THE magnetic field penetration depth lambda is a basic parameter of su
perconductivity, related to n(s)/m (superconducting carrier density/e
ffective mass) as lambda-2 is-proportional-to n(s)/m in the limit whe
re the coherence length xi is much shorter than the mean free path l (
the 'clean limit'). Muon spin relaxation (muSR) measurements1,2 of lam
bda in high-transition-temperature (high-T(c)) copper oxide supercondu
ctors have revealed remarkable correlations between T(c) and n(s)/m:
T(c) increases linearly with n(s)/m in the underdoped region, followe
d by a saturation with increasing carrier doping. Here we report muSR
measurements of lambda in ceramic specimens of the superconductor Tl2B
a2CuO6+delta (Tl-2201) in the 'overdoped' region where T(c) decreases
with increasing hole doping. Recent measurements of upper critical fie
ld and resistivity3 confirm that overdoped Tl-2201 lies well in the cl
ean limit with xi << L We find that the muon spin relaxation rate sigm
a(T --> 0) is-proportional-to lambda-2 is-proportional-to n(s)/m in T
l-2201 decreases with increasing hole doping, implying that either n(s
) no longer scales with the normal-state carrier density n(n), and/or
m for a superconducting pair becomes much larger than the value expec
ted from the normal-state effective mass m(n). This behaviour of over
doped Tl-2201 is in marked contrast to conventional metallic supercond
uctors having a retarded interaction, in which the normal-state proper
ties (n(n), m(n), l) directly represent the corresponding values in t
he superconducting state.