RESISTIVE UPPER CRITICAL-FIELD OF SINGLE-CRYSTALS OF TL2BA2CUO6

We have measured the resistive upper critical field of overdoped singl e crystals of Tl2Ba2CuO6 from the zero-field transition temperature T( c) (approximately 20 K) to temperatures as low as 12 mK, corresponding to less than 0.001 T(c). In sharp contrast to the predictions of stan dard theories of superconductivity, the critical field is found to ris e steeply with positive curvature as the temperature is reduced, and n o sign of saturation is observed down to the lowest temperatures reach ed.