BCS and generalized BCS superconductivity in relativistic quantum field theory. I. formulation

We investigate the BCS and generalized BCS theories in the relativistic quantum field theory. We select the gauge freedom as U(1), and introduce a BCS-type effective attractive interaction. After introducing the Gor'kov formalism and performing the group theoretical consideration of the mean fields, we solve the relativistic Gor'kov equation and obtain the Green's functions in analytical forms. We obtain various types of gap equations.Comment: 31 page

Spin gaps and spin-flip energies in density-functional theory

Energy gaps are crucial aspects of the electronic structure of finite and extended systems. Whereas much is known about how to define and calculate charge gaps in density-functional theory (DFT), and about the relation between these gaps and derivative discontinuities of the exchange-correlation functional, much less is know about spin gaps. In this paper we give density-functional definitions of spin-conserving gaps, spin-flip gaps and the spin stiffness in terms of many-body energies and in terms of single-particle (Kohn-Sham) energies. Our definitions are as analogous as possible to those commonly made in the charge case, but important differences between spin and charge gaps emerge already on the single-particle level because unlike the fundamental charge gap spin gaps involve excited-state energies. Kohn-Sham and many-body spin gaps are predicted to differ, and the difference is related to derivative discontinuities that are similar to, but distinct from, those usually considered in the case of charge gaps. Both ensemble DFT and time-dependent DFT (TDDFT) can be used to calculate these spin discontinuities from a suitable functional. We illustrate our findings by evaluating our definitions for the Lithium atom, for which we calculate spin gaps and spin discontinuities by making use of near-exact Kohn-Sham eigenvalues and, independently, from the single-pole approximation to TDDFT. The many-body corrections to the Kohn-Sham spin gaps are found to be negative, i.e., single particle calculations tend to overestimate spin gaps while they underestimate charge gaps.Comment: 11 pages, 1 figure, 3 table

Andreev reflection and Klein tunneling in graphene

This is a colloquium-style introduction to two electronic processes in a carbon monolayer (graphene), each having an analogue in relativistic quantum mechanics. Both processes couple electron-like and hole-like states, through the action of either a superconducting pair potential or an electrostatic potential. The first process, Andreev reflection, is the electron-to-hole conversion at the interface with a superconductor. The second process, Klein tunneling, is the tunneling through a p-n junction. Existing and proposed experiments on Josephson junctions and bipolar junctions in graphene are discussed from a unified perspective. CONTENTS: I. INTRODUCTION II. BASIC PHYSICS OF GRAPHENE (Dirac equation; Time reversal symmetry; Boundary conditions; Pseudo-diffusive dynamics) III. ANDREEV REFLECTION (Electron-hole conversion; Retro-reflection vs. specular reflection; Dirac-Bogoliubov-de Gennes equation; Josephson junctions; Further reading) IV. KLEIN TUNNELING (Absence of backscattering; Bipolar junctions; Magnetic field effects; Further reading) V. ANALOGIES (Mapping between NS and p-n junction; Retro-reflection vs. negative refraction; Valley-isospin dependent quantum Hall effect; Pseudo-superconductivity)Comment: 20 pages, 28 figures; "Colloquium" for Reviews of Modern Physic

Degenerate ground states and nonunique potentials: breakdown and restoration of density functionals

The Hohenberg-Kohn (HK) theorem is one of the most fundamental theorems of quantum mechanics, and constitutes the basis for the very successful density-functional approach to inhomogeneous interacting many-particle systems. Here we show that in formulations of density-functional theory (DFT) that employ more than one density variable, applied to systems with a degenerate ground state, there is a subtle loophole in the HK theorem, as all mappings between densities, wave functions and potentials can break down. Two weaker theorems which we prove here, the joint-degeneracy theorem and the internal-energy theorem, restore the internal, total and exchange-correlation energy functionals to the extent needed in applications of DFT to atomic, molecular and solid-state physics and quantum chemistry. The joint-degeneracy theorem constrains the nature of possible degeneracies in general many-body systems

Exchange-correlation vector potentials and vorticity-dependent exchange-correlation energy densities in two-dimensional systems

We present a new approach how to calculate the scalar exchange-correlation potentials and the vector exchange-correlation potentials from current-carrying ground states of two-dimensional quantum dots. From these exchange-correlation potentials we derive exchange-correlation energy densities and examine their vorticity (or current) dependence. Compared with parameterizations of current-induced effects in literature we find an increased significance of corrections due to paramagnetic current densities.Comment: 5 figures, submitted to PR

Bethe-Ansatz density-functional theory of ultracold repulsive fermions in one-dimensional optical lattices

We present an extensive numerical study of ground-state properties of confined repulsively interacting fermions on one-dimensional optical lattices. Detailed predictions for the atom-density profiles are obtained from parallel Kohn-Sham density-functional calculations and quantum Monte Carlo simulations. The density-functional calculations employ a Bethe-Ansatz-based local-density approximation for the correlation energy, which accounts for Luttinger-liquid and Mott-insulator physics. Semi-analytical and fully numerical formulations of this approximation are compared with each other and with a cruder Thomas-Fermi-like local-density approximation for the total energy. Precise quantum Monte Carlo simulations are used to assess the reliability of the various local-density approximations, and in conjunction with these allow to obtain a detailed microscopic picture of the consequences of the interplay between particle-particle interactions and confinement in one-dimensional systems of strongly correlated fermions.Comment: 14 pages, 11 figures, 1 table, submitte

Simple implementation of complex functionals: scaled selfconsistency

We explore and compare three approximate schemes allowing simple implementation of complex density functionals by making use of selfconsistent implementation of simpler functionals: (i) post-LDA evaluation of complex functionals at the LDA densities (or those of other simple functionals); (ii) application of a global scaling factor to the potential of the simple functional; and (iii) application of a local scaling factor to that potential. Option (i) is a common choice in density-functional calculations. Option (ii) was recently proposed by Cafiero and Gonzalez. We here put their proposal on a more rigorous basis, by deriving it, and explaining why it works, directly from the theorems of density-functional theory. Option (iii) is proposed here for the first time. We provide detailed comparisons of the three approaches among each other and with fully selfconsistent implementations for Hartree, local-density, generalized-gradient, self-interaction corrected, and meta-generalized-gradient approximations, for atoms, ions, quantum wells and model Hamiltonians. Scaled approaches turn out to be, on average, better than post-approaches, and unlike these also provide corrections to eigenvalues and orbitals. Scaled selfconsistency thus opens the possibility of efficient and reliable implementation of density functionals of hitherto unprecedented complexity.Comment: 12 pages, 1 figur

Spin currents and spin dynamics in time-dependent density-functional theory

We derive and analyse the equation of motion for the spin degrees of freedom within time-dependent spin-density-functional theory (TD-SDFT). Results are (i) a prescription for obtaining many-body corrections to the single-particle spin currents from the Kohn-Sham equation of TD-SDFT, (ii) the existence of an exchange-correlation (xc) torque within TD-SDFT, (iii) a prescription for calculating, from TD-SDFT, the torque exerted by spin currents on the spin magnetization, (iv) a novel exact constraint on approximate xc functionals, and (v) the discovery of serious deficiencies of popular approximations to TD-SDFT when applied to spin dynamics.Comment: now includes discussion of OEP and GGA; to appear in Phys. Rev. Let

Interaction Between Superconducting and Ferromagnetic Order Parameters in Graphite-Sulfur Composites

The superconductivity of graphite-sulfur composites is highly anisotropic and associated with the graphite planes. The superconducting state coexists with the ferromagnetism of pure graphite, and a continuous crossover from superconducting to ferromagnetic-like behavior could be achieved by increasing the magnetic field or the temperature. The angular dependence of the magnetic moment m(alpha) provides evidence for an interaction between the ferromagnetic and the superconducting order parameters.Comment: 11 pages, 4 figures, to be published in Phys. Rev.