Density Functional Theory for Superconductors
Density Functional Theory (DFT) provides the theoretical framework for first principles theories of the electronic structure of solids. DFT has been highly successful in describing metals, semiconductors, molecules and magnetism, as recognised by the award of the 1998 Nobel Prize for Chemistry to Walter Kohn. However, until recently DFT could not be directly applied to superconductors. The work of Olivera, Kohn and Gross laid the foundations for applying DFT to superconductors. They showed that the Kohn Sham equations could be generalised to the superconducting state becoming similar to the usual Bogoliubov de Gennes (BdG) equations. However, unlike the usual Hartree Fock derivation of the BdG equations, the DFT formalism implicitly includes the full exchange correlation functional. However, much work remains to be done, in particular to find reliable exchange-correlational functionals for the superconducting state.
The Daresbury/Bristol collaboration have used the DFT/BdG formalism to examine the nature of the pairing state in the cuprate high temperature superconductor (HTS) YBa2Cu3O7. In their semiphenomenological approach they have combined a particularly efficient parametrization of the effective electron-electron interaction, afforded by the DFT for superconductors, and a Tight-Binding-Linearized-Muffin-Tin-Orbital scheme for solving the corresponding Kohn-ShamBogoliubov-de Gennes equations [1-3]. This approach has facilitated a study of a number of possible pairing scenarios in YBa2Cu3O7, involving different sites and orbitals, coupled by an empirically determined attractive interaction. The strength of this attractive interaction has been chosen so, that the calculated Tc, would coincide with the experimentally observed Tc, of the optimally doped compound, namely 92K. The aim of this approach has been to identify the scenario, for which as many calculated superconducting properties as possible would agree with the available, high quality, experiments. For YBa2Cu3O7, it has turned out to be the scenario, where electrons of opposite spins and momenta, occupying the d(x^2-y^2) orbitals on neighbouring Cu sites are coupled by an attractive interaction of 0.68 eV. In this case they have studied the gap anisotropy, low temperature specific heat, Tc, vs. doping, maximum gap vs. doping, and most recently also penetration depths as a function of doping, and in all cases their results have agreed well with experiments [3-7]. Especially, the doping dependence of the gap and Tc, have turned out to be in good agreement with experiments. Moreover, they have shown that the Van Hove-like scenario is an essential feature of superconductivity in the high Tc, materials [4]. For the low temperature penetration depth they have obtained a linear dependence at all studied dopings [7]. At optimal doping, the calculated low temperature penetration depth have been compared to the measurements of A. Carrington et al. (Phys. Rev. B 59, R14173 (1999)), revealing significant importance of the chain in YBCO for zero temperature penetration depth [7].
The Daresbury group have studied with SIC-LSD calculations the valency of Cu in YBCO. They found that doping changed the valency of YBa2Cu3O6 from Cu2+ to Cu3+ in YBa2Cu3O7. Moreover they found a near degeneracy of Cu2+ and Cu3+ in YBa2Cu3O7, whilst in YBa2Cu3O6 the valency is well established as Cu2+ [8].
The Bristol group have calculated properties of supercondutor interfaces in s and d-wave superconductors using the BdG formalism [9,10]. Such interfaces play a major role as weak links limiting critical current in the HTS materials. In particular we made the first realistic tight binding calculations for grain boundary junctions in HTS materials [11]. We also calculated the self-consistent current in superconducting rings containing a grain boundary junction [12]. In this case we found that certain rings had currents following the standard Φ=nΦo quantisation of magnetic flux. However in exceptional cases we could construct superconducting rings showing a Φ=(n+1/2)Φo flux quantisation, as found recently by the group of Tsuei and Kirtley at IBM Yorktown Heights. The Bristol group have also pioneered the use of the coherent potential approximation (CPA) to describe the effects of disorder in superconductors. The CPA is well known in the electronic structure of disordered alloys, and can be implemented in first principles KKR-CPA calculations. We have recently shown that the CPA formalism can be applied to superconductors with both s-wave or d-wave pairing [13,14]. Interestingly, the numerical CPA results[13] for the critical temperature, Tc, as a function of both disorder and band-filling show a remarkable qualitative correspondence with those actually observed in experiments on the HTS system YBa2Cu3O7.
Publications
- W.M. Temmerman, Z. Szotek, B.L. Gyorffy, O.K. Anderson and O. Jepsen,
"Gap Anisotropy in the Layered High Temperature Superconductors",
Phys. Rev. Lett. 76, 307 (1996). - W.M. Temmerman, Z. Szotek, B.L. Gyorffy, O.K. Anderson and O. Jepson,
" Where is the Cooper Force in High Temperature Superconductors?",
HPC Profile, The National Publication for High Performance Computing Applications and Techniques, Eds. R. J. Allen, R. R. Whittington and M. F. Guest, 10 6 (1996). - B.L. Gyorffy, Z. Szotek, W.M. Temmerman, O.K. Andersen and O. Jepsen,
"On the QuasiParticle Spectra of High Temperature Superconductors",
Phys. Rev. B 58 1025 (1998). - Z. Szotek, B.L. Gyorffy, W.M. Temmerman and O.K. Andersen,
"The Van Hove Scenario and the Eight-Band Model for High Tc Superconductors",
Phys. Rev. B 58 522 (1998). - W.M. Temmerman, B.L. Gyorffy, Z. Szotek, O.K. Anderson and O. Jepsen,
"On the QuasiParticle Spectra of YBa2Cu3O7", in High-Performance Computing, Eds. R.J. Allan, M.F. Guest, A.D. Simpson, D.S. Henty and D.A. Nicole, Kluwer
Academic/Plenum Publishers, ISBN 0-30646034-3, (1999) 147-154. - Z. Szotek, B.L. Gyorffy, W.M. Temmerman, O.K. Andersen and O. Jepsen,
"A Semiphenomelogical Approach for Description of Quasiparticles in High Temperature Superconductors",
Lecture Notes in Physics, Springer-Verlag (1999), submitted. - Z. Szotek, B.L. Gyorffy, and W.M. Temmerman,
"Penetration depth",
in preparation. - W.M. Temmerman, Z. Szotek, H. Winter and A. Svane,
"Energetics of Divalent and Trivalent Cu in YBCO" ,
submitted to PRL. - A.M. Martin and J.F. Annett,
"Self-consistent properties of d- and s-wave superconductors",
Phys. Rev. B 57,8709 (1998). - A.M. Martin and J.F. Annett,
"The importance of self-consistency in determining interface properties in SIN and DIN structures",
Superlattices and Microstructures, 25, 1019 (1999). - J.J. Hogan O'Neill, A.M. Martin and J.F. Annett,
"Tilt grain boundary effects in s- and d-wave superconductors",
Phys. Rev. B 60, 3568 (1999). - J.J. Hogan O'Neill,
PhD thesis,
University of Bristol 1999. - G. Litak, A.M. Martin, B.L. Gyorffy, J.F. Annett and K.I. Wysokinski,
"Van Hove singularity and d-wave pairing in disordered superconductors",
Physica C 309, 257 (1998). - A.M. Martin, G. Litak, B.L. Gyorffy, J.F. Annett and K.I. Wysokinski,
"Coherent potential approximation for d-wave superconductivity in disordered sysytems",
Phys. Rev. B 60, 7523 (1999).
