The Theory Group

Physics in High Magnetic Fields

I.D.Vagner

Grenoble High Magnetic Field Laboratory (CNRS-MPI)
166X, F-48042, Grenoble, Cedex 9, France.
Tel: +33-4-76-88-11-27; Fax: +33-4-76-85-56-10.
E-Mail: vagner@labs.polycnrs-gre.fr

Physics and Engineering Research Institute (P.E.R.I.)
Ruppin Instutute for Higher Education
Emek Hefer 40250, Israel.
Tel: (+972)-9898-1340, (+972)-9898-3042;
Fax: (+972)-9898-6848
E-mail: perinst@netvision.net.il


Superconductivity

Since the new generation of superconductors (High - Tc superconductors) can sustain extremely high magnetic fields , we have developed a theory of quantum oscillations in the superconducting state [1] [2] [7] [8] [13].

This theory is aimed for the future experimental studies of the Fermi surfaces of the High-Tc superconductors and for sorting out of possible pairing mechanisms. Stimulated by the experiments on the anisotropy of the upper critical fields in the Y-Ba-Cu-O superconductors we have developed an analitical theory for calculation of the magnetic critical fields in superconductors with nonequivalent and anisotropic layers [6].

1. Quantum Oscillations near Hc2

Magnetic Quantum Oscillations have been recently observed in several type-II superconductors below . A systematic study of this effect has been impaired, however, by the lack of a complete quantitative theory of the de Haas-van Alphen (dHvA) effect in the vortex state, analogous to the Lifshitz-Kosevich theory in normal metals. Such a theory would require a detailed analysis of the effect of the SC order parameter on the magnetization oscillations in the vortex state, which turns out to be an extremely subtle theoretical problem.

A common feature reported by all experimental groups so far, which is far from being well understood, has been the observation of an additional damping in the dHvA amplitude below . Maki and Stephen considered the correction to the quasi-particles (QP) lifetime due to 'scattering' by the vortex lattice, as the origin of this additional damping; their approach was based on the assumption that, in the semiclassical limit, the vortex lattice acts like a random scattering potential for the QP, and took advantage of the averaging over the realizations of the vortex lattice to obtain a simple gaussian damping factor , where is the cyclotron frequency, and is the amplitude of the SC order parameter measured in units of the cyclotron energy.

Strictly speaking, however, the 'scattering' of QP by the inhomogeneous pair potential is a highly coherent process, similar to multiple Andreev reflection at a 2D periodic array of SC-normal phase boundaries.

We have shown that, within the Gorkov's perturbation theory in the semiclassical limit (i.e. where ), incoherent 'scattering' channels, which generate the dominant contribution in the random lattice approximation, are completely cancelled in the exact calculation, due to the presence of a strict phase coherence in the many electron- pair correlation functions.

As a result the actual damping of the dHvA amplitude below is significantly weaker than what is predicted by the Maki-Stephen gaussian factor, and a sign change of the dHvA amplitude may take place below .

We have found that in a 2D system this sign inversion is related to the splitting of the highest occupied Landau band, crossing the Fermi energy, into two major magnetic subbands by the SC order parameter. This splitting reflects the fact that the magnetic flux threading a unit cell in the Abrikosov lattice is one half electronic flux quantum (or a single Cooper-pair flux unit). Since it occurs in all Landau bands around the Fermi energy the related sign change in the dHvA amplitude is not expected to weaken significantly in 3D systems. Both studies indicate that disorder in the vortex lattice tends to destroy the coherence in the QP 'scattering' amplitude responsible for this effect.

  1. R. Markiewicz, I.D. Vagner, P. Wyder and T. Maniv ''Magnetooscillations in Quasi-2D Superconductors''. Solid State Commun. 67 , 43 (1988).
  2. T. Maniv, R.S. Markiewicz, I.D. Vagner and P. Wyder ''Magnetooscillations in Q2D Extreme Type II Superconductors''. Physica C153-155 , 1179 (1988).
  3. T. Maniv, R.S. Markiewich, I.D. Vagner et P. Wyder ''Reentrance of the Superconducting State in a Strong Magnetic Field''. Physica B165-166, 361 (1990).
  4. T. Maniv, A.I. Rom, R.S. Markiewicz, I.D. Vagner and P. Wyder ''The Interplay Between Superconductivity and Landau Quantization.'' In:''Physical Phenomena in High Magnetic Fields.'' (Addison-Wesley, 1991).
  5. T. Maniv, A.I. Rom, R.S. Markiewicz, I.D. Vagner and P. Wyder ''Superconductivity on Landau levels.'' J. Phys. Chem. Solids, 52,1392 (1991).
  6. L.N. Bulaevskii and I.D. Vagner ''MagneticCritical Fields of Y-Ba-Cu-O Superconductors.'' Phys. Rev. B, 43,8694 (1991).
  7. T. Maniv, R.S. Markiewicz, I.D. Vagner and P. Wyder ''Strong Quantum Oscillations in the Order Parameter of Two-Dimensional Type II Superconductors.'' Phys. Rev. B, 45,13084 (1992).
  8. T. Maniv, A.I. Rom, I.D. Vagner and P. Wyder ''De Haas-Van Alphen Effect in the Superconducting State.'' Phys. Rev. B, 46,8360 (1992).
  9. T. Maniv, A.I. Rom, I.D. Vagner et P. Wyder ''2D de Haas-van Alphen effect in the superconducting state.'' Helvetica Physica Acta, 65, 404 (1992).
  10. E.G. Haanappel, W. Joss, I.D. Vagner, P. Wyder, K. Trebenbach, H. Mattausch, A. Simon, F.M. Mueller and S. Askenazy ''Magneto-oscillations in YBa2Cu3O7 in high magnetic fields.'' Physica C, 209, 39 (1993).
  11. T. Maniv, A.I. Rom, I.D. Vagner and P. Wyder ''De Haas-van Alphen oscillations in extremely type-II nearly 2D superconductors.'' Physica C, 209, 35 (1993).
  12. T. Maniv, A.I. Rom, I.D. Vagner and P. Wyder ''The Analogue of the Lifshitz-Kosevich Formula for the dHvA effect in the vortex state of a Two-dimensional Superconductor.'' Physica C, 235-240, 1541 (1994).
  13. T. Maniv, R.Y. Rom, I.D. Vagner and P. Wyder ''Order parameter induced phase shift of the dHvA oscillations in the vortex state of type-II superconductors.'' Solid State Commun., 101,621 (1997).
  14. A.M. Dyugaev, I.D. Vagner and P. Wyder ''Competition between the nuclear magnetism and superconductivity.'' JETP Lett. 65, 812 (1998).
  15. V.N. Zhuravlev, Y. Maniv, I.D. Vagner and P. Wyder ''Coherence in the quasi-particle 'scattering' by the vortex lattice in pure type-II superconductors.'' Phys. Rev. B, 56, 14693 (1997).
  16. A.M. Dyugaev, I.D. Vagner and P. Wyder ''Contribution of the electron-nuclear interaction to the residual resistivity.'' JETP Lett. 64 ,207 (1996)



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