Bose-glass behavior of the vortex system in epitaxial ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{8+\mathrm{\delta }}$ films with columnar defects

A continuous transition of the vortex ensemble into a Bose-glass state in epitaxial ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{8+\mathrm{\delta }}$ films with columnar defects along the c axis, induced by irradiation with 2.7 GeV ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ ions was observed. The temperature variation of the resistivity, measured with the magnetic field B=${\mathrm{\mu }}_0$H applied parallel to the c axis, fits the expression ρ(T)∼(T-${\mathit{T}}_{\mathrm{BG}}$${)}^{\nu \left(\mathit{z}\mathrm{-}2\right)}$ at low levels, with a field-independent exponent up to B≊2 T. At very low fields, the magnetic-field dependence of the Bose-glass transition temperature ${\mathit{T}}_{\mathrm{BG}}$ is in good agreement with the predictions of theory of boson localization in the presence of correlated disorder, 1/${\mathit{T}}_{\mathrm{BG}}$-1/${\mathit{T}}_{\mathit{c}0}$∼${\mathit{B}}^{1/4}$. However, for applied field values significantly larger than the dose-equivalent field ${\mathit{B}}_{\mathrm{\phi }}$=1 T, the vortex delocalization in our samples seems to proceed via melting, the magnetic-field exponent becoming very close to 1/2. The occurrence of the Bose-glass transition in the case of intrinsically very anisotropic superconductors, as ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{8+\mathrm{\delta }}$, can be understood through an increase of the tilt modulus in the vortex ensemble in the presence of correlated disorder, which promotes vortex localization.