Small Fermi energy, zero point fluctuations and nonadiabaticity in MgB2_2

Small Fermi energy effects are induced in MgB$_2$ by the low hole doping in the $\sigma$ bands which are characterized by a Fermi energy $E_{\rm F}^\sigma \sim 0.5$ eV. We show that, due to the particularly strong deformation potential relative to the $E_{2g}$ phonon mode, lattice fluctuations are reflected in strong fluctuations in the electronic band structure. Quantum fluctuations associated to the zero-point lattice motion are responsible for an uncertainty of the Fermi energy of the order of the Fermi energy itself, leading to the breakdown of the adiabatic principle underlying the Born-Oppenheimer approximation in MgB$_2$ even if $\omega_{\rm ph}/E_{\rm F} \sim 0.1-0.2$, where $\omega_{\rm ph}$ are the characteristic phonon frequencies. This amounts to a new nonadiabatic regime, which could be relevant to other unconventional superconductors.Comment: to appear on Physical Review

Electron-phonon coupling and phonon self-energy in MgB2_2: do we really understand MgB2_2 Raman spectra ?

We consider a model Hamiltonian fitted on the ab-initio band structure to describe the electron-phonon coupling between the electronic $\sigma-$bands and the phonon E$_{2g}$ mode in MgB$_2$. The model allows for analytical calculations and numerical treatments using very large k-point grids. We calculate the phonon self-energy of the E$_{2g}$ mode along two high symmetry directions in the Brillouin zone. We demonstrate that the contribution of the $\sigma$ bands to the Raman linewidth of the E$_{2g}$ mode via the electron-phonon coupling is zero. As a consequence the large resonance seen in Raman experiments cannot be interpreted as originated from the $E_{2g}$ mode at $\Gamma$. We examine in details the effects of Fermi surface singularities in the phonon spectrum and linewidth and we determine the magnitude of finite temperature effects in the the phonon self-energy. From our findings we suggest several possible effects which might be responsible for the MgB$_2$ Raman spectra.Comment: 10 pages, 9 figure

Pauli susceptibility of A3C60 (A=K, Rb)

The Pauli paramagnetic susceptibility of A3C60 (A= K, Rb) compounds is calculated. A lattice quantum Monte Carlo method is applied to a multi-band Hubbard model, including the on-site Coulomb interaction U. It is found that the many-body enhancement of the susceptibility is of the order of a factor of three. This reconciles estimates of the density of states from the susceptibility with other estimates. The enhancement is an example of a substantial many-body effect in the doped fullerenes.Comment: 4 pages, revtex, 2 figures, submitted to Phys. Rev. B more information at http://www.mpi-stuttgart.mpg.de/dokumente/andersen/fullerene

Polaron in t-J model

We present numeric results for ground state and angle resolved photoemission spectra (ARPES) for single hole in t-J model coupled to optical phonons. The systematic-error free diagrammatic Monte Carlo is employed where the Feynman graphs for the Matsubara Green function in imaginary time are summed up completely with respect to phonons variables, while magnetic variables are subjected to non-crossing approximation. We obtain that at electron-phonon coupling constants relevant for high Tc cuprates the polaron undergoes self-trapping crossover to strong coupling limit and theoretical ARPES demonstrate features observed in experiment: a broad peak in the bottom of the spectra has momentum dependence which coincides with that of hole in pure t-J model.Comment: 4 pages, 4 figure

The Electron-Phonon Interaction of Low-Dimensional and Multi-Dimensional Materials from He Atom Scattering

Atom scattering is becoming recognized as a sensitive probe of the electron-phonon interaction parameter $\lambda$ at metal and metal-overlayer surfaces. Here, the theory is developed linking $\lambda$ to the thermal attenuation of atom scattering spectra (in particular, the Debye-Waller factor), to conducting materials of different dimensions, from quasi-one dimensional systems such as W(110):H(1$\times$1) and Bi(114), to quasi-two dimensional layered chalcogenides and high-dimensional surfaces such as quasicrystalline 2ML-Ba(0001)/Cu(001) and d-AlNiCo(00001). Values of $\lambda$ obtained using He atoms compare favorably with known values for the bulk materials. The corresponding analysis indicates in addition the number of layers contributing to the electron-phonon interaction that is measured in an atom surface collision.Comment: 23 pages, 5 figures, 1 tabl

Effect of electron-phonon interaction on spectroscopies in graphene

We calculate the effect of the electron-phonon interaction on the electronic density of states (DOS), the quasiparticle properties and on the optical conductivity of graphene. In metals with DOS constant on the scale of phonon energies, the electron-phonon renormalizations drop out of the dressed DOS, however, due to the Dirac nature of the electron dynamics in graphene, the band DOS is linear in energy and phonon structures remain, which can be emphasized by taking an energy derivative. There is a shift in the chemical potential and in the position in energy of the Dirac point. Also, the DOS can be changed from a linear dependence out of value zero at the Dirac point to quadratic out of a finite value. The optical scattering rate $1/\tau$ sets the energy scale for the rise of the optical conductivity from its universal DC value $4e^2/\pi h$ (expected in the simplest theory when chemical potential and temperature are both $\ll 1/2\tau$) to its universal AC background value $(\sigma_0=\pi e^2/2h)$. As in ordinary metals the DC conductivity remains unrenormalized while its AC value is changed. The optical spectral weight under the intraband Drude is reduced by a mass renormalization factor as is the effective scattering rate. Optical weight is transferred to an Holstein phonon-assisted side band. Due to Pauli blocking the interband transitions are sharply suppressed, but also nearly constant, below twice the value of renormalized chemical potential and also exhibit a phonon-assisted contribution. The universal background conductivity is reduced below $\sigma_0$ at large energies.Comment: 22 pages, 19 figures, submitted to PR

Effects of thermal- and spin- fluctuations on the band structure of purple bronze Li2_2Mo12_{12}O34_{34}

The band structures of ordered and thermally disordered Li$_2$Mo$_{12}$O$_{34}$ are calculated by use of ab-initio DFT-LMTO method. The unusual, very 1-dimensional band dispersion obtained in previous band calculations is confirmed for the ordered structure, and the overall band structure agrees reasonably with existing photoemission data. Dispersion and bandstructure perpendicular to the main dispersive direction is obtained. A temperature dependent band broadening is calculated from configurations with thermal disorder of the atomic positions within the unit cell. This leads a band broadening of the two bands at the Fermi energy which can become comparable to their energy separation. The bands are particularly sensitive to in-plane movements of Mo sites far from the Li-sites, where the density-of-states is highest. The latter fact makes the effect of Li vacancies on the two bands relatively small. Spin-polarized band results for the ordered structure show a surprisingly large exchange enhancement on the high DOS Mo sites. Consequences for spin fluctuations associated with a cell doubling along the conducting direction are discussed

Electron-phonon interaction at the Be(0001) surface

We present a first principle study of the electron-phonon (e-p) interaction at the Be(0001) surface. The real and imaginary part of the e-p self energy are calculated for the surface state in the binding energy range from the $\bar{\Gamma}$ point to the Fermi level. Our calculation shows an overall good agreement with several photoemission data measured at high and low temperatures. Additionally, we show that the energy derivative of real part of the self-energy presents a strong temperature and energy variation close to $E_{F}$, making it difficult to measure its value just at $E_{F}$.Comment: Accepted in Phys. Rev. Lett., 5 figure

Phonon spectroscopy through the electronic density of states in graphene

We study how phonon structure manifests itself in the electronic density of states of graphene. A procedure for extracting the value of the electron-phonon renormalization $\lambda$ is developed. In addition, we identify direct phonon structures. With increasing doping, these structures, along with $\lambda$, grow in amplitude and no longer display particle-hole symmetry.Comment: 5 page

Adiabatic and non-adiabatic phonon dispersion in a Wannier function approach

We develop a first-principles scheme to calculate adiabatic and non-adiabatic phonon frequencies in the full Brillouin zone. The method relies on the variational properties of a force-constants functional with respect to the first-order perturbation of the electronic charge density and on the localization of the deformation potential in the Wannier function basis. This allows for calculation of phonon dispersion curves free from convergence issues related to Brillouin zone sampling. In addition our approach justify the use of the static screened potential in the calculation of the phonon linewidth due to decay in electron-hole pairs. We apply the method to the calculation of the phonon dispersion and electron-phonon coupling in MgB$_2$ and CaC$_6$. In both compounds we demonstrate the occurrence of several Kohn anomalies, absent in previous calculations, that are manifest only after careful electron and phonon momentum integration. In MgB$_2$, the presence of Kohn anomalies on the E$_{2g}$ branches improves the agreement with measured phonon spectra and affects the position of the main peak in the Eliashberg function. In CaC$_6$ we show that the non-adiabatic effects on in-plane carbon vibrations are not localized at zone center but are sizable throughout the full Brillouin zone. Our method opens new perspectives in large-scale first-principles calculations of dynamical properties and electron-phonon interaction.Comment: 18 pages, 8 figure