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Fluctuation spectroscopy: From Rayleigh-Jeans waves to Abrikosov vortex clusters

Reading a major part of the textbooks one can have impression that the BCS theory of superconductivity is the exact one. Proposed review dispels this delusion, clearly indicating the limits of the mean field theory applicability and demonstrating existence of the wide circle of interesting phenomena being beyond its confines. The chapter presents itself both the review and the textbook of fluctuation phenomena in superconductors. Its first half is devoted to presentation of the phenomenological and microscopical methods in the description of fluctuations. The Ginzburg-Landau functional and corresponding general description of fluctuation thermodynamics in framework of the functional integration over fluctuation fields approach is introduced. Time-dependent Ginzburg-Landau equation is is applied for the description of the fluctuation transport in the vicinity of superconducting transition. The basic aspects of the microscopic description of fluctuation phenomena in superconductors in the frameworks of the quantum field theory are presented. In the second half the authors portray a panorama of the superconductive fluctuations manifestation in different observables. The microscopic analysis of the different fluctuation contributions to the conductivity, magnetoconductivity, Hall effect, tunneling conductivity, thermopower, NMR relaxation rate is presented. The physical origin of Aslamazov-Larkin, Maki-Thompson and density of states renormalization corrections are discussed.

Fluctuation Phenomena in Superconductors

High resolution SQUID magnetization measurements in lead nanoparticles are used to study the fluctuating diamagnetism in zero-dimensional condition, namely for particle size d lesser than the coherence length. The diamagnetic magnetization Mdia (H, T= const) as a function of the field H at constant temperature is reported in the critical region and compared with the behaviour in the temperature range where the first-order fluctuation correction is expected to hold. The magnetization curves are analysed in the framework of exact fluctuation theories based on the Ginzburg-Landau functional for the coherence length much greater than d. The role of the upturn field Hup where Mdia reverses the field dependence is discussed and its relevance for the study of the fluctuating diamagnetism, particularly in the critical region where the first-order fluctuation correction breaks down, is pointed out. The size and temperature dependence of Hup is theoretically derived and compared to the experimental data. The relevance and the magnetization curves for non-evanescent field and of the upturn field for the study of the fluctuating diamagnetism above the superconducting transition temperature is emphasized.

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Zero-dimensional superconducting fluctuations and fluctuating diamagnetism in lead nanoparticles

A scenario is presented, in which the presence of a quantum critical point due to formation of incommensurate charge density waves accounts for the basic features of the high temperature superconducting cuprates, both in the normal and in the superconducting states. Specifically, the singular interaction arising close to this charge-driven quantum critical point gives rise to the non-Fermi liquid behavior universally found at optimal doping. This interaction is also responsible for d-wave Cooper pair formation with a superconducting critical temperature strongly dependent on doping in the overdoped region and with a plateau in the optimally doped region. In the underdoped region a temperature dependent pairing potential favors local pair formation without superconducting coherence, with a peculiar temperature dependence of the pseudogap and a non-trivial relation between the pairing temperature and the gap itself. This last property is in good qualitative agreement with so far unexplained features of the experiments.

https://arxiv.org/pdf/cond-mat/9702112.pdf

Non-Fermi-liquid behavior and d-wave superconductivity near the charge-density-wave quantum critical point

Primarily motivated by the similarities between the underdoped superconducting cuprates and the granular systems in regards of electric conductivity, phase fluctuations of the order parameter, and nuclear spin-lattice relaxation, a study has been carried out in a NbN(111) textured film at controlled granularity by means of superconducting quantum interference device magnetization and $^{93}\text{N}\text{b}$ NMR measurements. The Meissner diamagnetism in zero-field-cooling and field-cooling conditions and for different orientation of the magnetic field and the isothermal magnetization curves around the superconducting transition temperature ${T}_{\text{c}}$, are studied. $^{93}\text{N}\text{b}$ spectra and relaxation measurements have been performed for two values of the external magnetic field in parallel and perpendicular geometry, in the temperature range 4\char21{}300 K. In the superconducting phase the experimental findings for the textured film are similar to the one in bulk NbN. The nuclear spin-lattice relaxation process is the same as in bulk NbN in the temperature range 50\char21{}300 K, confirming a dominant contribution to the density of states at the Fermi energy arising from the Nb $4d$ band. At variance, on cooling from about 40 K down to ${T}_{\text{c}}$ $(H)$, the $^{93}\text{N}\text{b}$ relaxation rate in the film dramatically departs from the expected behavior for the Fermi gas and mimics the opening of a spin gap. The interpretation of the spin-gap opening in terms of depletion in the density of states at the Fermi energy can justify the anomalous temperature behavior of the $^{93}\text{N}\text{b}$ relaxation rate on approaching ${T}_{\text{c}}$ $(H)$ from above. The experimental findings suggest the occurrence of superconducting fluctuations (density-of-states term) in one-dimensional regime, coupled to a reduction in the time of flight of the electrons, both effects being related to the granularity. The data also suggest that the spin-gap phase in underdoped cuprates could be connected more to granularity, rather than to exotic mechanisms of magnetic origin.

Superconducting properties of a textured NbN film from 93Nb NMR relaxation and magnetization measurements

The dependence of the Maki-Thompson and of the density of states (DOS) depletion contributions from superconducting fluctuations to nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) relaxation is derived in the framework of the diagrammatic theory, applied to layered three-dimensional (3-D) high-Tc superconductors. The regularization procedure devised for the conductivity (A. I. Buzdin, A. A. Varlamov: Phys. Rev. B58, 14195, 1998) is used in order to avoid the divergence of the DOS term. The theoretical results are discussed in the light of NMR-NQR measurements in YBCO and compared with the recent theory (M. Eschrig et al.: Phys. Rev. B59, 12095, 1999), on the basis of the assumption of a purely 2-D spectrum of fluctuations.

Magnetic field dependence of the superconducting fluctuation contribution to NMR-NQR relaxation

The dependence of the Maki-Thompson (MT) and of the density of states depletion (DOS) contributions from superconducting fluctuations (SF) to NMR-NQR relaxation is derived in the framework of the diagrammatic theory, applied to layered three dimensional (3D) high T_c superconductors. The regularization procedure devised for the conductivity (Buzdin and Varlamov, Phys. Rev. B, 58, 14195 (1998)) is used in order to avoid the divergence of the DOS term. The theoretical results are discussed in the light of NMR-NQR measurements in YBCO and compared with the recent theory (Eschrig et al., Phys. Rev. B 59, 12095 (1999)), based on the assumption of a purely 2D spectrum of fluctuations.

A. A. Varlamov

Papers

Magnetic field dependence of the superconducting fluctuation contribution to NMR-NQR relaxation

Magnetic field dependence of the superconducting fluctuation contribution to NMR-NQR relaxation