Two-dimensional superconductor-insulator transition in bulk single-crystal ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.38}$

We use a magnetic field to tune a highly anisotropic single crystal of oxygen-deficient ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ with a transition temperature of 2 K through the superconductor-insulator transition. The sheet resistance scales with temperature, 0.05≤T≤1.0 K, and field, 0≤H≤94 kOe, in a manner predicted by a theory for quantum phase transitions in disordered two-dimensional superconductors.