Y. Lépine

Structural phase transitions in crystals with coupled softening modes

Abstract Structural phase transitions in crystals with more than one softening phonon mode are investigated in mean field theory. It is found that, for negative coupling energies between two modes, the critical temperature of each mode increases. For large coupling, both modes become soft at the same temperature and the phase transition becomes of first order. For positive coupling energies, the critical temperatures rapidly go to zero but not for the same value of coupling. A phase diagram is given and a possible application to alkali-TCNQ salts is discussed.

Effect of pressure on the spin-Peierls temperature

Abstract Experiments have shown that a hydrostatic pressure increases the spin-Peierls transition temperature ( T c ) in MEM-(TCNQ) 2 while a lowering is observed in TTF-CuBDT. A mean field theory, involving an anharmonic coupling between the distortion and the strain and a possibility for both structural and spin-Peierls instabilities is presented. From this theory, we conclude that, depending on the sign of the coupling energy between the dimerization soft mode and the strain, T c can increase or decrease with pressure. Without this anharmonic coupling, T c decreases with pressure.

Ground state energy of the large polaron in a crystal with many LO phonon branches

Abstract The large polaron is studied in polyatomic crystals where more than one LO phonon branch is present. An upper bound to the ground state energy is obtained which is valid for all values of the electron-phonon coupling constants. For small coupling, we obtain the usual result that the ground state energy is the sum of the contributions of the different phonon branches. For large coupling, there is an extra contribution due to crossed terms between the different branches. Results are also given for intermediate coupling.

On the reduction of the critical velocity in a model of a superfluid Bose-gas with boundary interactions

Abstract The existence of superfluidity in a 3D Bose-gas can depend on boundary interactions with channel walls. We study a simple model where the dilute moving Bose-gas interacts with the walls via hard-core repulsion. Special boundary excitations are introduced, and their excitation spectrum is calculated within a semiclassical approximation. It turns out that the state of the moving Bose-gas is unstable with respect to the creation of these boundary excitations in the system gas + walls, i.e. the critical velocity vanishes in the semiclassical (Bogoliubov) approximation. We discuss how a condensate wave function, the boundary excitation spectrum and, hence, the value of the critical velocity can change in more realistic models, in which “smooth” attractive interaction between the gas and walls is taken into account.

Optical absorption weak coupling theory of polarons bound to defects

Abstract We calculate the infrared absorption of large polarons bound to defects in the weak coupling limit. Polar crystals with more than one longitudinal optical phonon branch coupled to the electrons are considered. Oscillator strengths corresponding to defect transitions without phonons and to transitions with emission of phonons are calculated using the Larsen wave-functions. The results are applied to infrared data in strontium titanate and it is found that weak coupling calculations are in better agreement than strong coupling ones.

Peierls and spin-Peierls phase transitions in structurally unstable quasi-one-dimensional solids

Abstract The Peierls and spin-Peierls phase transitions are studied in solids in which a structural instability is already present. It is found that the presence of this intrinsic mode can increase considerably the critical temperature. For small values of the critical temperature, the transition is of the BCS-type, like the Peierls (or spin-Peierls) phase transition, but with an effective electron (or spin)-phonon coupling constant renormalized by the anharmonicity and by the instability of the phonon. Numerical results are also presented for larger critical temperatures. Then the BCS behaviour is no longer observed.

Image states on impenetrable surfaces of metals

Abstract We calculate the binding energy of an exterior electron bound to an impenetrable metallic surface by its image potential. To describe the image state, we use a microscopic model, involving the coupling of the electron to dispersionless surface plasmons. This coupling is treated dynamically, in the framework of a Fock approximation derived from a Greens function approach. We find that, for an abrupt surface, the binding energy depends only on the frequency of the surface plasmons. Our results are compared with other theoretical treatments and with experimental data obtained for three transition metal (0 0 1) surfaces: Cu, Ag and Au.

Tight-binding optical polaron in the adiabatic limit

Abstract The problem of a tight-binding polaron interacting with the longitudinal optical phonons in a polar crystal is investigated in the adiabatic limit. A Pekar-type variational wavefunction, including a tight-binding electronic part is used in order to get the ground-state energy of the system. We find and characterize two limiting cases: a self-trapped state for large coupling and a band state for smaller electron-phonon interactions. The continuum Frohlich limit can also be found from our approach.

Effect of a Debye Cutoff on the ground-state energy of the Fröhlich polaron

Abstract The behaviour of a large Frohlich polaron in a polar crystal is investigated when a Debye cutoff is made on the phonon wave vectors. We find that the cutoff eliminates the strong-coupling behaviour (ground-state energy quadratic in the electron-phonon coupling) in the limit of large electron-phonon coupling. However, such a strong coupling behaviour is found for intermediate values of coupling and for moderate cutoffs.

Density of localized states in low-mobility materials: A numerical study

Abstract We describe a procedure for extracting the density of localized states in the gap of low-mobility materials from transient photocurrent measurements. We base our analysis on the multiple-trapping transport model, and present a deconvolution scheme which determines, for each discrete trap level, a set of time-temperature combinations which optimizes the information that can be extracted for this level. The density of states is then obtained from the currents using a numerical technique suitable for overdetermined linear systems. We apply our procedure to signals generated on the computer using, as a starting point, an exponential band tail, appropriate to amorphous semiconductors, as well as a delta-like distribution, either singly or doubly peaked, appropriate to doped crystalline systems. The deconvoluted distributions of states are in all cases found to be in excellent agreement with the original ones. We indicate how our method could be extended to the analysis of real data, currently not available in the time-temperature regime appropriate to our procedure.