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In complex transition metal oxides (TMO) an arrested electronic phaseseparation (PS) appears by tuning the system near a Lifshitz transition inmultiband Hubbard models. The PS in La2CuO4+y near insulator to metaltransition (IMT) is made of short range Charge Density Wave (CDW) orderinhomogeneity coexisting with quenched lattice disorder. While at high dopingy=0.1 percolation gives a single superconducting phase, near the IMT at y=0.06two coexisting superconducting phases appear: the first one with a criticaltemperature Tc1=16 K and the second one with Tc2=29K. It is known that the twosuperconducting phases are characterized by two different space geometrybecause of two different spatial distributions of both CDW order and dopantsself-organization. Here we show that these two phases show different fluxdynamic regimes using alternating current (AC) multi-harmonic susceptibilityexperiments. This is a unique technique capable to investigate multi-phasesuperconductors and characterize their transport properties in a percolativescenario. Results point out that the low critical temperature phase is welldescribed by a bulk-like flux pinning with a 2D geometry while the phase withhigher critical temperature shows a barrier pinning mechanism providing directevidence of two different superconducting vortex dynamics in different complexgeometrical spaces.

The flux dynamics behavior of the two competing high temperature superconducting phases in underdoped LaCuO4.06