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We present a study of the superconducting transition in MgB2 using the ab-initio pseudopotential density functional method and the fully anisotropic Eliashberg equation. Our study shows that the anisotropic Eliashberg equation, constructed…

This article presents a systematic theoretical enquiry concerning the conceptual foundations and the nature of phonon-mediated electron-electron interactions. Starting from the fundamental many-body Hamiltonian, we propose a simple scheme…

Using the {\it ab initio} anisotropic Eliashberg theory including Coulomb interactions, we investigate the electron-phonon interaction and the pairing mechanism in the recently-reported superconducting Ca-intercalated bilayer graphene. We…

Using a multistep renormalization group method, we study the low-temperature phases of the interacting one-dimensional (1D) electron gas coupled to phonons. We obtain analytic expressions for the weak-coupling quantum phase boundaries of…

In the present paper, we analyze the properties of the unbalanced superconducting state on a square lattice with the constant value of the electron-phonon coupling function. We conduct our analysis in the framework of the Eliashberg…

The electronic self-energy is studied for a two dimensional electron gas coupled to a spin-orbit Rashba field and interacting with dispersionless phonons. For the case of a momentum independent electron-phonon coupling (Holstein model) we…

Using the tight-binding model with long-range Coulomb interactions between electrons, we study some of the electronic properties of graphene. The Coulomb interactions are treated with the renormalized-ring-diagram approximation. By…

According to time-dependent density functional theory, the exact exchange-correlation kernel f$_{xc}$(n, q, $\omega$) determines not only the ground-state energy but also the excited-state energies/lifetimes and time-dependent linear…

We investigate the electron-phonon cooling power in disordered electronic systems with a special focus on mesoscopic superconducting proximity structures. Employing the quasiclassical Keldysh Green's function method, we obtain a general…

Employing the nonequilibrium Green's function method, we develop a fully quantum mechanical model to study the coupled electron-phonon transport in one-dimensional atomic junctions in the presence of a weak electron-phonon interaction. This…

Electron-phonon ($e$-ph) interactions are pervasive in condensed matter, governing phenomena such as transport, superconductivity, charge-density waves, polarons and metal-insulator transitions. First-principles approaches enable accurate…

Electron-phonon interaction and related self-energy are fundamental to both the equilibrium properties and non-equilibrium relaxation dynamics of solids. Although electron-phonon interaction has been suggested by various time-resolved…

We determined electronic relaxation times via pump-probe optical spectroscopy using sub-15 fs pulses for the normal state of two different cuprate superconductors.We show that the primary relaxation process is the electron-phonon…

The derivation of the Eliashberg -- type equations for a superconductor with strong correlations and electron--phonon interaction has been presented. The proper account of short range Coulomb interactions results in a strongly anisotropic…

Recent work on an electron-phonon model in two-dimensions is reviewed and some new results are presented. We utilize both Quantum Monte Carlo simulations and Migdal-Eliashberg theory. The type of electron-ion coupling considered is on-site.…

We formulate a semiclassical theory for electron transport in open quantum systems with electron-phonon interactions adequate for situations when the system's phonon dynamics is comparable with the electron transport timescale. Starting…

We present a comparative analysis of the validity of Eliashberg theory for the cases of fermions interacting with an Einstein phonon and with soft nematic fluctuations near an Ising-nematic/Ising-ferromagnetic quantum-critical point (QCP).…

Mathematical correct method for extraction of the complex superconducting energy gap parameter and electron- phonon interaction function from the tunnel density of states is presented. The computer program is shown to be robust against…

We present a comparison of electron-phonon interaction in NbB_2 and MgB_2, calculated using full-potential, density-functional-based methods in P6/mmm crystal structure. Our results, described in terms of (i) electronic structure, (ii)…

We present a theory of electronic excitation energies and optical absorption spectra which incorporates energy-level renormalization and phonon-assisted optical absorption within a unified framework. Using time-independent perturbation…