Large Electron-phonon Coupling Research Articles

Vibronic coupling in molecules and in solids.

We utilize the experience gained in our previous studies on the "chemistry of vibronic coupling" in simple homonuclear and heteronuclear molecules to begin assembling theoretical guidelines for the construction of potentially superconducting solids exhibiting large electron-phonon coupling. For this purpose we analyze similarities between vibronic coupling in isolated molecules and in extended solids. In particular, we study vibronic coupling along the antisymmetric stretch coordinate (Q(as)) in linear symmetric AAA molecules, and along the optical phonon "pairing" mode coordinate (Q(opt)) in corresponding one-dimensional [A]( infinity ) chains built of equidistant A atoms. This is done for a broad range of chemical elements (A). The following similarities between vibronic coupling in molecules and phonon coupling in solids emerge from our calculations: 1) The HOMO/LUMO electronic energy gap in an AAA molecule increases along Q(as), and the highest occupied crystal orbital/lowest unoccupied crystal orbital gap in [A]( infinity ) chain increases along Q(opt). 2) The maximum vibronic instability is invariably obtained for a half-filled, singly occupied molecular orbital in AAA molecules, and for a corresponding half-filled band in [A]( infinity ) chains. 3) The vibronic stability of an AAA molecule increases with a decrease of the AA bond length, as does the vibronic stability of [A]( infinity ) chains (external pressure may lead to a reversal of a Peierls distortion). 4) The high degree of s-p mixing and ionic/covalent forbidden curve crossing dramatically enhance the vibronic instability of both AAA molecules and [A]( infinity ) chains. We also introduce one quantitative relationship: The parameter log(R) (where R is molar refractivity, a parameter used by Herzfeld to prescribe the conditions for the metallization of the elements) correlates with a parameter f(AA) (defined as twice the electronegativity of A, divided by the equilibrium AA bond length), used by two of us previously to describe vibronic coupling in AAA molecules for a broad range of elements (A=halogen, H, or an alkali metal). We hope to illustrate that key chemical aspects of vibronic coupling in simple molecules may thus be profitably transferred to corresponding materials in the solid state.

Point-contact spectroscopy of single crystalLa0.75Sr0.25MnO3and resistivity due to electron-phonon interaction

In this paper we report point-contact spectroscopy (PCS) measurements on single crystals of metallic ${\mathrm{La}}_{0.75}{\mathrm{Sr}}_{0.25}{\mathrm{MnO}}_{3}.$ The electron-phonon coupling function as obtained from the PCS shows large peaks for phonon frequencies $20 \mathrm{meV}<~\ensuremath{\omega}<~100 \mathrm{meV}.$ This leads to a rather large electron-phonon coupling constant $\ensuremath{\lambda}\ensuremath{\simeq}1.2.$ We have shown that a sizable fraction of the total resistivity in the temperature range $T<~{0.4T}_{c}$ can be of phononic origin and can be explained using the experimentally observed electron-phonon coupling function. As $\stackrel{\ensuremath{\rightarrow}}{T}{T}_{c},$ extra contribution to resistivity arising from spins dominate. We find that the magnetoresistance vanishes in the temperature range $T<~{0.4T}_{c},$ where the predominant contribution to $\ensuremath{\rho}$ arises from phonons. We have also performed PCS in 6 T magnetic field. The resistivity calculated from the spectrum at 6 T does not differ appreciably from that calculated at 0 T. Our experiment has been validated by a similar experiment on a nonmagnetic perovskite oxide system, ${\mathrm{Na}}_{0.9}{\mathrm{WO}}_{3}.$

Electron–phonon coupling in negatively charged acene- and phenanthrene-edge-type hydrocarbon crystals

Vibronic interaction and its role in the occurrence of possible superconductivity in the monoanions of phenanthrene-edge-type aromatic hydrocarbons are studied. The vibrational frequencies and the vibronic coupling constants are computed and analyzed and the electron–phonon coupling constants are estimated. The results for phenanthrene-edge-type hydrocarbons are compared with those for acene-edge-type hydrocarbons. The lowest frequency mode and the C–C stretching modes of 1400–1600 cm−1 afford large electron–phonon coupling constants in the monoanions of acene- and phenanthrene-edge-type hydrocarbons. The total electron–phonon coupling constants decrease with an increase in the number of carbon atoms in both acene- and phenanthrene-edge-type hydrocarbons, but those for the monoanions of phenanthrene-edge-type hydrocarbons are larger than those for the monoanions of acene-edge-type hydrocarbons. Possible superconducting transition temperatures Tcs for the monoanions are estimated. The monoanions of phenanthrene-edge-type hydrocarbons would have higher Tcs than the monoanions of acene-edge- type hydrocarbons if phenanthrene-edge-type hydrocarbons exhibit superconductivity. These results suggest that molecular edge structures as well as molecular sizes have relevance to the strength of electron–phonon coupling and Tcs. The fragment molecular-orbital method (FMO) method successfully characterizes the distinct electronic structures of the two small polynuclear aromatic hydrocarbons (PAHs) with different type of edges such as anthracene and phenanthrene.

Vibronic interactions and superconductivity in acene anions and cations

Vibronic interaction and its role in the occurrence of superconductivity in the monoanions and cations of benzene and acenes are studied. The vibrational frequencies and the vibronic coupling constants for benzene and acenes are computed and analyzed and electron—phonon coupling constants in the monoanions and cations are evaluated. The C–C stretching E2g mode of 1656 cm−1 affords large electron—phonon coupling constants in the monoanion and cation of benzene. The C–C stretching Ag modes of 1400–1600 cm−1 and the lowest frequency Ag mode play an important role in the electron–phonon coupling in the monoanions of acenes, while the only C–C stretching Ag modes of 1400–1600 cm−1 afford large electron–phonon coupling constants in the monocations of acenes. We estimate possible superconducting transition temperatures Tcs for the monoanions and cations of benzene and acenes. The predicted Tcs for the monocations of benzene and acenes are much lower than those for the monoanions. Possible high-temperature superconductivity in the monoanion and cation of benzene is suggested.

Spin waves and large electron-phonon coupling near the metal-insulator transition in hole-doped high-Tcoxides

A theory for spin and lattice couplings to the electronic states in high-T$_C$ oxides is presented, with HgBa$_2$CuO$_4$ as an example. A simple analytical model suggests that the barrel band is sensitive to potential perturbations with long-range Fourier components, and that gaps can be opened at the Fermi energy. This is confirmed in self-consistent band calculations for modulations in elongated supercells, where spin waves and phonon coupling compete for equal q-vectors. It is argued that the wavelengths of spin-wave modulations and of the phonon modes with large coupling, depend on the doping. This mechanism supports the idea that pseudogaps are caused by stripe like spin-modulations in underdoped systems, while superconductivity is attributed to enhanced electron-phonon coupling for long wavelength phonons.

The complex nature of superconductivity in MgB2 as revealed by the reduced total isotope effect.

Magnesium diboride, MgB2, was recently observed to become superconducting at 39 K, which is the highest known transition temperature for a non-copper-oxide bulk material. Isotope-effect measurements, in which atoms are substituted by isotopes of different mass to systematically change the phonon frequencies, are one of the fundamental tests of the nature of the superconducting mechanism in a material. In a conventional Bardeen-Cooper-Schrieffer (BCS) superconductor, where the mechanism is mediated by electron-phonon coupling, the total isotope-effect coefficient (in this case, the sum of both the Mg and B coefficients) should be about 0.5. The boron isotope effect was previously shown to be large and that was sufficient to establish that MgB2 is a conventional superconductor, but the Mg effect has not hitherto been measured. Here we report the determination of the Mg isotope effect, which is small but measurable. The total reduced isotope-effect coefficient is 0.32, which is much lower than the value expected for a typical BCS superconductor. The low value could be due to complex materials properties, and would seem to require both a large electron-phonon coupling constant and a value of mu* (the repulsive electron-electron interaction) larger than found for most simple metals.

Tuning the spectral and temporal response in PtAu core–shell nanoparticles

Ultrafast laser spectroscopy has been used to measure the electron–phonon coupling constant in PtAu core–shell bimetallic nanoparticles. A chemical reduction method was used to prepare Pt cores of 12.5 nm diameter and a γ-radiolytic deposition technique was then used to grow Au shells of variable thickness. The resulting nanoparticles have a spectrum that is characteristic of Au. It is found that the electron–phonon coupling time for these hybrid nanoparticles (τe–ph∼200 fs) is over a factor of 3 shorter than that for plain Au nanoparticles (τe–ph∼650 fs). The faster dynamical response is due to the large electron–phonon coupling constant for Pt, which provides efficient scattering of the excited electrons. Platinum dominates the temporal response, even for a 1:6 molar ratio of Pt to Au, because it has a much larger density of states near the Fermi level compared to Au.

Simple estimate of electron-phonon coupling in small fullerenes

Simple scaling arguments show how contributions to the electron-phonon coupling strength vary with the number of atoms in a carbon fullerene. Smaller fullerenes have higher curvature, which yields larger electron-phonon coupling. The enhancement in coupling is inversely proportional to the number of atoms in the fullerene molecule. Recent ab initio theoretical results on ${\mathrm{C}}_{36}$ fit well within this simple model.

Coherent phonon and electron spectroscopy on surfaces using time-resolved second-harmonic generation

(ω)Eprobe*(ω)|Eprobe(ω)|2. This is much easier to detect than transient grating, photon echo, or four-wave mixing schemes that use higher-order nonlinearities. We have applied this technique to measure the energy gap and dephasing time of the dangling bond interband transition on the GaAs(110)-relaxed (1×1) surface. Surface-carrier/surface-phonon interaction plays an important and perhaps dominant role in surface carrier dephasing consistent with the larger electron-phonon coupling on the surface compared to the bulk.

Luminescence from V3+ in tetrahedral oxo-coordination

Luminescence from trivalent vanadium in tetrahedral oxo-coordination is observed in LiGaO 2 , LiAlO 2 , and SrAl 2 O 4 . In LiGaO 2 the V 3+ ion exhibits the most intense broad-band emission between 1400 and 2000 nm with lifetimes of 89 and 11 μs at 12 and 300 K, respectively. The decrease in the lifetime is mainly caused by non-radiative decay processes, the quantum efficiency at room temperature is about 2.5%. In LiAlO 2 and SrAl 2 O 4 the non-radiative quenching process is even stronger because of the smaller energy gap between the participating levels and the larger electron–phonon coupling. In all crystals, even at low temperature, significant non-radiative decay occurs.

Contribution of nonequilibrium optical phonons to the Peltier and Seebeck effects in polar semiconductors

Additive contributions to the Seebeck and Peltier coefficients made by nonequilibrium longitudinal optical phonons have been calculated. The results obtained are valid for any temperature and applicable to polar nondegenerate semiconductors with low carrier concentrations. The calculated components of the thermoelectric coefficients are exponentially small in the low-temperature domain and reach a maximum at kBT∼ħω0. In materials with a large carrier mass and strong electron-phonon coupling the contribution of optical phonons to the Seebeck coefficient can exceed 1 mV/K.

Photoconductivity of undoped, nitrogen- and boron-doped CVD- and synthetic diamond

Abstract Nitrogen-doped CVD- and synthetic type IIa and Ib diamonds were investigated by the constant photocurrent method (CPM). Nominally undoped CVD-films containing nitrogen show broad absorption bands with threshold energies at 1, 2.3, 3 and 4.2 eV. The typical nitrogen donor absorption band with a threshold at 1.7 eV is partially masked by the 1 eV band in CVD-films. The absorption bands are too broad to be described by simple theories based on photoionization of single unbroadened impurity levels. Boron-doped CVD- and type IIb synthetic diamond was studied by photoconductivity and photothermal ionization in the near infra-red. The large electron-phonon coupling in diamond gives rise to oscillatory photoconductivity minima due to fast capture of holes by the excited states of boron acceptors. In CVD-films with boron concentrations around 1019 cm−3, the oscillation pattern inverts at low temperatures and sharp minima were found in the spectrum.

Electronic and relaxation contribution to linear molecular polarizability. An analysis of the experimental values

This paper reports and comments on the experimental values of \\ ̄ ga e and \\ ̄ ga r of more than 650 molecules, where \\ ̄ ga e and \\ ̄ ga r are the mean values of the electronic polarizability tensor α e and of the relaxation polarizability tensor α r, respectively. It is assumed that α e and α r sum up to α, the static polarizability of the molecule that can be directly measured through the dielectric constant. Thus, only values of α e independent of the frequency are reported. The principal targets of this paper are: (1) to collect from literature the largest amount of experimental data of \\ ̄ ga e and \\ ̄ ga r and try to group the data for classification and characterization of the electrical behaviour of molecules; (2) to find out which classes of molecules have unusual \\ ̄ ga e and/or \\ ̄ ga r ; (3) to interpret the data in terms of charge distribution; and (4) to provide a basis for comparing with experiment the values \\ ̄ ga e and \\ ̄ ga r calculated by quantum chemical methods. The main conclusions are: \\ ̄ ga e increases with the number Z of electrons in the molecule so that the polarizability per electron ( \\ ̄ ga e Z ) is reasonably constant except for conjugated molecules (where it is slightly larger) and for halogenated molecules (where it is much smaller); \\ ̄ ga r ranges from very low to rather large values, apparently without any correlation nor with the corresponding \\ ̄ ga e or the number Z of electrons or the number v of oscillators in the molecule; the largest values of \\ ̄ ga r are reached for molecules having spherical shape and the largest ratio \\ ̄ ga r \\ ̄ ga e is attained by molecules containing several halogen atoms. These data seem to suggest an additive scheme for the mean value of the electronic polarizabllity. On the contrary, \\ ̄ ga r does not obey any additive scheme; large \\ ̄ ga r and large \\ ̄ ga r \\ ̄ ga e seem to be connected to large charge fluxes associated to vibrations and therefore to large electron-phonon coupling. All the above considerations hold for the mean values of the polarizability tensors. A different behaviour of the single components of α e and α r is also discussed.

Non-polynomial phonon action for a dimer with one electron

The partition function of a dimer with one electron, interacting with two local Einstein phonons, is reduced to the pure phonon partition function. It is investigated analytically in the coherent-state path-integral representation in order to recognize the competition between electron hopping and electron-phonon interaction. The non-polynomial term in the phonon action, promoted by electron hopping, is deduced. The low-temperature resonance decoupling between electron and phonon systems destroys the low-temperature tendency of electron localization in the case of small hopping and large electron-phonon coupling. The comparison with polaronic theory is completed.

Polaron defects in a charge density wave: a model for lightly doped BaBiO3

A model for BaBiO3 was introduced by Rice and Sneddon, which treats this material as a simple three-dimensional version of a Peierls insulator, where the insulating gap is a consequence of the ordered distortion of the oxygen atoms. Charge accumulates on half the atoms and depletes from the other half. Experimentally, when holes are added to BaBiO3 by doping, it remains insulating until a very large hole concentration is reached, at which point it becomes superconducting. In the Rice-Sneddon model, at large enough electron-phonon coupling, a mechanism for insulating behavior of doped samples is formation of small polarons or bipolarons which trap carriers in bound states in the Peierls gap. A variational calculation of the polaron binding in this model is given, and compared with “exact” numerical results on large clusters with periodic boundary conditions.

Effect of temperature on polaronic and bipolaronic structures of the adiabatic Holstein model

It is proved that the polaronic and bipolaronic structures found in the adiabatic Holstein model at large electron-phonon coupling by Aubry, Abramovici, and Raimbault survive under connection of the electrons to a low-temperature heat bath, uniformly in the size of the system. Bounds are computed for one-dimensional nearest neighbor chains, and some sample solutions are continued numerically.

Electron relaxation in the conduction band of wide-band-gap oxides.

Using quantum kinetic equations with memory we calculate the time-dependent distribution function of an electron gas injected suddenly in the conduction band of a wide-band-gap insulator. A comparison is made with the semiclassical Boltzmann equation approach. We show that due to the large electron-phonon coupling occurring in such materials a quantum approach is needed.

Theoretical evidence forc-axis phonon-plasmon coupling and phonon renormalization in La2CuO4

A suitable decomposition of the electronic density response and of the electron-phonon interaction into local and nonlocal contributions is extended to the nonadiabatic regime taking dynamical screening into account. It is shown for La2CuO4 that the already large (nonlocal) adiabatic electron-phonon coupling is further strongly enhanced for certain phonons along the λ∼(0, 0, 1) direction. In this region of wave-vector space we also have a low-lying plasmon mode which mixes strongly with the phonons of appropriate symmetry leading to an anomalous renormalization for certain phonons. The coexistence of phononlike and plasmonlike resonances in the same frequency range is argued to be a specific feature of the layered high-temperature superconductors.

Non-2kF charge density wave induced by phonon dispersion in one-dimensional Peierls conductors

Standard Peierls theory predicts that the wave-vector of the charge density wave (CDW) induced by the electron-phonon coupling in the ground-state of a one-dimensional conductor is twice the Fermi wave-vector 2kF. At moderately large electron-phonon coupling, beyond the TBA (transition by breaking of analyticity), it is known that this CDW becomes an array of interacting bipolarons. In the simplest models, such as the 1D adiabatic Holstein model, the bipolaron interactions are repulsive and the ground state remains a 2kF CDW of equidistant bipolarons. We show that (apparently) minor changes in the phonon spectrum of the model induce extra elastic forces between the bipolarons, which could break the bipolaronic 2kF CDW ordering. This effect is studied in detail in the modified 1D Holstein model, where the optical phonon has a non-zero dispersion which is chosen positive in order that an extra force that appears between the bipolarons be attractive. The Coulomb forces between the bipolarons are initially neglected. An accurate numerical study modelled on the standard analysis of multiphase points confirms that, in a large part of the phase diagram, the CDW ground state separates in two phases, which correspond to two CDW with different 2kF wave-vectors (which are generally commensurate) and thus different electronic densities. These separations, into phases called either 'parent' or 'non-parent', are studied on the basis of the Farey construction of rational numbers. The long-range Coulomb interaction between the charged bipolarons, forbids any macroscopic phase separation in two phases with different electronic densities. The bipolaron structure then has to be a periodic sequence of alternate domains of the two CDW phases on the microscopic scale. The resulting structure is a new CDW with a modulation wave-vector that is not 2kF. We suggest that the aberrant wave-vector observed in the real CDW system (TaSe4)2I could be interpreted along the ideas developed in this paper. Although this compound shares many of the usual properties of quasi-one-dimensional conductors with CDW, the component of the modulation wave-vector 0.085c* in the chain direction is, unusually, quite different from the value 2kF=c* expected from band filling. The CDW in (TaSe4)2I could correspond to a nonstandard bipolaron ordering due to a strong attractive elastic interaction between the bipolarons along the chain competing with the long-range Coulomb forces.

Experimental molecular hyperpolarizabilities from vibrational spectra in systems with large electron-phonon coupling

Abstract Experimental data are presented and discussed on the relaxation contribution (β r and γ r ) to first- and second-order molecular hyperpolarizabilities of classes of polyconjugated organic materials. These data are obtained from the measure of classical vibrational observables, i.e., vibrational frequencies, infrared intensities and Raman cross sections. It turns out that the values of β r and γ r are very similar (both in values and trends) to the electronic molecular hyperpolarizabilities β and γ obtained from traditional direct experiments. It is concluded that for the molecular systems considered, β r and γ r may be a good estimate of static, non-resonant β and γ. The justification for such conclusions is that in polyconjugated systems very large electron-phonon coupling takes place such that vibrational displacements are strictly related to and cannot be separated from electronic excitations.