice deformation due to thermal vibrations. The interplay of the two natures results in the U-M tail below the exciton absorption peak. The result can be interpreted in terms of the Franck-Condon principle where the mobile nature is incorporated in the giant oscillator strength of the momentarily trapped exciton. Emission from this trapped state is discussed in connection with the U-M rule.

Exciton Polarons of Molecular Crystal Model. I. : Dynamical CPA

Energy spectrum of exciton polaron is studied with the dynamical CPA (coherent potential approximation), which is introduced for inelastic scattering by Einstein phonons at every lattice site. The coherent potential at energy E is determined by the potentials at energies apart from E by integral times the phonon energy. We determine applicability ranges of the concepts used in the limiting cases; (I) the nearly free exciton for weak coupling, (II) multiple bands of the vibronic excitons for small excitation transfer, and (III) the self-trapped exciton for strong coupling. An ambiguous boundary separating (II) and (III) lies about S ≃6, with S representing the ratio of the energy gain of exciton localization to the phonon energy. The change with increasing excitation transfer for a fixed S is characterized by the sharp crossing of (III) with (I) for \(S{\gtrsim}6\), while by the gradual merging of (II) into (I) for \(S{\lesssim}6\).

Exciton Polarons of Molecular Crystal Model. II. Optical Spectra

Absorption and emission spectra of excitons interacting with optical or intramolecular vibrations are calculated with the dynamical coherent-potential approximation proposed previously. Investigations are made for various situations to which limiting concepts of nearly-free, self-trapped and vibronic excitons are not applicable straightforwardly. An interpretation is proposed that the absorption structure of alkali halides around the exciton peak originates from a situation where the self-trapped state is energetically close to the lowest edge of the nearly-free state. In this case, where the exciton-phonon and the excitation-transfer interactions are comparable to each other and strong, configuration mixing between the two types of states is small. When the two types of interaction are weak and comparable to each other, an intermediate state between the nearly-free and the vibronic-exciton states is realized. This situation explains the progressional structure in the exciton absorption band of crystallin...

On the Exciton Luminescence at Low Temperatures: Importance of the Polariton Viewpoint

The intensity ratio of the LO-phonon sideband to the zero-phonon line and the width of the zero-phonon line in the free-exciton luminescence spectrum can never be understood, especially at low temperatures, by the usual theory with the assumption of the thermal equilibrium for excitons. The theory assuming exciton thermal-equilibrium gives too small values for these quantities compared with the observed ones. These large discrepancies are removed by considering the exciton luminescence from the polariton viewpoint. In this viewpoint, polaritons accumulate around the bottleneck in polariton decay lower a little than the lowest exciton energy E 0. Polaritons at the bottleneck determine the zero-phonon line, while polaritons maintaining approximately the thermal-equilibrium distribution in the energy region above E 0 determine the LO-phonon sideband. The temperature and crystal-thickness dependences of the luminescence spectrum and the quenching of the luminescence by impurities are also discussed in terms of the polariton bottleneck.

Exciton-Phonon Interaction in the Coherent Potential Approximation with Application to Optical Spectra

Exciton in the phonon field is treated with the coherent potential approximation which has originally been developed for electron in random lattice. Scattering potential at each lattice site is a random variable which takes a Gaussian distribution originating from thermal vibrations of the lattice. The approximation describes the change of character of exciton in the phonon field near the band edge. In the weak scattering case, the absorption line shape calculated is Lorentz-like in the main part and in the high energy tail of the peak due to the motional narrowing, while it switches over, below the peak, to the Urbach-Martienssen tail representing the localized feature of exciton. The emission spectrum changes from the resonance type to the Stokes-shifted type as exciton-phonon coupling increases. Overall line shape of optical spectrum is obtainable over the whole range of coupling strength. The approximation corresponps to the self-consistent version of the theory by Sumi and Toyozawa (J. Phys. Soc. Jap...

Energy Transfer between Localized Electronic States —From Non-Adiabatic to Adiabatic Hopping Limits—

A thermally-activated transition rate W between two localized electronic states is given which bridges the adiabatic limit, where the two states are mixed well at the activated lattice configuration, and the non-adiabatic limit, where they are not even there. Frequency dispersion of lattice vibrations is fully incorporated which is important to assure irreversibility of the system. Basic quantities are the interaction. energy J between the two states and the average amplitude D and velocity \(\overline{v}\) of thermal fluctuations of the energy difference between adiabatic potentials associated with these states. The semiclassical condition \(D{\ll}\hbar\overline{\omega}\) is assumed with \(\overline{\omega}{\equiv}\overline{v}/D\). The pre-exponential factor of W is given as a function of \(\gamma{\equiv}\pi J^{2}/(\hbar\overline{v})\) which determines the adiabatic limit for γ≫1 and the non-adiabatic limit for γ≪1. The attempt frequency in W is given by \(\overline{\omega}/2\pi\) which is written as an ...

Polaron Conductions from Band to Hopping Types

Transport properties of polaron are investigated theoretically in the case of acoustic phonon coupling. Large polaron states with very little polarization cloud and small polaron states with large lattice distortion co-exist almost orthogonally to each other. Critical coupling strength at which the ground state changes from large to small polarons is smaller than the coupling strength at which the activated state for the hopping of small polaron becomes lower than the large polaron continuum. The polaron conduction changes successively among three types as the coupling strength increases. The first is the band conduction of large polaron with no activation energy, while the third is the thermally activated hopping of small polaron. In the intermediate type, thermally populated large polaron states play dominant role in the conduction while the small polaron is energetically stable. The drift mobility and the thermoelectric power are calculated for the three types. Optical absorption is also mentioned.

Self-Trapping of Excitons Beginning with Tunneling Nucleation

The rate of self-trapping (ST) is calculated, considering that ST begins with quantum-mechanical tunneling of a free exciton to a state of nucleation less localized than the relaxed self-trapped one. Three cases appear depending on the site-diagonal and off-diagonal exciton-phonon interaction energies S 1 and S 2 relative to the half width B of the exciton band. When \(S_{2}/B \gtrsim 0.21\), ST through the nucleation state of two-center type predominates. When \(S_{2}/B \lesssim 0.21\) and \(S_{1}/B \lesssim 1.25\), only ST through that of one-center type occurs. When \(S_{2}/B \lesssim 0.21\) but \(S_{1}/B \gtrsim 1.25\), the latter channel predominates at low temperatures but it is over-come by the former one with increasing temperature. Alkali halides except iodides are classified into the first case, RbI into the second one, and KI into the third one. The so called E x luminescence observed only in alkali iodides should be emitted from a still unknown self-trapped state of one-center type.

Diffusive Conductivity in Quasi One-Dimensional Conductor TMTTF-TCNQ

The temperature-dependent behavior of the conductivity σ c perpendicular to the 1-d axis of TMTTF-TCNQ is explained in terms of diffusive hopping process between the Bloch-band electronic states of neighboring 1-d columns. It is pointed out that σ c can be used to extract the conductivity component σ S P ascribable to electrons in the single-particle states from the conductivity σ b along the 1-d axis. The deviation (of about 20%) of σ b from σ S P around the maximum-conductivity region is ascribed to the contribution of the charge density waves.

Energy Transfer between Localized Electronic States.II.Transition during Vibrational Relaxation

Energy transfer (ET) is greatly enhanced in a very short time after the initial electronic state was prepared by photon excitation. ET is assisted by violent lattice vibrations which have not been relaxed yet, when electrons interact strongly with phonons in the two electronic states (coupled by the matrix element J ). An expression of the quantum yield of ET, which bridges the nonadiabatic (small J ) and the adiabatic (large J ) limits, is given as a function of time elapsed after pulsed excitation at an energy E . In the case of steady excitation, transitions during vibrational relaxation manifest themselves in a strong E dependence of the quantum yield. Generalization of Forsters formula for ET in this dynamic regime is also mentioned. We use a formulation developed in the part I (J. Phys. Soc. Jpn. 49 (1980) 1701) which treat transitions after vibrational relaxation. The Landau-Zener formula plays an important role in describing ET.