The Hubbard model has been investigated widely by many authors, while this work may be new in two aspects.One, we focus on the possible effects of the positions of the gaps associated with the pairing and the spin density wave. Two, we suggest that the models with different parameters are appropriate for different materials (or a material in different doped regions). This will lead to some new insights into the high temperature superconductors. It is shown that the SDW can appear at some temperature region when the on-site Coulomb interaction is larger, while the SC requires a decreased U at a lower temperature. This can qualitatively explain the relationship between superconducting and pseudogap states of Cu-based superconductors in underdoped and optimally doped regions. The superinsulator is also discussed. 75.30.Fv, 74.20.Rp, 74.20.-z 2 quasiparticles could not be defined around the Fermi level for k Δ ≠0, the Fermi surface is broken. In this case, we say that the gap occupies the Fermi level. We think that the position of a gap is the key to understand the high temperature superconductivity, and how and why the pairing gap varies in a material has to be investigated. This investigation will reveal that there should be a crossover from the SDW dominated pseudogap to the SC state in Cu-based superconductors when they develop from the underdoped region to the optimally doped region or from the high temperature range to the low temperature range, and the possible existence of a critical point [9] is also supported by this investigation.
PACS:
Calculations and resultsLet us first discuss the model parameters. Although one expects that the properties of high temperature superconductors may be included in a model with the fixed parameters, the electronic structures of these materials must be changed with doping, and then the model parameters should be changed with doping. In the Hubbard model to describe the physics of materials, the hopping matrix element t will decrease with the increase of U when the electrons (holes) tend toward being localized, and this can be found in the derivations of a Hamiltonian. Thus a large U model (or the t-j model) should be used to describe antiferromagnetic insulator, and we will not discuss this case. When we consider a metal, U should be not too large (although the non-half-filled large-U model includes the metal), in this case, other interactions should be considered also.However, we will qualitatively model some high temperature superconductors, the Hubbard model (U>0) is still considered, other interactions are neglected, and the Hubbard model can be written in
Considering the electron states inside and outside the solid, we derive a formula of photoemission intensity. A general theoretical way to determine electronic structures of solids from ARPES experiments is outlined. It is shown that the spectral function inside the solids cannot be measured directly by ARPES, the effects of free electron states on the electronic structure observed by ARPES measurements must be considered, and the results from ARPES experiments cannot be understood until these results have been made consistent with a theoretical calculation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.