Quantum Monte Carlo Study On Superconducting Pairs

This thesis mainly studied the possible electron-electron induced superconductivity pairing in graphene through quantum Monte Carlo method. The author calculated the Hubbard Model on 2-dimensional honeycomb lattice graphene using an unbiased methodology, the determinant quantum Monte Carlo computational method, compared pairing susceptibility of singlet s wave pairing and d wave pairing, discussed the influences of electronic density n and next-nearest-neighbor hopping term t’over superconductivity pairing. The calculating results show that near half filling, d wave pairing dominates the instability and the next-nearest-neighbor hopping enhances s wave and d wave pairing. S wave pairing becomes the main part when t’is large and n is small.The author has used 5 chapters to describe his work. In the 1st Chapter, the introduction, the carbon-based material and its variant appliances were introduced, as well as the motivation of the author’s research. Then a detailed description of graphene’s properties, including monolayer graphene’s lattice structure, energy band structure and some of graphene’s most peculiar electronic properties in the next chapter. The 3rd Chapter focuses on the current situation in the field that the author has taken interests in, the superconductivity of graphene. Divided in three parts, study of proximity mediated superconductivity, intrinsic superconductivity and pairing symmetry of graphene valence electrons, the chapter interprets the significance of the field. Quantum Monte Carlo computational method is discussed in the 4th chapter which paves the way for the study of the subject. The 5th Chapter argues whether d wave pairing dominates in the near half filling graphene’s superconductivity, based on the calculation that is carried out by the DQMC method on the graphene model with t’ in it, and reveals the way of how t’affect the superconductivity.Believing in the future, under the development and progress of the deepening of the scientific research, the overcome of technical difficulties, broadening the range of application, the day of the coming into existence of graphene devices should not be long from now. One can look forward to this a "magic materials" in the 21st century and what kind of surprise it will bring upon mankind. In the research of the new properties of the wonder material, the quantum Monte Carlo method study of graphene’s superconducting pairing interaction shall be interesting and necessary.