  A low-frequency resistance noise study in highly underdoped thick films of
La$_{2-x}$Sr$_{x}$CuO$_{4}$ ($x=0.07$ and 0.08) reveals slow, correlated
dynamics and breaking of ergodicity near the superconducting transition of the
Berezinskii-Kosterlitz-Thouless type. The observed correlated behavior is
strongly suppressed by disorder.
