El-ph Coupling Research Articles

Quantum dynamics of polaron formation

We calculate the real space and time formation of a polaron quasiparticle from a bare electron. The time-dependent Schr\odinger equation for the Holstein model of electron-phonon coupling is numerically integrated in a large Hilbert space to obtain the time evolution of the electron and phonon densities and the electron-phonon (el-ph) correlation functions. The quantum dynamical nature of the phonons is preserved. As the el-ph coupling increases, qualitative changes in polaron formation occur when the one-phonon polaron bound state forms. A potential barrier between the quasifree and heavy polaron states exists in dimensions $D\ensuremath{\geqslant}2$, consistent with earlier adiabatic theory. We compare to recent experiments.

Phase diagram and isotope effects of the quasi-one-dimensional electron gas coupled to phonons

Using a multistep renormalization group method, we study the low-temperature phases of the interacting one-dimensional (1D) electron gas coupled to phonons. We obtain analytic expressions for the weak-coupling quantum phase boundaries of the 1D extended Holstein-Hubbard model and the 1D extended Peierls-Hubbard model for general band-filling and phonon frequency. Away from half-filling, the phase diagrams are characterized by a delicate competition between spin density wave, charge density wave, and superconducting orders. We study the dependence of the ground state on the electron-phonon (el-ph) and electron-electron (el-el) coupling strengths, the screening length, electron bandwidth, phonon frequency, doping, and type of phonon. Unlike the case in Fermi liquids, in 1D the el-ph coupling is strongly renormalized, often to stronger values. Even when the bare phonon-induced attraction is weak compared to the bare el-el repulsion, a small amount of retardation can cause the renormalized el-ph interaction to dominate the problem. We find cases in which a repulsive el-el interaction enhances the superconducting susceptibility in the presence of a retarded el-ph interaction. The spin gap and superconducting susceptibility are found to be strongly dependent on the deviation from half-filling (doping). In some cases, the superconducting susceptibility varies nonmonotonically with doping and exhibits a maximum at a particular doping. For a quasi-1D array of weakly coupled, fluctuating 1D chains, the superconducting transition temperature T_c also exhibits a maximum as a function of doping. The effect of changing the ion mass (isotope effect) on T_c is found to be largest near half-filling and to decrease rapidly with doping.

Electronic structure and anisotropic superconductivity in diborides and borocarbides

We compare calculated Fermi surface sheet (FSS) areas F and masses of MgB 2 and ZrB 2 with dHvA data. Deviations in F in MgB 2 can be removed by a small mutual shift of σ- and π bands. The dHvA masses lead to orbit averaged el–ph coupling constants λ ̄ σ ≈1.03 and λ ̄ π ≈0.32 , while for ZrB 2 only λ ̄ <0.1 holds. The anisotropy of the Fermi velocities and the orbital character of various FSS of rare earth (R) transition metal (T) borocarbides RT 2B 2C, their relationship to the H c2-anisotropy, and the coexistence of magnetism and superconductivity are discussed.

Triplet excitons in acyl- and alkyl-substituted polycarbazolyldiacetylenes: A spectroscopical and photophysical study

Absorption, photoluminescence, and photoinduced absorption (PIA) spectra of films of red phase polycarbazolyldiacetylenes (polyCzDAs) carrying selected acyl (polyDPCHD) or alkyl (polyDCHD-HS) groups are reported. The absorption spectrum of polyDCHD-HS, which is almost independent of the temperature down to 20 K, shows an excitonic absorption followed by an inhomogeneously broadened vibronic progression. Very different is instead the case of polyDPCHD whose thin films show a very sharp excitonic transition and a vibronic progression with a lower electron-phonon (el-ph) coupling with respect to that of polyDCHD-HS. These peculiar characteristics allow the detection of additional features in the spectra, which are assigned on the basis of quantum chemical calculations to string modes of the backbone. As far as thick films of polyDPCHD are concerned, broad electronic spectra are observed. Raman spectroscopy studies suggest that this broadening is due to the presence of two forms of the polymer. Unlike other polydiacetylenes (PDA's) including polyDCHD-HS films, polyDPCHD films are also strongly luminescent, thus suggesting a different ordering of the dipole forbidden and allowed states. For these materials, the photoinduced absorption spectra are dominated by triplet excitons. Effects of different forms in acyl substituted polymers are observed also in the PIA spectra. The rise and decay of the triplet signal for polyDCHD-HS are accounted for through a dynamical model, which includes saturation effects in the monomolecular decay regime. A more complex kinetics is instead observed for polyDPCHD. From the study of the kinetics of the PIA spectra both the triplet generation efficiency and the density of traps are evaluated.

Electron-phonon vertex in the two-dimensional one-band Hubbard model

Using quantum Monte Carlo techniques, we study the effects of electronic correlations on the effective electron-phonon (el-ph) coupling in a two-dimensional one-band Hubbard model. We consider a momentum-independent bare ionic el-ph coupling. In the weak- and intermediate-correlation regimes, we find that the on-site Coulomb interaction U acts to effectively suppress the ionic el-ph coupling at all electron and phonon momenta. In this regime, our numerical simulations are in good agreement with the results of perturbation theory to order ${U}^{2}.$ However, entering the strong-correlation regime, we find that the forward-scattering process stops decreasing and begins to substantially increase as a function of U, leading to an effective el-ph coupling which is peaked in the forward direction. Whereas at weak and intermediate Coulomb interactions, screening is the dominant correlation effect suppressing the el-ph coupling, at larger U values irreducible vertex corrections become more important and give rise to this increase. These vertex corrections depend crucially on the renormalized electronic structure of the strongly correlated system.

Jahn-Teller Effect and Electron Correlation in Manganites

Jahn-Teller (JT) effect in manganites is studied theoretically both in the absence and presence of the Coulomb interaction. The focus is on the role of orbital degeneracy, i.e., multiband effect, in the electron-phonon (el-ph) interaction. The kinetic energy gain K, which is directly related to the spin-wave stiffness, is calculated to compare with the experiments. Without the Coulomb interaction, the perturbative analysis gives the reduction ΔK of K due to the JT coupling as ΔK≅(0.7-1.9)(Ω/t 0 )(g 2 /MΩ 2 ) with the prefactor determined mostly by the density of states at the Fermi energy [g: electron-phonon (el-ph) coupling constant. M: mass of the oxygen atom; Ω: frequency of the phonon; t 0 : transfer integral]. Although there occur many second-order perturbative processes, ΔK roughly scales with the density of states at the Fermi energy. The magnitude of ΔK is at most 3% of K and is negligible in this case. In the limit of strong electron correlation. on the other hand, the magnitude of the orbital polarization saturates and the relevant degrees of freedom are its direction. An effective action is derived, and it is found that the JT interaction is enhanced compared with the noninteracting case, and AK is given by the lattice relaxation energy E L for the localized electrons, although the electrons remains itinerant with the bandwidth of the order of t 0 , which is larger than E L . Therefore there should be an appreciable reduction of the spin stiffness due to JT coupling in manganites.

Jahn-Teller effect and electron correlation in manganites

Jahn-Teller (JT) effect both in the absence and presence of the strong Coulomb correlation is studied theoretically focusing on the reduction $\Delta K$ of the kinetic energy gain which is directly related to the spin wave stiffness. Without the Coulomb interaction, the perturbative analysis gives $\Delta K / (g^2/M\Omega^2) \cong 0.05-0.13$ depending on the electron number [$g$: electron-phonon(el-ph) coupling constant, $M$: mass of the oxygen atom, $\Omega$: frequency of the phonon]. Although there occurs many channels of the JT el-ph interaction in the multiband system, the final results of $\Delta K$ roughly scales with the density of states at the Fermi energy. In the limit of strong electron correlation, the magnitude of the orbital polarization saturate and the relevant degrees of freedom are the direction (phase) of it. An effective action is derived for the phase variable including the effect of the JT interaction. In this limit, JT interaction is {\it{enhanced}} compared with the non-interacting case, and $\Delta K$ is given by the lattice relaxation energy $E_{L}$ for the localized electrons, although the electrons remains itinerant. Discussion on experiments are given based on these theoretical results.

Conventional Electronic Structure of MgB2 and ZrB2: LDA vs. de Haas-v. Alphen & ARPES Data

We compare full potential LDA band calculations of the Fermi surfaces areas and band masses of MgB2 and ZrB2 previously reported and new dHvA data. Discrepancies in areas in MgB2 can be removed by a small shift of σ bands relative to π bands. Comparison of effective masses lead to orbit averaged el-ph coupling constants λσ=1.3 and λπ=0.5, whereas for ZrB2 only weak el-ph coupling with λ<0.3 is found. The ARPES data can be also well described by the LDA showing the presence of surface states.

Pressure-induced electronic coupling in CdSe semiconductor quantum dots

While previous high-pressure optical and vibrational studies on CdSe quantum dots (QD's) have observed no evidence for size-dependent scaling laws in the experimental pressure behavior, we have found that low-pressure studies exhibit anomalous pressure dependencies that can be analyzed in two specific size regimes $(rl{a}_{0}$ and $r\ensuremath{\sim}{a}_{0},$ where r is the particle radius and ${a}_{0}$ is the Bohr radius). This corresponds to the limits of strong and weak confinement of the exciton for CdSe. By using photoluminescence and resonance Raman spectroscopies, we find optical and vibrational coefficients (82 meV ${\mathrm{GPa}}^{\mathrm{\ensuremath{-}}1}$ and 3.51 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ ${\mathrm{GPa}}^{\mathrm{\ensuremath{-}}1}$, respectively, for 22.5 \AA{} radius dots) that significantly deviate from reported bulk values (37 meV ${\mathrm{GPa}}^{\mathrm{\ensuremath{-}}1}$) when $rl{a}_{0}.$ At the largest QD sizes studied $(r=40\AA{}),$ bulk-like pressure dependence is observed as expected. We believe the anomalous size dependent pressure behavior arises from changes in the nature of the electron-phonon (el-ph) coupling due to polaronic coupling in the QD lattice. Analyses of longitudinal optical mode Gr\uneisen parameters $({\ensuremath{\gamma}}_{\mathrm{LO}})$ show the expected el-ph coupling strengths derived from ${\ensuremath{\gamma}}_{\mathrm{LO}}$ agree well with calculated values for el-ph coupling strengths in CdSe QD's. An empirical pressure-dependent model is proposed which argues that polaronic decoupling occurs following a $1/r$ scaling law, which may be due to changes in el-ph coupling in these dimensionally restricted materials.

Role of the electron-phonon interaction in the strongly correlated cuprate superconductors

Using high resolution angle-resolved photoemission data in conjunction with that from neutron and other probes, we show that electron-phonon (el-ph) coupling is strong in cuprates superconductors and it plays an important role in pairing. In addition to the strong electron correlation, the inclusion of phonons provides a theoretical framework explaining many important phenomena that cannot be understood by a strongly correlated electronic model alone. Especially it is indispensable to explain the difference among materials. The phonons with the wave number around the (0,qx) and (qx,0) axes create the d-wave pairing while that near (pi,pi) are pair breaking. Therefore the half-breathing mode of the oxygen motions helps d-wave superconductivity.

Electronic structure and superconductivity of nonmagnetic transition metal borocarbides

The electronic structure of tetragonal (RC(N))m(TB)2, m=1−3, compounds, with R= Y,Lu,La, T=Ni,Pt is studied. Total and partial densities of states N(E) are calculated and compared with orbital resolved x-ray absorption data. Special attention is paid to the structure of N(E) near the Fermi-level and its consequences for thermodynamic properties in the superconducting and the normal states. A medium el-ph coupling constant 0.5≤λ≤ 1.2 is found. There is no simple correlation between N(0) and Tc. The analysis of the upper critical field reveals the presence of at least two groups of electrons with quite different Fermi velocities vFin accord with dHvA data, and with calculated distributions of vFaround the Fermi surface

Halogen-bridged mixed valence Pt complexes: Comparison with mixed and segregated stack charge-transfer crystals

Halogen-bridged mixed valence Pt (Pd, Ni) complexes (MX chains) are compared with other one-dimensional (ID) half filled systems having segregated or mixed stack structure. Hamiltonians describing MX chains and mixed stacks are found to be equivalent, so that the neutral-ionic (N-I) interface of mixed stacks and the sCDW-bCDW interface (site- and bond-charge density wave) of segregated stacks share the same physics. The resulting picture is confirmed by valence bond (VB) calculations on segregated stack systems. The fundamental role of interelectronic (e-e) interactions in determining the stack geometry is underlined. The effects of electron-molecular vibration (e-mv) and electron-lattice phonon (e-lph) couplings are investigated by making resort to results of VB calculations on mixed regular and segregated dimerized stacks.

Effect of e-mv coupling on the dimerization and neutral-ionic instabilities of quasi-1D charge-transfer crystals: Finite vs infinite U results

A brief account of the results of valence bond (VB) calculations on finite U (on-site interelectronic interaction) mixed stack charge transfer (CT) crystals is given. The results are compared with the previously reported U = ∞ ones. The effects of electron-molecular vibration (e-mv) and electron-lattice phonon (e-lph) couplings on the phase stability of the system are discussed and the cooperation between them in setting up the chain dimerization is underlined.

Microscopic theory of electron-phonon interaction in insulators or semiconductors

A unified treatment of the electron-phonon interaction matrix $M$ in insulators (or semiconductors at low temperatures) is given in terms of the complete linear electron response within the adiabatic approximation. The effective electron-one-phonon (el-ph) potential $M$ which is constructed, analogously to metals, as a screened vertex-corrected renormalized (bare) ion potential is defined, including all many-body corrections. We derive the small-wave-vector ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$) limit of $M$ leading to multipole as well as short-range contributions by separating out the electron response for fixed macroscopic electric field and using the analytical properties of the inverse dielectric tensor ${\ensuremath{\epsilon}}^{\ensuremath{-}1}$. We obtain explicit expressions for all standard types of el-ph couplings in terms of microscopic quantities in principle calculable from band structure. The main results of Lawaetz are rederived and new---indirectly induced---multipole terms are obtained. A new quadrupole sum rule for $\ensuremath{\epsilon}$ is proved which guarantees, together with the already known acoustic sum rule, the well-known behavior of the acoustic scattering potential as a function of $q$ in the elastic limit. An effective el-two-ph scattering is investigated; further sum rules are proved representing constraints on a nonlinear response function.