Superconductivity Theory

1.1.  MODELING USING  PHENOMENOLOGICAL  THEORIES

Up to now Ginzburg-Landau theory remains a powerful method in study  of fundamental  physical properties of superconductors. This theory has been widely accepted as a successfully phenomenological model for a  superconductor. Last year  many classes of  multiband and anisotropic  superconductors such as cuprate compounds, borocarbides, MgB2   and FeAs based superconductors were discovered. Ginzburg-Landau theory was generalized  for the case superconductors with many band and anisotropic superconductors. Unconventional order parameter symmetry (d-wave  and p-wave symmetry) taken into account in investigations. Another phenomenological models related with  invsetigations of vortex dynamics, AC susceptibility and magnetization  in intermediate state  of II type superconductors.

AU group has experience on simulation and modeling of two-band Ginzburg-Landau equations. There are close collaborations betweenBelgium, Ukrainian  theoretical groups. At the moment, AU group  to fulfill  the development of a new calculations using anisotropic and many band Ginzburg-Landau equations. For the first two years, the research will concentrate on modeling and simulation of time-dependent Ginzburg-Landau equations for the application to transport and fluctuation phenomena in superconductors. TheAnkaragroup is currently working on this aspect. For the five years, the research progress will include application of obtained results to real objects. Development of vortex dynamics investigations, calculations of magnetic quantities and generalization of Ginzburg-Landau theory  to the case of existence of superconductivity and magnetism (as in unconventional compounds) in the scope of this stage. Final  stages  of investigations are comparison of obtained results with  experimental  data and  possible  implementation will be considered.

For the realization of this topic, at least 5-6 researches are required.

1.2. MICROSCOPICAL THEORY OF SUPERCONDUCTIVITY AND AB INITIO CALCULATIONS

Microscopical origin of superconductivity remains one of the most interesting research areas in physics and stood as a major scientific mystery for a large part of effors of  teoreticians. It is well known that Eliashberg theory and  its weak coupling limit BCS theory   is applicable to electron-phonon based superconductors. İt is well known that CuO and FeAs based superconductors  are unconventional superconductors. These  systems  can be considered strong correlate electron systems (see 1.3). However generalized to the case electron-boson  interaction Eliashberg (BCS) theory  highly  interesting  for application to  unconventional superconductors.

AU group has experience on analytical calculations of BCS and Eliashberg theories. At the moment, AU group  to fulfill  the development of a new calculations using anisotropic and many band Eliashberg equations. For the first two years, the research will concentrate on calculation  of Eliashberg equations for the application to study doping and isotope effects in  CuO and FeAs based superconductors. TheAnkaragroup is currently working on this aspect. For the five years, the research progress will include full numerical calculations in application to real objects. Ab initio  simulations of electronic and phononic spectrum of superconducting compounds with further using in Eliashberg equations  are planned. Inhomogeneous Coulomb interaction also will be included into calculations. Final  stage of will be  prediction of possible superconductivity in  new compounds.

For the realization of this topic, at least 5 researches are required.

1.3. PEDAGOGICAL  ASPECTS  OF  SUPERCONDUCTIVITY

Education of young scientist to modern methods of solid state physics seems  very important  for the realization of RoadMap. Overview of current topics in superconductivity, modern numerical and  experimental  methods and corresponding recent developments in these areas  will be be subject of periodical schools on superconductivity in the USTAM. Organization of periodical  Ankara seminars on Problems of Superconductivity also necessary.