Resistive upper critical field of thin films of underdoped ${\mathrm{YBa}}_2$(${\mathrm{Cu}}_{0.97}$${\mathrm{Zn}}_{0.03}$${)}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$

We report measurements of the magnetic-field dependence of the superconducting transitions of a series of underdoped ${\mathrm{YBa}}_2$(${\mathrm{Cu}}_{0.97}$ ${\mathrm{Zn}}_{0.03}$ ${)}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ thin films with transition temperatures (${\mathit{T}}_{\mathit{c}}$) of 9.4, 12.5, 23, and 56.5 K. The ab-plane resistivity was measured in magnetic fields of up to 21 T applied both parallel and perpendicular to the c axis, at temperatures between 1.5 and 100 K, and for one sample down to 50 mK in fields of up to 16 T. The resistive critical field shows strong positive curvature all the way down to 0.006${\mathit{T}}_{\mathit{c}}$, similar to that observed previously for overdoped ${\mathrm{Tl}}_2$ ${\mathrm{Ba}}_2$ ${\mathrm{CuO}}_{6+\mathrm{\delta }}$ single crystals.