Mapping the Striped Phase Diagram of La$_{2-x}$Ba$_x$CuO$_4$ with Resistance Fluctuation Spectroscopy*

La$_{2-x}$Ba$_x$CuO$_4$ (LBCO) is an exceptional high-temperature superconductor in which, near x=1/8 doping, superconductivity is suppressed and `striped' charge order emerges. The charge stripes cause short-range conductance anisotropy that may be observed as fluctuations in resistance. In thin film LBCO devices grown by pulsed laser deposition, we measure time-resolved resistance as a function of bias current, temperature, and doping. As is consistent with charge stripes, the resistance noise exhibits a critical onset temperature and suppression at high currents. Combining resistance fluctuation spectroscopy with combinatorial laser deposition techniques, we are able to tune the doping of of LBCO and map its phase diagram.