Origin of the variable-range vortex hopping in Bi₂Sr₂Ca_1-xY_xCu₂O₈ with columnar defects

We report on the vortex transport in Bi₂Sr₂Ca_1-xY_xCu₂O₈ single crystals irradiated in a parallel direction with the c axis with 5.8-GeV Pb ions at fluences of 3.75×10¹⁰cm^-2 and 7.5×10¹⁰cm^-2. A detailed investigation of the vortex transport using current-voltage measurements is carried out with the magnetic field applied along the c axis. First, we investigate the critical behavior of the linear and nonlinear conductivity near the Bose-glass melting line. We obtain field and sample-independent critical exponents z^′ and ν^′ consistent with a compressible Bose glass (i.e., ν_∥=2ν_⊥≡2ν^′). Using the values z^′=5.28±0.05 and ν^′=1.04±0.06, the data collapse into two single-scaling functions. Second, we report on conductivity measurements over a wide filling factor (B/B_φ) range from 0.04 up to 0.9 within the Bose-glass phase. Our data provide support for a variable-range hopping mechanism for low current densities, in accordance with the ideas of Nelson and Vinokur [Phys. Rev. B 48, 13 060 (1993)]. We determine a glass exponent value of 1/3 for all the filling factors investigated at large ratios of the penetration depth to the average defect distance (λ_ab/d∼10). This finding implies that no Coulomb gap occurs in the pinning energy spectrum. Furthermore, our results show that for low filling factors (<1/2) the on-site disorder plays a major role in the bandwidth of flux-binding energies. Finally, the appearance of a well-defined crossover near half filling is consistent with the field B^* separating the strongly pinned Bose-glass regime from the weakly pinned Bose-glass regime.