Protected superconductivity at the boundaries of charge-density-wave domains

Solid 4He may acquire superfluid characteristics due to the frustration of the solid phase at grain boundaries. Here, introducing a negative-U generalized Hubbard model and a coarse-grained semiclassical pseudospin model, we show that an analogous effect occurs in systems with competition among charge-density-waves (CDW) and superconductivity in the presence of disorder, as cuprate or dichalcogenide superconductors. The CDW breaks apart in domains with topologically protected filamentary superconductivity at the interfaces. Our transport measurements, carried out in underdoped La2-x Sr x CuO4, with the magnetic field acting as a control parameter, are shown to be in excellent agreement with our theoretical prediction. Assuming superconductivity and CDW phases have similar energies, at intermediate temperatures, the magnetic field drives the system from a fluctuating superconductor to a CDW as expected in the clean limit. Lowering the temperature, the expected clean quantum critical point is avoided and a filamentary phase appears, analogous to 'glassy' supersolid phenomena in 4He. The transition line ends at a second quantum critical point at high-fields. Within our scenario, the filamentary superconducting phase is parasitic with CDW and bulk superconducting phases playing the role of primary competing order parameters.