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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, we show that an analogous effect occurs in systems with competition among charge-density-waves (CDWs) and superconductivity in the presence of disorder, as cuprate or dichalcogenide superconductors. The CDWs breaks apart in domains with topologically protected filamentary superconductivity (FSC) at the interfaces. Transport experiments carried out in underdoped cuprates with the magnetic field acting as a control parameter are shown to be in excellent agreement with the theoretical expectation. At high temperature and low fields we find a transition from CDWs to fluctuating superconductivity, weakly affected by disorder, while at high field and low temperature the protected filamentary superconducting phase appears in close analogy with "glassy" supersolid phenomena in 4He.