Phonon-induced many-body renormalization of the electronic properties of graphene

We develop a theory for the electron-phonon interaction effects on the electronic properties of graphene. We analytically calculate the electron self-energy, spectral function, and the band velocity renormalization due to phonon-mediated electron-electron interaction, finding that phonon-mediated electron-electron coupling has a large effect on the graphene band structure renormalization. Our analytic theory successfully captures the essential features of the observed graphene electron spectra in the angle-resolved photoemission experiments, predicting a kink at approximately 200 meV below the Fermi level and a reduction of the band velocity by approximately 10-20% at the experimental doping level.     

Intermediate phase of the one dimensional half-filled Hubbard-Holstein model

We present a numerical study of the Hubbard-Holstein model in one dimension at half filling, including finite-frequency quantum phonons. At half filling, the effects of the electron-phonon and electron-electron interactions compete with the Holstein phonon coupling acting as an effective negative Hubbard on-site interaction U that promotes on-site electron pairs and a Peierls charge-density wave state. Most previous work on this model has assumed that only Peierls or Mott phases are possible at half filling. However, there has been speculation that a third metallic phase exists between the Peierls and Mott phases. We confirm the intermediate phase, and show that the Luttinger liquid correlation exponent K(rho) >1 in this region, indicating dominant superconducting pair correlations. We explore the full phase diagram as a function of Hubbard U, phonon coupling constant, and phonon frequency.     

Density-matrix renormalization group study of pairing when electron-electron and electron-phonon interactions coexist: effect of the electronic band structure

The density-matrix renormalization group is used to study the pairing when both electron-electron and electron-phonon interactions are strong in the Holstein-Hubbard model at half filling in a region intermediate between the adiabatic (Migdal's) and antiadiabatic limits. We have found (i) the pairing correlation obtained for a one-dimensional system is nearly degenerate with the charge density-wave correlation in a region where the phonon-induced attraction is comparable with the electron-electron repulsion, but (ii) pairing becomes dominant when we destroy the electron-hole symmetry in a trestle lattice. This provides an instance in which pairing can arise, in a lattice-structure dependent manner, from coexisting electron-electron and electron-phonon interactions.     

Effect of Interaction on the Majorana Zero Modes in the Kitaev Chain at Half Filling

The one-dimensional interacting Kitaev chain at half filling is studied. The symmetry of the Hamiltonian is examined by dual transformations, and various physical quantities as a function of the fermion-fermion interaction U are calculated systematically using the density matrix renormalization group method. A special value of interaction Up is revealed in the topological region of the phase diagram. We show that at Up the ground states are strictly two-fold degenerate even though the chain length is finite and the zero-energy peak due to the Majorana zero modes is maximally enhanced and exactly localized at the end sites. Here Up may be attractive or repulsive depending on other system parameters. We also give a qualitative understanding of the effect of interaction under the self-consistent mean field framework.     

On the Tc of dilute alloys

The equation for the critical temperature T_c, of a dilute superconducting alloy due to Markowitz and Kadanoff (MK) is generalized to include renormalization effects due to the electron-phonon interaction. Such corrections constitute a 50% effect in weak coupling superconductors like aluminum while in strong coupling systems like lead this correction gives a factor of 2.5. The mean square anisotropy parameter appearing in the T_c equation is also generalized to remove the separability assumption of the electron-phonon interaction. Some consequences of these two corrections to the analysis and systematization of data for dilute superconducting alloys is discussed.     

THEORY OF RAMAN SCATTERING FROM CHARGE DENSITY-WAVE SUPERCONDUCTORS

A theory is developed for the Raman scattering of light from a charge-density-wave (CDW) superconductor on the basis of a modified Balseiro-Falicov interactibn pro.posed by the authors and including renormalization of both the Coulomb interaction at the small q limit, and the residual coupling between electrons. Both the electron-photon and electron-phonon vertices are taken into account. It is shown that there always exist poles at frequency ω=2Δ (Δ is superconducting gap) in the effective electron polarization and in the phonon self-energy, and these poles survive the Coulomb screening and the renormalization of the residual electron interactions if the coupling parameter g₂(k) is anisotropic, in contrast with an isotropic electron gas. The effect of the Littlewood-Varma interaction in a coexistent CDW-siiperconductcr is also discussed.     

Electronic structure and kinetic properties of tight-binding metals at high temperature

The influence of the electron-phonon interaction on the electronic properties of tight-binding metals is considered with the one-band approximation. It is shown by using the previous results that the existence of the twofold effect is due to phonons. Firstly, phonons lead to a non-coherent scattering of electrons and as a result a finite lifetime for the electron states. Secondly, phonons lead to a renormalization of the periodic cristal potential. Latter was well known for the nearly free-electron crystals to be expressed as Debye-Waller corrections to the lattice potential. Such effect in tight-binding metals is shown here to result in the temperature dependence of overlap integrals. It gives rise to the increase of the band width and the electron velocity for the one-band approximation. The negative temperature coefficient of resistivity is shown to may arise in result at high temperatures.     

Electron-phonon interaction close to a Mott transition

The effect of Holstein electron-phonon interaction on a Hubbard model close to a Mott-Hubbard transition at half filling is investigated by means of dynamical mean-field theory. We observe a reduction of the effective mass that we interpret in terms of a reduced effective repulsion. When the repulsion is rescaled to take into account this effect, the quasiparticle low-energy features are unaffected by the electron-phonon interaction. Phonon features are only observed within the high-energy Hubbard bands. The lack of electron-phonon fingerprints in the quasiparticle physics can be explained interpreting the quasiparticle motion in terms of rare fast processes.     

The Two-Dimensional Hubbard Model on the Honeycomb Lattice

We consider the two-dimensional (2D) Hubbard model on the honeycomb lattice, as a model for a single layer graphene sheet in the presence of screened Coulomb interactions. At half filling and weak enough coupling, we compute the free energy, the ground state energy and we construct the correlation functions up to zero temperature in terms of convergent series; analyticity is proved by making use of constructive fermionic renormalization group methods. We show that the interaction produces a modification of the Fermi velocity and of the wave function renormalization without changing the asymptotic infrared properties of the model with respect to the unperturbed non-interacting case; this rules out the possibility of superconducting or magnetic instabilities in the thermal ground state.     

Mass of a lattice polaron from an extended Holstein model using the Yukawa potential

Renormalization of the mass of an electron is studied within the framework of the Extended Holstein model at strong coupling regime and nonadiabatic limit. In order to take into account an effect of screening of an electron-phonon interaction on a polaron it is assumed that the electron-phonon interaction potential has the Yukawa form and screening of the electron-phonon interaction is due to the presence of other electrons in a lattice. The forces are derived from the Yukawa type electron-phonon interaction potential. It is emphasized that the early considered screened force of (Kornilovitch (1998), Spencer et al. (2005), Hague et al. (2006), Hague and Kornilovitch (2009)) Refs. [7], [18], [19] and [22] is a particular case of the force deduced from the Yukawa potential and is approximately valid at large screening radiuses compared to the distances under consideration. The Extended Holstein polaron with the Yukawa type potential is found to be a more mobile than polaron studied in early works at the same screening regime.     

Theoretical study of NMR relaxation due to rattling phonons

We calculate the NMR relaxation rate due to quadrupolar coupling of the nucleus to a local, strongly anharmonic phonon mode. As a model potential for a “rattling” motion we consider a square-well potential. We calculate the free phonon Green's function analytically and derive the low and high temperature limits of the NMR relaxation rate. It is shown that the temperature dependence of the NMR relaxation rate possesses a peak in contrast to harmonic phonons but in qualitative agreement with a recent NMR study on KOs₂O₆. We discuss the influence of phonon renormalization due to electron-phonon interaction.     

Electron-electron interactions in the 2D electron system

In this paper, we report studies of the electron-electron interaction effects in 2D electron systems. The interaction manifests in renormalization of the effective spin susceptibility, effective mass, g^∗-factor, conductivity etc. By applying in-plane magnetic field, we tuned the effective interaction between the electrons and compared with theory the temperature dependence of the conductivity. We find a good agreement with interaction corrections calculated within the Fermi liquid theory. To address the question on the origin of the metal-insulator transition (MIT) in 2D, we explored transport and magnetotransport properties in the vicinity of the MIT and compared our data with solutions of two equations of the renormalization group (RG) theory, which describes temperature evolutions of the resistivity and interaction parameters for 2D electron system. We found a good agreement between the ρ(T,B_∥) data and the RG-theory in a wide range of the in-plane fields. These results support the Fermi liquid type origin of the metallic state and the interpretation of the observed 2D MIT as the true quantum phase transition.     

Gap formation and soft phonon mode in the Holstein model

We investigate electron-phonon coupling in many-electron systems using the dynamical mean-field theory in combination with the numerical renormalization group. This nonperturbative method reveals significant precursor effects to the gap formation at intermediate coupling strengths. The emergence of a soft phonon mode and very strong lattice fluctuations can be understood in terms of Kondo-like physics due to the development of a double-well structure in the effective potential for the ions.     

Similarity renormalization of the electron-phonon coupling

We study the problem of the phonon-induced electron-electron interaction in a solid. Starting with a Hamiltonian that contains an electron-phonon interaction, we perform a similarity renormalization transformation to calculate an effective Hamiltonian. Using this transformation singularities due to degeneracies are avoided explicitly. The effective interactions are calculated to second order in the electronphonon coupling. It is shown that the effective interaction between two electrons forming a Cooper pair is attractive in the whole parameter space. For a simple Einstein model we calculate the renormalization of the electronic energies and the critical temperature of superconductivity.     

Effects of Electron-Phonon Interaction on Linear and Nonlinear Optical Absorption in Cylindrical Quantum Wires

The electron-phonon interaction influences on lineax and nonfineax optical absorption in cylindrical quantum wires （CQW） with an infinite confining potential axe investigated. The optical absorption coefficients are obtained by using the compact-density-matrix approach and iterative method, and the numerical results are presented for GaAs CQW. The results show that the electron-phonon interaction makes a distinct influence on optical absorption in CQW. The electron-phonon interaction on the wave functions of electron dominates the values of absorption coefficients and the correction of the electron-phonon effect on the energies of the electron makes the absorption peaks blue shift and become wider. Moreover, the electron-phonon interaction influence on optical absorption with an infinite confining potential is different from that with a finite confining potential.     

Chirality-induced dynamic kohn anomalies in graphene

We develop a theory for the renormalization of the phonon energy dispersion in graphene due to the combined effects of both Coulomb and electron-phonon (e-ph) interactions. We obtain the renormalized phonon energy spectrum by an exact analytic derivation of the phonon self-energy, finding three distinct Kohn anomalies (KAs) at the phonon wave vector q=omega/v, 2k_{F}+/-omega/v for LO phonons and one at q=omega/v for TO phonons. The presence of these new KAs in graphene, in contrast to the usual KA q=2k_{F} in ordinary metals, originates from the dynamical screening of e-ph interaction (with a concomitant breakdown of the Born-Oppenheimer approximation) and the peculiar chirality of the graphene e-ph coupling.     

Band filling and interband scattering effects in MgB2: carbon versus aluminum doping

We argue, based on band structure calculations and the Eliashberg theory, that the observed decrease of T(c) of Al and C doped MgB2 samples can be understood mainly in terms of a band filling effect due to the electron doping by Al and C. A simple scaling of the electron-phonon coupling constant lambda by the variation of the density of states as a function of electron doping is sufficient to capture the experimentally observed behavior. Further, we also explain the long standing open question of the experimental observation of a nearly constant pi gap as a function of doping by a compensation of the effect of band filling and interband scattering. Both effects together generate a nearly constant pi gap and shift the merging point of both gaps to higher doping concentrations, resolving the discrepancy between experiment and theoretical predictions based on interband scattering only.     

Analytical approach to the quantum-phase transition in the one-dimensional spinless Holstein model

We study the one-dimensional Holstein model of spinless fermions interacting with dispersion-less phonons by using a recently developed projector-based renormalization method (PRM). At half-filling the system shows a metal-insulator transition to a Peierls distorted state at a critical electron-phonon coupling where both phases are described within the same theoretical framework. The transition is accompanied by a phonon softening at the Brillouin zone boundary and a gap in the electronic spectrum. For different filling, the phonon softening appears away from the Brillouin zone boundary and thus reflects a different type of broken symmetry state.     

Q-dependent light scattering by electrons in LaB6

The inelastic light scattering by intraband electronic excitations in metallic lanthanum hexaboride has been studied in the temperature range of 10–300 K. General agreement has been obtained between the measured spectra and the spectra calculated within the band theory taking into account the renormalization of electron energies owing to electron-phonon scattering. The electron-phonon coupling constant λ and electron relaxation frequency Γ have been estimated. The dependence of the electron self-energies on the direction and magnitude of the wave vector has been revealed, implying the anisotropic electron-phonon interaction or the contribution from other electron scattering mechanisms.     

Electron-phonon interaction and antiferromagnetic correlations

We study effects of the Coulomb repulsion on the electron-phonon interaction (EPI) in the Holstein-Hubbard model, using the antiferromagnetic (AF) dynamical mean-field approximation. AF correlations strongly enhance EPI effects on the electron Green's function with respect to the paramagnetic correlated system, but the net effect of the Coulomb interaction is a moderate suppression of the EPI. Doping leads to additional suppression. In contrast, the Coulomb interaction strongly suppresses EPI effects on phonons, but the suppression weakens with doping.