Fluctuating superconductivity and pair-density wave order in the cuprate superconductors

Abstract

High-temperature superconductors are some of nature’s most enigmatic materials. Besides carrying a supercurrent, these materials manifest a range of electronic and structural orders. A state of modulated superconductivity, called a pair-density wave (PDW), has been suggested to occur in copper-based (cuprate) high-temperature superconductors, with the possibility of explaining these various orders, and perhaps even superconductivity itself. This thesis is based upon four appended papers and concerns the nature of the PDWstate and the cuprate superconductors. In the first two papers, we consider a so-called pair-hopping interaction that can stabilize a (mean-field) PDWstate. In the first paper, we use this interaction to study the supercurrent carried by a PDW state, which, due to it being a multiplecomponent order, can lead to phase-separation and additional symmetry breaking. In the second paper, we study the competition between a PDWstate and an ordinary uniform superconducting state in the context of a BCS-BEC crossover. We find a suppressed superfluid stiffness in the vicinity of a PDWinstability, with implications on the nature of the underdoped cuprates. The third paper includes an experimental study on thin films of La_2-x Sr_xCuO_4, which above Tc develops a highly anisotropic resistive response, especially pronounced for underdoped samples, pointing towards an exotic pseudogap phase in the underdoped cuprates with quasi-1D phase superfluid stiffness. We interpret these results in terms of nematic order manifested in the superconducting fluctuations. In the last paper of this thesis, we consider a scenario where the cuprate pseudogap phase consists of a thermally disorder PDW state with vestigial order. We show that a vestigial PDWnematic order coexisting with a uniformsuperconducting order yields an anisotropic superconductor on a formconsistent with the fluctuations seen in La_2-x Sr_xCuO_4. Finally, in addition to providing background for the appended papers, this thesis contains an introduction to the general phenomenology of the cuprate superconductors.