Electron-phonon coupling phenomena in metals: A computational perspective

The interaction of electrons and lattice vibrations lies at the heart of many physical phenomena like electrical and heat conductivity, phonon-mediated superconductivity, dynamics of excited electrons and holes, and various temperature-dependent properties. Detailed knowledge of the electron-phonon interaction is therefore of basic interest for many phenomena in condensed matter physics. Modern DFT based techniques nowadays provide powerful tools to analyze and predict electronphonon interaction on a microscopic level including its full momentum structure. I will demonstrate the usefulness of this computational approach for several examples focusing on metallic systems. First the characterization of quantum size effects on electron and phonon quasiparticles as well as on superconductivity in ultrathin Pb films will be discussed. Then I will address the stability of topological surface states of Bi2Se3 against phononinduced many-body interactions, and finally discuss the role of the electron-phonon interaction in driving charge-density wave transitions in layered transition-metal dichalcogenides

Eliashberg theory with ab-initio Coulomb interactions: a minimal numerical scheme applied to layered superconductors

We present a minimal approach to include static Coulomb interactions in Eliashberg theory of superconductivity from first principles. The method can be easily implemented in any existing Eliashberg code (isotropic or anisotropic) to avoid the standard use of the semiempirical parameter $\mu^*$, which adds unnecessary uncertainty to Tc predictions. We evaluate the prediction accuracy of the method by simulating the superconducting properties of a set of layered superconductors, which feature unconventional Coulomb effects: CaC6, MgB2, Li-doped β-ZrNCl and YNi2B2C. We find that the estimated critical temperatures are consistent with those from ab-initio density functional theory for superconductors, and in close agreement with the experimental values

Momentum dependence of the electron-phonon coupling and self-energy effects in YBa_2Cu_3O_7 within the local density approximation

Using the local density approximation (LDA) and a realistic phonon spectrum we determine the momentum and frequency dependence of $\alpha^2F({\bf k},\omega)$ in YBa$_2$Cu$_3$O$_7$ for the bonding, antibonding, and chain band. The resulting self-energy $\Sigma$ is rather small near the Fermi surface. For instance, for the antibonding band the maximum of $Re \Sigma$ as a function of frequency is about 7 meV at the nodal point in the normal state and the ratio of bare and renormalized Fermi velocities 1.18. These values are a factor 3-5 too small compared to the experiment showing that only a small part of $\Sigma$ can be attributed to phonons. Furthermore, the frequency dependence of the renormalization factor $Z({\bf k},\omega)$ is smooth and has no anomalies at the observed kink frequencies which means that phonons cannot produce well-pronounced kinks in stoichiometric YBa$_2$Cu$_3$O$_7$, at least, within the LDA.Comment: Figure 1 slightly revised, text shortened, accepted as a PR

Electron-phonon coupling in topological surface states: The role of polar optical modes

The use of topological edge states for spintronic applications could be severely hampered by limited lifetimes due to intrinsic many-body interactions, in particular electron-phonon coupling. Previous works to determine the intrinsic coupling strength did not provide a coherent answer. Here, the electron-phonon interaction in the metallic surface state of 3D topological insulators is revised within a first principles framework. For the archetypical cases of Bi2Se3 and Bi2Te3, we find an overall weak coupling constant of less than 0.15, but with a characteristic energy dependence. Derived electronic self-energies compare favorably with previous angle-resolved photoemission spectroscopy results. The prevailing coupling is carried by optical modes of polar character, which is weakly screened by the metallic surface state and can be reduced by doping into bulk bands. We do not find any indication of a strong coupling to the A1g mode or the presence of a Kohn anomaly in the surface phonon spectrum. The weak intrinsic electron-phonon coupling guarantees long-lived quasiparticles at elevated temperatures

Electron-phonon coupling and superconductivity in α\alpha-MoB2_2 as a function of pressure

We have studied the lattice dynamics, electron-phonon coupling, and superconducting properties of $\alpha$-MoB$_2$, as a function of applied pressure, within the framework of density functional perturbation theory using a mixed-basis pseudopotential method. We found that phonon modes located along the A$-$H, H$-$L, and L$-$A high-symmetry paths exhibit large phonon linewidths and contribute significantly to the electron-phonon coupling constant. Although linewidths are particularly large for the highest-frequency optical phonon modes (dominated by B vibrations), their contribution to the electron-phonon coupling constant is marginal. The latter is largely controlled by the acoustic low-frequency modes of predominantly Mo character. It was observed that at a pressure of $90$~GPa, where $\alpha$-MoB$_2$ forms, the phonon-mediated pairing falls into the strong-coupling regime, and the estimate for the superconducting critical temperature $T_c$ agrees well with experimental observations. When further increasing the applied pressure, a reduction of $T_c$ is predicted, which correlates with a hardening of the acoustic low-frequency phonon modes and a decrease of the electron-phonon coupling parameter.Comment: Updated and accepted for publication versio

Minority-spin conduction in ferromagnetic Mn5_5Ge3_3Cx_x and Mn5_5Si3_3Cx_x films derived from anisotropic magnetoresistance and density functional theory

The anisotropic magnetoresistance (AMR) of ferromagnetic Mn$_5$Ge$_3$C$_x$ (0 $\le$ x $\le$ 1) and Mn$_5$Si$_3$C$_x$ (0.5 $\le$ x $\le$ 1) thin films was investigated and compared with density functional theory calculations from which the spin-split electronic density of states at the Fermi level and the spin polarization were obtained. The isostructural compounds exhibit different AMR behavior. While only Mn5Si3C0.5 shows a positive AMR ratio and a positive spin polarization, the negative AMR ratio of all other compounds is due to a negative spin polarization. The correlation between the sign of the AMR and the degree of spin polarization is in agreement with theoretical calculations of the AMR ratio indicating that the magnetoelectronic transport in both compounds is dominated by minority-spin conduction. The dominating role of minority-spin conduction remains unaffected even after incorporation of carbon into the crystalline lattice which weakens both AMR and spin polarization

Electron–phonon coupling and superconductivity in a 2D Tl–Pb compound on Si(111)

[EN] Electron-phonon interaction in a single-layer Tl-Pb compound on Si(111) is investigated within the density-functional theory and linear-response approach in the mixed-basis pseudopotential representation. It is found that phonon-induced scattering of electrons at the Fermi level is primarily determined by surface electronic states responsible for bonding at the interface and by low-energy, predominantly shear-vertical vibrations of adatoms. The contribution of substrate-localized vibrations involved in the electron-phonon scattering turns out to be small. We have also estimated the superconducting transition temperature T-c by solving the linearized gap equation of the Eliashberg theory. An analysis of phonon-mediated transitions for a number of electronic states in the Tl-Pb surface bands showed that the strength of the coupling varies with the binding energy, increasing as it approaches the Fermi level, and significantly depends on the surface band to which the state belongs.This work was supported by the University of the Basque Country (Grants no. GIC07-IT-366-07 and No. IT-756-13) and the Spanish Ministry of Science and Innovation (Grant no. FIS2016-75862-P). The authors acknowledge support by the state of Baden-Wurttemberg through bwHPC

Properties of the phonon-induced pairing interaction in YBa2_2Cu3_3O7_7 within the local density approximation

The properties of the phonon-induced interaction between electrons are studied using the local density approximation (LDA). Restricting the electron momenta to the Fermi surface we find generally that this interaction has a pronounced peak for large momentum transfers and that the interband contributions between bonding and antibonding band are of the same magnitude as the intraband ones. Results are given for various symmetry averages of this interaction over the Fermi surface. In particular, we find that the dimensionless coupling constant in the d-wave channel $\lambda^d$, relevant for superconductivity, is only 0.022, i.e., even about ten times smaller than the small value of the s-wave channel. Similarly, the LDA contribution to the resistivity is about a factor 10 times smaller than the observed resistivity suggesting that phonons are not the important low-energy excitations in high-T$_c$ oxides.Comment: 6 pages, 7 figure