Fluctuation Phenomena in Unconventional Superconductors

Abstract

The origin of unconventional superconductors (SC), which cannot be described by the conventional BCS theory, remains an open question that has attracted immense interest. Fluctuation phenomena provide an invaluable window to investigate the unique properties of unconventional SC and help uncover their microscopic origin. In this thesis, superconducting, magnetic, and nematic fluctuations will be studied in different regions of the phase diagrams of selected unconventional SC, namely strontium ruthenate (Sr2RuO4), nickelates, and iron pnictides. First, I will study the superconducting fluctuations and the induced diamagnetism at temperature above but close to Tc. The contribution of superconducting fluctuations to the linear susceptibility is difficult to isolate from the large normal state contribution. In contrast, a recently developed nonlinear third-harmonic response technique can probe the nonlinear magnetic susceptibility, which is dominated by contributions from superconducting fluctuations. We apply the Lawrence-Doniach phenomenological model to derive the third-harmonic magnetic response generated by superconducting fluctuations. The model successfully captures the power-law temperature dependence of this quantity observed in conventional SC, but fails to explain the data of the unconventional SC Sr2RuO4. Including Tc inhomogeneity accounts for the enlarged fluctuation range in Sr2RuO4. However, the exact temperature dependence could not be captured, suggesting effects beyond Gaussian fluctuations. Then I will investigate the magnetic-fluctuation spectrum inside the superconducting state, in particular, the spin resonance mode that is observed in the spectrum at a finite excitation energy below 2∆ and at a wavevector QAFM associated with the nearby magnetic state. The spin resonance mode is widely invoked as a strong evidence for a sign-changing gap and, by extension, magnetic fluctuation-mediated pairing. Inspired by the recent discovery of a nickelate SC, which has a less anisotropic dispersion, we investigate the robustness of the spin resonance mode in two-dimensional (2D) and three-dimensional (3D) SC with a d-wave gap by computing the RPA dynamic spin susceptibility. In 2D, we find a sharp resonance peak. In 3D, the sharpness of the peak is related to the topology of hot lines, i.e., lines of on the Fermi surface connected by QAFM. When the hot lines are closed, the resonance mode is suppressed, while when they remain open, the resonance mode persists. Finally, I will study normal state fluctuations that surround the superconducting dome. In particular, I focus on nematic fluctuations, which may promote superconducting pairing in some unconventional SC. The recently discovered 1144-iron-pnictide CaKFe4As4 displays relatively high Tc. Yet, it does not display stripe spin-density wave (SSDW) magnetic order or long-range nematic order. Instead, its phase diagram features a tetragonal-symmetric spin-vortex crystal (SVC) ground state. We employ a Ginzburg-Landau approach to calculate the nematic susceptibility of such a system. We show that when the system is close to the SVC-SSDW degeneracy point, nematic fluctuations are sizable even though there is no long-range nematic order. We also show that they are suppressed by the inequivalent As atoms above and below the iron plane, which is a property of the 1144 crystal structure. The temperature dependence of the nematic fluctuations calculated theoretically agrees qualitatively with the elastoresistivity and elastic modulus experiments, indicating closely competing SVC and SSDW states.