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Glass-like low frequency ac response of ZrB$_{12}$ and Nb single crystals in the surface superconducting state

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 Added by Menachem Tsindlekht
 Publication date 2005
  fields Physics
and research's language is English




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We report experimental studies of the low frequency electrodynamics of ZrB$_{12}$ and Nb single crystals. AC susceptibility at frequencies 3 - 1000 Hz have been measured under a dc magnetic field, $H_0$, applied parallel to the sample surface. In the surface superconducting state, for several $H_0$, the real part of the ac magnetic susceptibility exhibits a logarithmic frequency dependence as for spin-glass systems. Kramers-Kronig analysis of the experimental data, shows large losses at ultra low frequencies ($<3$ Hz). The wave function slope at the surface was found. The linear response of the order parameter to the ac excitation was extracted from the experimental data.



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The large nonlinear response of a single crystal ZrB$_{12}$ to an ac field (frequency 40 - 2500 Hz) for $H_0>H_{c2}$ has been observed. Direct measurements of the ac wave form and the exact numerical solution of the Ginzburg-Landau equations, as well as phenomenological relaxation equation, permit the study of the surface superconducting states dynamics. It is shown, that the low frequency response is defined by transitions between the metastable superconducting states under the action of an ac field. The relaxation rate which determines such transitions dynamics, is found.
Bulk and surface properties of high-quality single crystals of zirconium dodecaboride have been studied in the temperature range from 4.5 K up to the superconducting transition temperature which is found to be nearly 6.06 K. Scanning tunnelling spectroscopy data, together with dc and ac magnetization measurements, are consistent with the conventional s-wave pairing scenario, whereas they disagree in estimates of the electron-phonon coupling strength. We explain the divergence, supposing a great difference between the surface and bulk superconducting characteristics of the compound. This assertion is supported by our findings of a non-linear magnetic response to an amplitude-modulated alternating magnetic field, testifying to the presence of surface superconductivity in the ZrB$_{12}$ samples at dc fields exceeding the thermodynamic critical field.
We report optical (6 meV - 4 eV) properties of a boride superconductor ZrB$_{12}$ ($T_c$ = 6 K) in the normal state from 20 to 300 K measured on high-quality single crystals by a combination of reflectivity and ellipsometry. The Drude plasma frequency and interband optical conductivity calculated by self-consistent full-potential LMTO method agree well with experimental data. The Eliashberg function $alpha_{tr}^2F(omega)$ extracted from optical spectra features two peaks at about 25 and 80 meV, in agreement with specific heat data. The total coupling constant is $lambda_{tr}=1.0pm0.35$. The low energy peak presumably corresponds to the displacement mode of Zr inside $B_{24}$ cages, while the second one involves largely boron atoms. In addition to the usual narrowing of the Drude peak with cooling down, we observe an unexpected removal of about 10 % of the Drude spectral weight which is partially transferred to the region of the lowest-energy interband transition ($sim$ 1 eV). This effect may be caused by the delocalization of the metal ion from the center of the $B_{24}$ cluster.
Our measurements of the low frequency ac conductivity in strongly disordered two-dimensional films near the magnetic field-tuned superconductor-to-insulator transition show a sudden drop in the phase stiffness of superconducting order with either increased temperature or magnetic field. Surprisingly, for two different material systems, the abrupt drop in the superfluid density in a magnetic field has the same universal value as that expected for a Berezinskii-Kosterlitz-Thouless transition in zero magnetic field. The characteristic temperature at which phase stiffness is suddenly lost can be tuned to zero at a critical magnetic field, following a power-law behavior with a critical exponent consistent with that obtained in previous dc transport studies on the dissipative side of the transition.
323 - A.J.Moreno , V. Bekeris 1999
We measured the first and third harmonic of the complex AC susceptibility in YBCO single crystals with different oxygen content. The amplitude of the AC field was varied in presence of an external DC field both applied parallel to the c axis of the crystals. We show evidence that deoxygenation leads to a reduction of bulk pinning strength and consequently to a stronger contribution of geometrical barriers.
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