The coexisting of insulating and metallic/superconducting phases and their competing effects in various underdoped cuprates

We show that the unconventional electron-phonon interactions and polaronic effects, charge inhomogeneity and charge ordering in underdoped cuprates result in the nanoscale phase separation and the occurrence of competing and coexisting of insulating and metallic/superconducting phases. We identify possible types of localized and mobile charge carriers in these systems, which segregate into insulating (carrier-poor) and metallic/superconducting (carrier-rich) regions as a result of their specific ordering. We found that the coexistence of two competing insulating and metallic phases can persist in the lightly doped cuprates on a local scale, while the coexistence of three competing insulating, metallic and superconducting phases is expected in the underdoped cuprates on a global scale. We demonstrated that the competing effects of these coexisting insulating and metallic/superconducting phases are manifested in the unusual temperature dependences of the magnetic susceptibility and resistivity and in the suppression of superconductivity in various underdoped cuprates.