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We report a study of the basal-plane anisotropy of the superfluid density inunderdoped YBa$_{2}$Cu$_{4}$O$_{8}$ (Y124), showing the effects of both theCuO$_{2}$ planes and the fully occupied CuO chains. From small-angle neutronscattering measurements of the vortex lattice, we can infer the superconducting(SC) properties for a temperature ($T$) range $T=$ 1.5 K to $T_{\rm c}$ andmagnetic induction $B$ from 0.1 to 6 T. We find that the superfluid densityalong \textbf{a} has a simple $d$-wave T-dependence. However, along \textbf{b}(the chain direction) the superfluid density falls much more rapidly with $T$and also with increasing field. This strongly suggests the suppression ofproximity-effect induced superconductivity in the CuO chains. In addition, ourresults do not support a common framework for the low field in-plane SCresponse in Y124 and related YBa$_{2}$Cu$_{3}$O$_{7}$, and also indicate thatany magnetic field-induced charge-density-wave order in Y124 exists only forfields above 6 T.

physical review. b, condensed matter and materials physics

Magnetic field-dependence of the basal-plane superconducting anisotropy  in YBa2Cu4O8 from small-angle neutron scattering measurements of the vortex  lattice