Transition temperature of strong-coupled superconductors.
TL;DR: In this paper, the superconducting transition temperature is calculated as a function of the electron-phonon and electron-electron coupling constants within the framework of strong coupling theory.
Abstract: The superconducting transition temperature is calculated as a function of the electron-phonon and electron-electron coupling constants within the framework of the strong-coupling theory. Using this theoretical result, we find empirical values of the coupling constants and the "band-structure" density of states for a number of metals and alloys. It is noted that the electron-phonon coupling constant depends primarily on the phonon frequencies rather than on the electronic properties of the metal. Finally, using these results, one can predict a maximum superconducting transition temperature.
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TL;DR: A broad review of recent research work on the preparation and the remarkable properties of intercalation compounds of graphite can be found in this paper, covering a wide range of topics from the basic chemistry, physics and materials science to engineering applications.
Abstract: A broad review of recent research work on the preparation and the remarkable properties of intercalation compounds of graphite, covering a wide range of topics from the basic chemistry, physics and materials science to engineering applications.
1,956 citations
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...…ˆ 112:5 mK, and Hc…T ˆ 0† ˆ 16g. Application of McMillan’s formula Tc ˆ ³D 1:45 exp ¡ 1:04…1 ‡ ¶† ¶ ¡ ·¤…1 ‡ 0:62¶† » ¼ …4:59† yields a value of ¶ ˆ 0:32 § 0:01 for the electron±phonon coupling constant, using ·¤ ˆ 0:1 for the e ective Coulomb repulsion parameter, as suggested by McMillan (1968)....
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TL;DR: The demonstration of a superconducting detector that is easily fabricated and can readily be incorporated into large arrays, and its sensitivity is already within an order of magnitude of that needed for CMB observations, and the energy resolution is similarly close to the targets required for future X-ray astronomy missions.
Abstract: Cryogenic detectors are extremely sensitive and have a wide variety of applications (particularly in astronomy), but are difficult to integrate into large arrays like a modern CCD (charge-coupled device) camera. As current detectors of the cosmic microwave background (CMB) already have sensitivities comparable to the noise arising from the random arrival of CMB photons, the further gains in sensitivity needed to probe the very early Universe will have to arise from large arrays. A similar situation is encountered at other wavelengths. Single-pixel X-ray detectors now have a resolving power of ΔE < 5 eV for single 6-keV photons, and future X-ray astronomy missions anticipate the need for 1,000-pixel arrays. Here we report the demonstration of a superconducting detector that is easily fabricated and can readily be incorporated into such an array. Its sensitivity is already within an order of magnitude of that needed for CMB observations, and its energy resolution is similarly close to the targets required for future X-ray astronomy missions.
1,429 citations
TL;DR: A detailed review of the superconductivity of FePnictide and chalcogenide (FePn/Ch) superconductors can be found in this paper.
Abstract: Kamihara and coworkers' report of superconductivity at ${T}_{c}=26\text{ }\text{ }\mathrm{K}$ in fluorine-doped LaFeAsO inspired a worldwide effort to understand the nature of the superconductivity in this new class of compounds. These iron pnictide and chalcogenide (FePn/Ch) superconductors have Fe electrons at the Fermi surface, plus an unusual Fermiology that can change rapidly with doping, which lead to normal and superconducting state properties very different from those in standard electron-phonon coupled ``conventional'' superconductors. Clearly, superconductivity and magnetism or magnetic fluctuations are intimately related in the FePn/Ch, and even coexist in some. Open questions, including the superconducting nodal structure in a number of compounds, abound and are often dependent on improved sample quality for their solution. With ${T}_{c}$ values up to 56 K, the six distinct Fe-containing superconducting structures exhibit complex but often comparable behaviors. The search for correlations and explanations in this fascinating field of research would benefit from an organization of the large, seemingly disparate data set. This review provides an overview, using numerous references, with a focus on the materials and their superconductivity.
1,349 citations
TL;DR: Chen et al. as discussed by the authors reported the discovery of bulk superconductivity in the related compound SmFeAsO1-xF x, which has a ZrCuSiAs-type structure.
Abstract: The recently discovered layered rare-earth metal oxypnictides have reinvigorated research into high-temperature superconductivity. The first of these, found only a few months ago, had a transition temperature of 26 K. A recent paper in Nature reported an iron–arsenic-based material superconducting at 43 K with the application of pressure. Previously only copper oxides superconductors had beaten the 40 K barrier. Now Chen et al. report bulk superconductivity in the samarium–arsenide oxide SmFeAsO1−xFx with a transition temperature of 43 K without this pressure. A report on the discovery of bulk superconductivity in samarium-arsenide oxides SmFeAsO1−xFx with a transition temperature as high as 43 K. Since the discovery of high-transition-temperature (high-Tc) superconductivity in layered copper oxides, extensive effort has been devoted to exploring the origins of this phenomenon. A Tc higher than 40 K (about the theoretical maximum predicted from Bardeen–Cooper–Schrieffer theory1), however, has been obtained only in the copper oxide superconductors. The highest reported value for non-copper-oxide bulk superconductivity is Tc = 39 K in MgB2 (ref. 2). The layered rare-earth metal oxypnictides LnOFeAs (where Ln is La–Nd, Sm and Gd) are now attracting attention following the discovery of superconductivity at 26 K in the iron-based LaO1-xF x FeAs (ref. 3). Here we report the discovery of bulk superconductivity in the related compound SmFeAsO1-xF x , which has a ZrCuSiAs-type structure. Resistivity and magnetization measurements reveal a transition temperature as high as 43 K. This provides a new material base for studying the origin of high-temperature superconductivity.
1,325 citations
TL;DR: In this article, the dependence of the strength of the electron-phonon coupling and the electron heat capacity on the electron temperature was investigated for eight representative metals, Al, Cu, Ag, Au, Ni, Pt, W, and Ti.
Abstract: The dependence of the strength of the electron-phonon coupling and the electron heat capacity on the electron temperature is investigated for eight representative metals, Al, Cu, Ag, Au, Ni, Pt, W, and Ti, for the conditions of strong electron-phonon nonequilibrium. These conditions are characteristic of metal targets subjected to energetic ion bombardment or short-pulse laser irradiation. Computational analysis based on first-principles electronic structure calculations of the electron density of states predicts large deviations (up to an order of magnitude) from the commonly used approximations of linear temperature dependence of the electron heat capacity and a constant electron-phonon coupling. These thermophysical properties are found to be very sensitive to details of the electronic structure of the material. The strength of the electron-phonon coupling can either increase (Al, Au, Ag, Cu, and W), decrease (Ni and Pt), or exhibit nonmonotonic changes (Ti) with increasing electron temperature. The electron heat capacity can exhibit either positive (Au, Ag, Cu, and W) or negative (Ni and Pt) deviations from the linear temperature dependence. The large variations of the thermophysical properties, revealed in this work for the range of electron temperatures typically realized in femtosecond laser material processing applications, have important implications for quantitative computational analysis of ultrafast processes associated with laser interaction with metals.
1,165 citations
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TL;DR: In this article, a theory of superconductivity is presented, based on the fact that the interaction between electrons resulting from virtual exchange of phonons is attractive when the energy difference between the electrons states involved is less than the phonon energy, and it is favorable to form a superconducting phase when this attractive interaction dominates the repulsive screened Coulomb interaction.
Abstract: A theory of superconductivity is presented, based on the fact that the interaction between electrons resulting from virtual exchange of phonons is attractive when the energy difference between the electrons states involved is less than the phonon energy, $\ensuremath{\hbar}\ensuremath{\omega}$. It is favorable to form a superconducting phase when this attractive interaction dominates the repulsive screened Coulomb interaction. The normal phase is described by the Bloch individual-particle model. The ground state of a superconductor, formed from a linear combination of normal state configurations in which electrons are virtually excited in pairs of opposite spin and momentum, is lower in energy than the normal state by amount proportional to an average ${(\ensuremath{\hbar}\ensuremath{\omega})}^{2}$, consistent with the isotope effect. A mutually orthogonal set of excited states in one-to-one correspondence with those of the normal phase is obtained by specifying occupation of certain Bloch states and by using the rest to form a linear combination of virtual pair configurations. The theory yields a second-order phase transition and a Meissner effect in the form suggested by Pippard. Calculated values of specific heats and penetration depths and their temperature variation are in good agreement with experiment. There is an energy gap for individual-particle excitations which decreases from about $3.5k{T}_{c}$ at $T=0\ifmmode^\circ\else\textdegree\fi{}$K to zero at ${T}_{c}$. Tables of matrix elements of single-particle operators between the excited-state superconducting wave functions, useful for perturbation expansions and calculations of transition probabilities, are given.
9,619 citations
TL;DR: In this paper, the key steps in the development of the microscopic understanding of superconductivity are discussed, and a detailed review of the main steps in this process is presented. But,
Abstract: Key steps in the development of the microscopic understanding of superconductivity are discussed.
1,969 citations
TL;DR: In this paper, it was shown that the Meissner effect can be maintained in the quasi-particle picture by taking into account a certain class of corrections to the chargecurrent operator due to the phonon and Coulomb interaction.
Abstract: Ideas and techniques known in quantum electrodynamics have been applied to the Bardeen-Cooper-Schrieffer theory of superconductivity In an approximation which corresponds to a generalization of the Hartree-Fock fields, one can write down an integral equation defining the self-energy of an electron in an electron gas with phonon and Coulomb interaction The form of the equation implies the existence of a particular solution which does not follow from perturbation theory, and which leads to the energy gap equation and the quasi-particle picture analogous to Bogoliubov'sThe gauge invariance, to the first order in the external electromagnetic field, can be maintained in the quasi-particle picture by taking into account a certain class of corrections to the chargecurrent operator due to the phonon and Coulomb interaction In fact, generalized forms of the Ward identity are obtained between certain vertex parts and the self-energy The Meissner effect calculation is thus rendered strictly gauge invariant, but essentially keeping the BCS result unaltered for transverse fieldsIt is shown also that the integral equation for vertex parts allows homogeneous solutions which describe collective excitations of quasi-particle pairs, and the nature and effects of such collective states are discussed
1,125 citations
TL;DR: In this article, it is shown that advantage of crystal symmetry can be taken to construct wave functions which are best described as the smooth part of symmetrized Bloch functions.
Abstract: For metals and semiconductors the calculation of crystal wave functions is simplest in a plane wave representation. However, in order to obtain rapid convergence it is necessary that the valence electron wave functions be made orthogonal to the core wave functions. Herring satisfied this requirement by choosing as basis functions "orthogonalized plane waves." It is here shown that advantage can be taken of crystal symmetry to construct wave functions ${\ensuremath{\phi}}_{\ensuremath{\alpha}}$ which are best described as the smooth part of symmetrized Bloch functions. The wave equation satisfied by ${\ensuremath{\phi}}_{\ensuremath{\alpha}}$ contains an additional term of simple character which corresponds to the usual complicated orthogonalization terms and has a simple physical interpretation as an effective repulsive potential. Qualitative estimates of this potential in analytic form are presented. Several examples are worked out which display the cancellation between attractive and repulsive potentials in the core region which is responsible for rapid convergence of orthogonalized plane wave calculations for $s$ states; the slower convergence of $p$ states is also explained. The formalism developed here can also be regarded as a rigorous formulation of the "empirical potential" approach within the one-electron framework; the present results are compared with previous approaches. The method can be applied equally well to the calculation of wave functions in molecules.
921 citations
TL;DR: In this paper, the energy gap and other parameters of the superconducting state are calculated from the Bardeen-Cooper-Schrieffer theory in Gor'kov-Eliashberg form, using a realistic electron-electron interaction via phonons and including the Coulomb repulsion.
Abstract: The energy gap and other parameters of the superconducting state are calculated from the Bardeen-Cooper-Schrieffer theory in Gor'kov-Eliashberg form, using a realistic retarded electron-electron interaction via phonons and including the Coulomb repulsion. The solution is facilitated by observing that only the local phonon interaction, mediated entirely by short-wavelength phonons, is important, and that a good approximation for the phonon spectrum is therefore an Einstein model rather than Debye model. The resulting equation is solved by an approximate iteration procedure. The results are similar to earlier gap equations but the derivation gives a precise meaning to the interaction and cutoff parameters of earlier theories. The numerical results are in good order-of-magnitude agreement with the observed transition temperatures but lead to an isotope effect at least 15% less than the accepted -\textonehalf{} exponent (${T}_{c}$ proportional to ${M}^{\ensuremath{-}\frac{1}{2}}$). Also, the present theory predicts that all metals should be superconductors, although those not observed to do so would have remarkably low transition temperatures.
696 citations