Unveiling the phase diagram of a striped cuprate at high magnetic fields: Hidden order of Cooper pairs

Abstract

The interplay of charge orders with superconductivity in underdoped cuprates at high magnetic fields ($H$) is an open question, and even the value of the upper critical field ($H_{c2}$), a measure of the strength of superconductivity, has been the subject of a long-term debate. We combined three complementary transport techniques on underdoped La$_{1.8-x}$Eu$_{0.2}$Sr$_{x}$CuO$_{4}$ with a "striped" charge order and a low $H=0$ transition temperature $T_{c}^{0}$, to establish the $T-H$ phase diagram and reveal the ground states in CuO$_2$ planes: a superconductor, a wide regime of superconducting phase fluctuations (i.e. a vortex liquid), and a high-field normal state. The relatively high $H_{c2}$ is consistent with the opening of a superconducting gap above $T_{c}^{0}$, but only at $T\sim (2$-$3)T_{c}^{0}$, an order of magnitude below the pseudogap temperature. Within the vortex liquid, an unanticipated, insulatinglike region, but with strong superconducting correlations, begins to emerge already at $T\lesssim T_{c}^{0}$. The results suggest that the presence of stripes plays a crucial role in the freezing of Cooper pairs in this novel state. Our findings provide a fresh perspective on the pairing strength in underdoped cuprates, and introduce a new avenue for exploring the interplay of various orders.