Field dependence of the vortex core size probed by scanning tunneling microscopy

Abstract

We study the spatial distribution of the density of states (DOS) at zero bias N(r) in the mixed state of single and multigap superconductors. We provide an analytic expression for N(r) based on deGennes' relationship between DOS and the order parameter that reproduces well scanning tunneling microscopy (STM) data in several superconducting materials. In the single gap superconductor β-Bi2Pd, we find that N(r) is governed by a length scale ξH=φ0/2πH, which decreases in rising fields. The vortex core size C, defined via the slope of the order parameter at the vortex center, C (dΔ/dr|r→0)-1, differs from ξH by a material dependent numerical factor. The new data on the tunneling conductance and vortex lattice of the 2H-NbSe1.8S0.2 show the in-plane isotropic vortices, suggesting that substitutional scattering removes the in-plane anisotropy found in the two-gap superconductor 2H-NbSe2. We fit the tunneling conductance of 2H-NbSe1.8S0.2 to a two gap model and calculate the vortex core size C for each band. We find that C is field independent and has the same value for both bands. We also analyze the two-band superconductor 2H-NbS2 and find the same result. We conclude that, independently of the magnetic field induced variation of the order parameter values in both bands, the spatial variation of the order parameter close to the vortex core is the same for all bands ; The work was supported by the Spanish Ministry of Economy and Competitiveness (FIS2014-54498-R, MAT2014-56143-R, MDM-2014-0377, and MDM2015-0538, Network of Excellence in Molecular Nanoscience MAT2014-52919-REDC), by the Comunidad de Madrid through program Nanofrontmag-CM (S2013/MIT- 2850), the Generalidad Valenciana through program Prometeo, and by EU (Cost MP-1201 and COST CA-15128). E.H. acknowledges support of COLCIENCIAS Programa Doctorados en el Exterior Convocatoria 568-2012 and S.M. of MECD: FPU14/04407. M.G. acknowledges the European Union Horizon 2020 Marie Curie Actions under the project SPIN2D (H2020/2014-659378). We acknowledge SEGAINVEX workshop of UAM and Banco Santander. The work of I.G. receives support from Axa Research Fund, FP7-PEOPLE-2013-CIG 618321 and the European Research Council (Grant No. 679080). Work of V.K. was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. The Ames Laboratory is operated for the U.S. DOE by Iowa State University under Contract No. DE-AC02-07CH11358