Mustre de Leonet al.Reply:

Abstract

Mustre de Leon et al. Reply: Koval et al. [1] appear to agree with the physical results obtained in Ref. [2], but assert that our exact results for the coupled electron-phonon model can also be calculated accurately in an adiabatic approximation.We partially agree with this conclusion for some properties, but note that it can be reached only by comparison with a (numerically) exact calculation. In addition, we show that while an adiabatic approximation explains several of the exact results, it fails for at least two important properties in the intermediate and strong coupling regimes: the tunnel splitting and the strength of the optical absorption. In view of rapidly improving experimental probes for polarons and polarization, controlled quantitative calculations are necessary.There are several versions of the adiabatic approximation used in the literature: (a) The ionic coordinates are treated as parameters, and the total energy is minimized as a function of these parameters. (b) The total energy is expanded to quadratic order about a minimum, and the zero-point and harmonic phonon excitations are included.(c) The total energy is calculated for all relevant ionic coordinates, resulting in a multivariable nonlinear potential coupling all of the ionic degrees of freedom. This nonlinear problem is then solved "exactly. " It is clear that versions (a) and (b) of the adiabatic approximation fail qualitatively for intermediate and strong coupling, because they neglect tunneling between degenerate minima. Koval et al. consider the more sophisticated version (c), which results in a difficult calculation.The electronic energy must be obtained for all relevant phonon coordinates, and used to calculate a large, nonsparse Hamiltonian in the basis of infrared and Raman phonons~ntR, n~). The Hamiltonian matrix must then be diagonalized numerically.To calculate absorption spectra, one must take into account that the dipole operator has an electronic as well as a phonon contribution, and thus in the adiabatic approximation is a nontrivial function of the phonon coordinates that must be numerically tabulated and used to obtain matrix elements. In contrast, for the exact method used in Ref.[2], the Hamiltonian matrix is sparse and trivial to calculate, and the dipole operator is also trivial. (Our Hamiltonian matrix is, however, somewhat larger. ) The adiabatic calculation is thus significantly more difficult to program than the exact one, and may not even save computer resources or allow calculations for larger systems, as compared to our exact numerical approach.It is, nonetheless, of interest to know whether one will obtain accurate results if one goes to the trouble of calculating in the adiabatic approximation.We have quantitatively compared energies and eigenstates by diagonalizing the Hamiltonian in the exact and in the adiabatic approximation version (c), with the coupling to Raman phonons Az set to zero for simplicity. We find that for strong electron-IR phonon coupling, AiR, the adiabatic approximation yields ground an...

Unconventional isotope effects in superconductors

“…According to various experimental data ͑x-rays and Raman spectroscopy, transport data, see, e.g., Ref. 18 and recent ion-channeling measurements 19 ͒, the apical oxygen position has two close minima, and this leads to the IE described by Eq. ͑8͒.…”

Isotope effect in high-T c materials: role of non-adiabaticity and magnetic impurities

“…Another example is given by manganites [(La,Ca)MnO 3 ] [7] where the charge transfer occurs between Manganese atoms via an oxygen ion located between them. Several experiments [8,9] as well as theoretical studies [10] have established that in both above-mentioned systems oxygen and copper ions display a non-adiabatic behaviour. This affects the charge transfer between the reservoir and the conducting layer, because the latter process involves the motion of the non-adiabatic ions.…”

Comparison of local structure measurements fromc-axis polarized XAFS between a film and a single crystal ofYBa2CuBooth1, Bridges2, Boyce3 et al. 1996Phys. Rev. B693180View full textAdd to dashboardCite

“…A dynamic model that would lead to either a broadening or a split O͑4͒ position is the hopping small-polaron model, with the polaron hopping on and off the Cu-O͑4͒ bonds as discussed by Mustre de Leon et al 6 Ranninger 13 has calculated the XAFS signatures for the presence of polarons and shown that as the hopping speed decreases, the pairdistribution function first broadens and then splits; less than a factor of 2 in hopping speed is required to change from a broadened peak to a split peak. This is expected from the following simple argument.…”

“…13 Å͒ in YBCO that decreases somewhat or disappears (␦rՇ0.11 Å͒ near T c . 5,6 Both of these measurements were initially treated with a fair amount of skepticism, because obtaining a reliable signal for measuring such small changes is difficult. The result of Horn et al has since been confirmed both by diffraction 7 and by capacitive dilatometry measurements 8 and consequently must be considered real, although its relation to T c is still unclear.…”