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Superconductivity in the Presence of Repulsive Interaction in Lattice Models

Mahdaei, Hossein | 2025

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 58413 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Vaezi, Mir Abolhassan
  7. Abstract:
  8. This thesis investigates superconductivity generated by the Kohn–Luttinger mechanism in a model defined on a two-dimensional square lattice. The model allows for several band dispersions and includes onsite Hubbard and nearest-neighbor density–density interactions. We analyze the system using a perturbative renormalization-group approach. We begin by summarizing the basic features of conventional and unconventional superconductors. We then examine the Cooper instability, the generic weak-coupling instability of a Fermi liquid and the basis of BCS theory for conventional superconductivity. Next, we present the renormalization-group framework as a general tool for describing phase instabilities in Fermi liquids. We first study the Kohn–Luttinger mechanism in a three-dimensional free Fermi gas with spherical symmetry, analyzing the resulting RG flow equations via a sphericalharmonic decomposition. In line with the original work of Kohn and Luttinger, the presence of a well-defined Fermi surface and spherical symmetry is essential in this limit. We then extend the analysis to systems with reduced symmetry, in particular those lacking full rotational invariance. Using group-theoretical methods, we derive the irreducible representations and basis functions of the point group C4v, which allows us to classify pairing channels and investigate the emergence of superconductivity across them
  9. Keywords:
  10. Superconductivity ; Renormalization Group ; Instability ; Landau Fermi Liquid ; Repulsive Interactions ; Kohn-Luttinger Mechanism

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