Resistive upper critical field of ${\mathrm{Tl}}_2$${\mathrm{Ba}}_2$${\mathrm{CuO}}_6$ at low temperatures and high magnetic fields

The resistive upper critical field of overdoped single crystals of ${\mathrm{Tl}}_2$ ${\mathrm{Ba}}_2$ ${\mathrm{CuO}}_6$ has been measured from the zero field transition temperature ${\mathit{T}}_{\mathit{c}}$(0) (approximately 20 K) to temperatures as low as 12 mK, corresponding to less than 0.001${\mathit{T}}_{\mathit{c}}$(0). In sharp contrast to the predictions of standard theories of superconductivity, the critical field is found to rise steeply with positive curvature as the temperature is reduced, and no sign of saturation is observed down to the lowest temperatures reached.