Determination of the Coherence Length and the Cooper-Pair Size in Unconventional Superconductors by Tunnelling Spectroscopy

The main purpose of the paper is to discuss a possibility of the determination of the values of the coherence length and the Cooper-pair size in unconventional superconductors by using tunnelling spectroscopy. In the mixed state of type-II superconductors, an applied magnetic field penetrates the superconductor in the form of vortices which form a regular lattice. In unconventional superconductors, the inner structure of a vortex core has a complex structure which is determined by the order parameter of the superconducting state and by the pairing wavefunction of the Cooper pairs. In clean superconductors, the spatial variations of the order parameter and the pairing wavefunction occur over the distances of the order of the coherence length and the Cooper-pair size, respectively. Therefore, by performing tunnelling spectroscopy along a line passing through a vortex core, one is able, in principle, to estimate the values of the coherent length and the Cooper-pair size.Comment: 13 pages, including 17 figure

Effects of gap anisotropy upon the electronic structure around a superconducting vortex

An isolated single vortex is considered within the framework of the quasiclassical theory. The local density of states around a vortex is calculated in a clean type II superconductor with an anisotropy. The anisotropy of a superconducting energy gap is crucial for bound states around a vortex. A characteristic structure of the local density of states, observed in the layered hexagonal superconductor 2H-NbSe2 by scanning tunneling microscopy (STM), is well reproduced if one assumes an anisotropic s-wave gap in the hexagonal plane. The local density of states (or the bound states) around the vortex is interpreted in terms of quasiparticle trajectories to facilitate an understanding of the rich electronic structure observed in STM experiments. It is pointed out that further fine structures and extra peaks in the local density of states should be observed by STM.Comment: 11 pages, REVTeX; 20 PostScript figures; An Animated GIFS file for the star-shaped vortex bound states is available at http://mp.okayama-u.ac.jp/~hayashi/vortex.htm

A Self-Consistent Microscopic Theory of Surface Superconductivity

The electronic structure of the superconducting surface sheath in a type-II superconductor in magnetic fields $H_{c2}<H<H_{c3}$ is calculated self-consistently using the Bogoliubov-de Gennes equations. We find that the pair potential $\Delta(x)$ exhibits pronounced Friedel oscillations near the surface, in marked contrast with the results of Ginzburg-Landau theory. The role of magnetic edge states is emphasized. The local density of states near the surface shows a significant depletion near the Fermi energy due to the development of local superconducting order. We suggest that this structure could be unveiled by scanning-tunneling microscopy studies performed near the edge of a superconducting sample.Comment: 12 pages, Revtex 3.0, 3 postscript figures appende

Relation between Vortex core charge and Vortex Bound States

Spatially inhomogeneous electron distribution around a single vortex is discussed on the basis of the Bogoliubov-de Gennes theory. The spatial structure and temperature dependence of the electron density around the vortex are presented. A relation between the vortex core charge and the vortex bound states (or the Caroli-de Gennes-Matricon states) is pointed out. Using the scanning tunneling microscope, information on the vortex core charge can be extracted through this relation.Comment: 5 pages, 3 figures; minor changes; Version to appear in JPSJ 67, No.10, 199

Quasiparticles of d-wave superconductors in finite magnetic fields

We study quasiparticles of d-wave superconductors in the vortex lattice by self-consistently solving the Bogoliubov-de Gennes equations. It is found for a pure $d_{x^2-y^2}$ state that: (i) low-energy quasiparticle bands in the magnetic Brillouin zone have rather large dispersion even in low magnetic fields, indicating absense of bound states for an isolated vortex; (ii) in finite fields with $k_F \xi_0$ small, the calculated tunneling conductance at the vortex core shows a double-peak structure near zero bias, as qualitatively consistent with the STM experiment by Maggio-Aprile et al. [Phys. Rev. Lett. {\bf 75} (1995) 2754]. We also find that mixing of a $d_{xy}$- or an s-wave component, if any, develops gradually without transitions as the field is increased, having little effect on the tunneling spectra.Comment: 4 pages, 4 figures, LaTe

Evidence for coexistence of the superconducting gap and the pseudo - gap in Bi-2212 from intrinsic tunneling spectroscopy

We present intrinsic tunneling spectroscopy measurements on small Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ mesas. The tunnel conductance curves show both sharp peaks at the superconducting gap voltage and broad humps representing the $c$-axis pseudo-gap. The superconducting gap vanishes at $T_c$, while the pseudo-gap exists both above and below $T_c$. Our observation implies that the superconducting and pseudo-gaps represent different coexisting phenomena.Comment: 5 pages, 4 figure

Vortex structure in dd-wave superconductors

Vortex structure of pure $d_{x^2-y^2}$-wave superconductors is microscopically analyzed in the framework of the quasi-classical Eilenberger equations. Selfconsistent solution for the $d$-wave pair potential is obtained for the first time in the case of an isolated vortex. The vortex core structure, i.e., the pair potential, the supercurrent and the magnetic field, is found to be fourfold symmetric even in the case that the mixing of $s$-wave component is absent. The detailed temperature dependences of these quantities are calculated. The fourfold symmetry becomes clear when temperature is decreased. The local density of states is calculated for the selfconsistently obtained pair potential. From the results, we discuss the flow trajectory of the quasiparticles around a vortex, which is characteristic in the $d_{x^2-y^2}$-wave superconductors. The experimental relevance of our results to high temperature superconductors is also given.Comment: 22 pages, RevTex, 23 figures available upon reques

High-resolution measurement of the time-modulated orbital electron capture and of the β+\beta^+ decay of hydrogen-like 142^{142}Pm60+^{60+} ions

The periodic time modulations, found recently in the two-body orbital electron-capture (EC) decay of both, hydrogen-like $^{140}$Pr$^{58+}$ and $^{142}$Pm$^{60+}$ ions, with periods near to 7s and amplitudes of about 20%, were re-investigated for the case of $^{142}$Pm$^{60+}$ by using a 245 MHz resonator cavity with a much improved sensitivity and time resolution. We observed that the exponential EC decay is modulated with a period $T = 7.11(11)$s, in accordance with a modulation period $T = 7.12(11)$ s as obtained from simultaneous observations with a capacitive pick-up, employed also in the previous experiments. The modulation amplitudes amount to $a_R = 0.107(24)$ and $a_P = 0.134(27)$ for the 245 MHz resonator and the capacitive pick-up, respectively. These new results corroborate for both detectors {\it exactly} our previous findings of modulation periods near to 7s, though with {\it distinctly smaller} amplitudes. Also the three-body $\beta^+$ decays have been analyzed. For a supposed modulation period near to 7s we found an amplitude $a = 0.027(27)$, compatible with $a = 0$ and in agreement with the preliminary result $a = 0.030(30)$ of our previous experiment. These observations could point at weak interaction as origin of the observed 7s-modulation of the EC decay. Furthermore, the data suggest that interference terms occur in the two-body EC decay, although the neutrinos are not directly observed.Comment: In memoriam of Prof. Paul Kienle, 9 pages, 1 table, 5 figures Phys. Lett. B (2013) onlin

Expansion of the Vortex Cores in YBa2Cu3O6.95 at Low Magnetic Fields

Muon spin rotation spectroscopy has been used to measure the effective size of the vortex cores in optimally doped YBa2Cu3O6.95 as a function of temperature and magnetic field deep in the superconducting state. While the core size at H=2T is close to 20 angstroms and consistent with that measured by STM at 6T, we find a striking increase in the core size at lower magnetic fields, where it approaches an extraordinarily large value of about 100 angstroms. This suggests that the average value of the superconducting coherence length in cuprate superconductors may be larger than previously thought at low magnetic fields.Comment: 9 pages, 4 figures, 1 text fil

Flux-Induced Vortex in Mesoscopic Superconducting Loops

We predict the existence of a quantum vortex for an unusual situation. We study the order parameter in doubly connected superconducting samples embedded in a uniform magnetic field. For samples with perfect cylindrical symmetry, the order parameter has been known for long and no vortices are present in the linear regime. However, if the sample is not symmetric, there exist ranges of the field for which the order parameter vanishes along a line, parallel to the field. In many respects, the behavior of this line is qualitatively different from that of the vortices encountered in type II superconductivity. For samples with mirror symmetry, this flux-induced vortex appears at the thin side for small fluxes and at the opposite side for large fluxes. We propose direct and indirect experimental methods which could test our predictions.Comment: 6 pages, Latex, 4 figs., uses RevTex, extended to situations far from cylindrical symmetr