Ab initio theory of plasmonic superconductivity within the Eliashberg and density-functional formalisms

We extend the two leading methods for the ab initio computational description of phonon-mediated superconductors, namely Eliashberg theory and density-functional theory for superconductors (SCDFT), to include plasmonic effects. Furthermore, we introduce a hybrid formalism in which the Eliashberg approximation for the electron-phonon coupling is combined with the SCDFT treatment of the dynamically screened Coulomb interaction. The methods have been tested on a set of well-known conventional superconductors by studying how the plasmon contribution affects the phononic mechanism in determining the critical temperature (TC). Our simulations show that plasmonic SCDFT leads to a good agreement between predicted and measured TC's, whereas Eliashberg theory considerably overestimates the plasmon-mediated pairing and, therefore, TC. The hybrid approach, on the other hand, gives results close to SCDFT and overall in excellent agreement with experiments

Time-Dependent Quasiparticle Current Density Functional Theory of X-Ray Nonlinear Response Functions

A real-space representation of the current response of many-electron systems with possible applications to x-ray nonlinear spectroscopy and magnetic susceptibilities is developed. Closed expressions for the linear, quadratic and third-order response functions are derived by solving the adiabatic Time Dependent Current Density Functional (TDCDFT) equations for the single-electron density matrix in Liouville space.Comment: 11 page

Bound States in Time-Dependent Quantum Transport: Oscillations and Memory Effects in Current and Density

The presence of bound states in a nanoscale electronic system attached to two biased, macroscopic electrodes is shown to give rise to persistent, non-decaying, localized current oscillations which can be much larger than the steady part of the current. The amplitude of these oscillations depends on the entire history of the applied potential. The bound-state contribution to the {\em static} density is history-dependent as well. Moreover, the time-dependent formulation leads to a natural definition of the bound-state occupations out of equilibrium.Comment: 4 pages, 3 figure