Spin Dynamics In Cuprates

High-temperature superconductivity is one of the most challenging topics in con-densed matter physics. Much progresses had been made since its discovery. However, some fundamental issues including the anomalous linear temperature dependence of resistance in the normal state, the origin of pseudogap and its relationship with su-perconductivity and the mechanism of superconductivity, remain unclear. Supercon-ductivity arises from doping into the parent compounds which exhibit the long-range antiferromagnetic order. Due to the proximity of antiferromagnetism and superconduc-tivity, it is generally believed there exists an intrinsic link between these two phases. The investigation on the spin dynamics in cuprates will shed light on the mechanism of high-temperature superconductivity. The dissertation consists of five chapters:In chapter one, a brief review of high-temperature superconductivity is presented, including the history of high-temperature superconductivity, the main experimental techniques, the exotic properties and some proposed theories.In chapter two, the spin dynamics in the underdoped cuprates is investigated based on a recently proposed effective Hamiltonian, which provides a possible origin of pseu-dogap. The theoretical results are in qualitative agreement with the experimental data both in the pseudogap and superconducting state. The well known’hourglass’disper-sion of magnetic excitation(ME) around (π,π) detected by inelastic neutron scattering (INS) is well established. We illustrate that ME in the underdoped cuprates originates from pseudogap rather than superconductivity. This is distinct from the previous d-wave based theories. The weak temperature dependence of ME across Tc is a natural result of our theory. Furthermore, the MEs around (0,0) exhibit magnon-like disper-sion, qualitatively consisting with the resonant inelastic X-ray scattering(RIXS) obser-vation. The magnon-like dispersion consists of two branches, which is an fingerprint of our theory.In chapter three, the commensurate magnetic excitations in the electron-doped cuprates around optimal doping are studied. Based on the spin density wave(SDW) de-scription, we clearly demonstrate that the commensurate ME originates from the band splitting and the Fermi surface topology, and is not directly related to superconductiv-ity. Therefore, the commensurate ME is a normal state behavior. The unconventional commensurate ME in the electron-doped cuprates can still be understood within the fermiology framework. Furthermore, based on the random phase approximation treat-ment of the spin susceptibility, we illustrate that the goldstone mode still exists in the coexistence of antiferromagnetism and superconductivity.In chapter four, based on the SDW description, we investigate the scaling between the superconducting resonant energy Eres and the superconducting gap△. A universal scaling with the ratio Eres/(2△)～0.6is revealed in the condition of the standard d-wave symmetry, which is well consistent with the INS and STM data. We numerically show that the ratio is not sensitive to the selected parameters, reflecting the intrinsic na-ture of the d-wave superconductivity. The other possible pairing symmetry are further checked. For the on-site s-wave pairing, there exists no superconducting resonance, attributing to the absence of the sign reversal of the superconducting gaps. For the ex-tended s-wave pairing, the superconducting resonance is absent due to the vanishing of the gap function on the electron-pocket. For the nonmonotonic d-wave pairing, a scaling between Eres and△emerges, however the corresponding ratio is much larger than the experimental data. In this sense, we have proposed a feasible way to judge the pairing symmetry of superconductors by means of INS measurements. Moreover, our theoretical results manifest that the pairing symmetry in the electron-doped cuprates remains the simple d-wave.The summary is made in the last chapter, together with some outlook for future studies.