Magnetic flux can penetrate a type-II superconductor in the form of Abrikosov vortices (also called flux lines, flux tubes, or fluxons) each carrying a quantum of magnetic flux phi 0=h/2e. These tiny vortices of supercurrent tend to arrange themselves in a triangular flux-line lattice (FLL), which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-Tc superconductors (HTSCs) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSCs the FLL is very soft mainly because of the large magnetic penetration depth lambda . The shear modulus of the FLL is c66~1/ lambda 2, and the tilt modulus c44(k)~(1+k2 lambda 2)-1 is dispersive and becomes very small for short distortion wavelengths 2 pi /k<< lambda . This softness is enhanced further by the pronounced anisotropy and layered structure of HTSCs, which strongly increases the penetration depth for currents along the c axis of these (nearly uniaxial) crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may `melt` the FLL and cause thermally activated depinning of the flux lines or ofthe two-dimensional `pancake vortices` in the layers. Various phase transitions are predicted for the FLL in layered HTSCs. Although large pinning forces and high critical currents have been achieved, the small depinning energy so far prevents the application of HTSCs as conductors at high temperatures except in cases when the applied current and the surrounding magnetic field are small.

https://iopscience.iop.org/article/10.1088/0034-4885/58/11/003/pdf

The flux-line lattice in superconductors

Magnetic flux can penetrate a type-II superconductor in form of Abrikosov vortices. These tend to arrange in a triangular flux-line lattice (FLL) which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-$T_c$ supercon- ductors (HTSC's) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSC's the FLL is very soft mainly because of the large magnetic penetration depth: The shear modulus of the FLL is thus small and the tilt modulus is dispersive and becomes very small for short distortion wavelength. This softness of the FLL is enhanced further by the pronounced anisotropy and layered structure of HTSC's, which strongly increases the penetration depth for currents along the c-axis of these uniaxial crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may melt the FLL and cause thermally activated depinning of the flux lines or of the 2D pancake vortices in the layers. Various phase transitions are predicted for the FLL in layered HTSC's. The linear and nonlinear magnetic response of HTSC's gives rise to interesting effects which strongly depend on the geometry of the experiment.

The Flux-Line Lattice in Superconductors

Recent studies on high-Tc superconductors have aroused new interest in tunnelling effects in unconventional superconductors. Unlike in conventional s-wave superconductors, the d-wave pairing state in these materials has an internal phase of the pair potential. The internal phase as a function of the wavevector of the Cooper pairs has a large influence on the electric properties of tunnelling junctions. Important effects of the internal phase on the Josephson current were first predicted theoretically. The idea has been established through several experiments using high-Tc Josephson junctions, which detect ?-phase shift between the a- and b-axis directions and fractional flux quanta. These results give convincing evidence for d-wave symmetry in high-Tc superconductors. In addition, the existence of new interference effects in the quasiparticle states near surfaces and boundaries has been suggested through theoretical predictions. Experimentally, a large number of tunnelling spectroscopy data showed zero-bias conductance peaks (ZBCPs), the origin of which cannot be explained in terms of the classical concept that a tunnelling conductance spectrum is a phase-insensitive probe of the electronic states. It is clarified theoretically that the observed ZBCPs reflect the formation of zero-energy states on the surface due to the ?-phase shift of internal phase in the d-wave pairing symmetry. The formulation developed for tunnelling spectroscopy suggests that tunnelling spectroscopy is essentially phase sensitive. In addition, the formation of the bound states has been shown to have a serious influence on the electrical properties of Josephson junctions. Several anomalous properties including strong enhancement of the Josephson current in the low-temperature region have been predicted theoretically. In this report, recent developments in tunnelling effects on surface bound states in unconventional superconductors are reviewed.

https://iopscience.iop.org/article/10.1088/0034-4885/63/10/202/pdf

Tunnelling effects on surface bound states in unconventional superconductors

Compact solid-state sources of terahertz (THz) radiation are being sought for sensing, imaging, and spectroscopy applications across the physical and biological sciences. We demonstrate that coherent continuous-wave THz radiation of sizable power can be extracted from intrinsic Josephson junctions in the layered high-temperature superconductor Bi 2 Sr 2 CaCu 2 O 8 . In analogy to a laser cavity, the excitation of an electromagnetic cavity resonance inside the sample generates a macroscopic coherent state in which a large number of junctions are synchronized to oscillate in phase. The emission power is found to increase as the square of the number of junctions reaching values of 0.5 microwatt at frequencies up to 0.85 THz, and persists up to ∼50 kelvin. These results should stimulate the development of superconducting compact sources of THz radiation.

/pdf/emission-of-coherent-thz-radiation-from-superconductors-3jdj9zqfqk.pdf

Emission of coherent THz radiation from superconductors.

Recent studies of the electromagnetic response of high-Tc superconductors using terahertz, infrared, and optical spectroscopies are reviewed. In combination these experimental techniques provide a comprehensive picture of the low-energy excitations and charge dynamics in this class of materials. These results are discussed with an emphasis on conceptual issues, including evolution of the electronic spectral weight in doped Mott-Hubbard insulators, the d-wave superconducting energy gap and the normal-state pseudogap, anisotropic superfluid response, electronic phase segregation, emergence of coherent electronic state as a function of both temperature and doping, the vortex state, and the energetics of the superconducting transition. Because the theoretical understanding of these issues is still evolving the review is focused on the analysis of the universal trends that are emerging out of a large body of work carried on by many research teams. Where possible data generated by infrared/optical techniques are compared with the data from other spectroscopic and transport methods.

/pdf/electrodynamics-of-high-t-c-superconductors-1p3dck85rg.pdf

Electrodynamics of high- T c superconductors

We report on a new type of correlated nanometer-scale pinning structure observed in a melt-processed $({\mathrm{N}\mathrm{d}}_{0.33}{\mathrm{E}\mathrm{u}}_{0.38}{\mathrm{G}\mathrm{d}}_{0.28}){\mathrm{B}\mathrm{a}}_{2}{\mathrm{C}\mathrm{u}}_{3}{\mathrm{O}}_{y}$ (NEG-123). It consists of $\mathrm{N}\mathrm{E}\mathrm{G}/\mathrm{B}\mathrm{a}$-rich clusters in the stoichiometric NEG-123 matrix forming a lamellar array with a period of a few nanometers. These lamellas appear within regular twins, thus representing their fine substructure---sometimes straight, sometimes wavy. This new material structure correlates well with the significant enhancement of pinning at high fields, represented by irreversibility field above 14 T at 77 K ($B\ensuremath{\parallel}c$). We believe that the new pinning medium enables one to significantly broaden the limits for high-field applications.

/pdf/new-type-of-vortex-pinning-structure-effective-at-very-high-1fjlcxjjxi.pdf

New type of vortex pinning structure effective at very high magnetic fields.

Flux creep in Bi 2 Sr 2 CaCu 2 O 8 crystals exhibits two different regimes as a function of time, as well as of temperature and magnetic field. The short-time, low-temperature regime has a peak in current density versus field, which is enhanced by irradiation defects. The long-time, high-temperature regime has a monotonic and sharp falloff (step) in current density versus magnetic field, which is suppressed by irradiation defects. The former is identified with bulk pinning, and the latter with a surface barrier

Flux-creep crossover and relaxation over surface barriers in Bi2Sr2CaCu2O8 crystals.

We report on the study of the electronic anisotropy of the MgB 2 superconductor using the in-plane resistivity measurements in the magnetic field applied perpendicular and parallel to Mg and B planes of MgB 2 single crystals. The results show the temperature dependent anisotropy of the upper critical field with the anisotropy ratio γ=H c 2 | | /H c 2 increasing from 2.2 close to T c up to about 3 below 30 K. Our estimation of the in-plane and out-of-plane coherence length of about ξ a b (0) = 68 A and ξ c (0) = 23 A and the electronic mean-free path l a b =240 A and l c =60 A, respectively, indicates MgB 2 single crystal approaches the clean limit type-II superconductor.

Anisotropic superconducting properties of MgB2 single crystals probed by in-plane electrical transport measurements

Local vortex dynamics in Bi2Sr2CaCu2O8 single crystals was studied using novel microscopic GaAs/AlGaAs Hall-sensor arrays. The irreversibility line (IL) is found to exist in the absence of bulk pinning. At high temperatures the IL is due to geometrical barriers whereas at intermediate temperatures the irreversible behavior is determined by surface barriers. Bulk pinning governs the IL only at T < 22 K.

https://iopscience.iop.org/article/10.1209/0295-5075/30/6/009/pdf

Nature of the Irreversibility Line in Bi2Sr2CaCu2O8

We report the first detailed and quantitative study of the Josephson coupling energy in the vortex liquid, Bragg glass, and vortex glass phases of Bi(2)Sr(2)CaCu(2)O(8+delta) by the Josephson plasma resonance. The measurements revealed distinct features in the T and H dependencies of the plasma frequency omega(pl) for each of these three vortex phases. When going across either the Bragg-to-vortex glass or the Bragg-to-liquid transition line, omega(pl) shows a dramatic change. We provide a quantitative discussion on the properties of these phase transitions, including the first order nature of the Bragg-to-vortex glass transition.

http://arxiv.org/pdf/cond-mat/0002196.pdf

Noriko Chikumoto

Papers

New type of vortex pinning structure effective at very high magnetic fields.

Flux-creep crossover and relaxation over surface barriers in Bi2Sr2CaCu2O8 crystals.

Anisotropic superconducting properties of MgB2 single crystals probed by in-plane electrical transport measurements

Nature of the Irreversibility Line in Bi2Sr2CaCu2O8

Abrupt change of josephson plasma frequency at the phase boundary of the bragg glass in Bi(2)Sr(2)CaCu(2)O(8+delta)