In underdoped cuprates, the relationship between the pseudogap, superconductivity, and charge and spin ordering has been of key interest. Since high magnetic fields are commonly used to suppress superconductivity and probe the nature of this unusual normal state, one of the central issues is to understand the interplay of superconductivity with charge and spin orders in the limit of high magnetic fields. This talk will describe the results of a comprehensive series of experiments using several complementary electrical transport techniques on underdoped La-214 cuprates, in which charge and spin orders appear in the form of stripes that are most pronounced for doping x~1/8. Our results a) establish a robust phase diagram for superconducting vortices in underdoped cuprates, b) provide much-needed transport signatures of the elusive pair-density wave state in the regime where superconductivity is destroyed by quantum phase fluctuations, and c) reveal striking, novel properties of the normal state of cuprates with intertwined orders. The broader relevance of our findings to cuprate physics will be also discussed.
