Quantum fluctuations in charge glass manifested by the hysteresis of Hall resistivity

The Hall effect studies on the underdoped La$_{\mathrm{2-x}}$Sr$_{\mathrm{x}}$CuO$_{\mathrm{4}}$ films grown by Molecular Beam epitaxy (MBE) show dramatic hysteretic behavior at temperatures below 1.5 K, in agreement with the hypothesis that the low temperature ground state is a Coulomb glass. The fluctuations in the Hall resistivity R$_{\mathrm{H}}$ reach several hundred percent and even change the sign of R$_{\mathrm{H}}$, thus making the Hall effect measurement a very sensitive probe of the glassy state. Using a continuous doping gradient (COMBE), we scanned the dependence of R$_{\mathrm{H}}$ on the doping level x in extremely fine steps (x \textless 0.0001), in order to precisely map out the phase boundary between the charge glass state and the superconducting state.