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Understanding the Role of Energy Bands with Dirac and Flat Dispersions and Van-Hove Singularities in Phases of Materials with Kagome Lattice

Grigorian, Vrej | 2025

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 58509 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Kargarian, Mehdi
  7. Abstract:
  8. The kagome lattice, owing to the presence of Van Hove singularities, a flat band across the entire Brillouin zone, and the existence of Dirac cones, has attracted considerable attention over the past decades. The principal reason is that upon the inclusion of interactions within such a band structure, complex phases may emerge, some of which exhibit nontrivial topological properties. The realization of these phases becomes possible when the Fermi energy lies in the vicinity of the said regions in the energy band. Under such conditions, the electronic structure develops instabilities toward superconductivity and charge ordering. Nevertheless, the identification and synthesis of materials possessing a kagome lattice structure had long remained severely limited. In recent years, however, a class of kagome-structured materials has been synthesized in various laboratories. In 2019, vanadium-based compounds with kagome structure were successfully synthesized, exhibiting quasi-two-dimensional characteristics both chemically and electronically. These materials are described by the formula AV_3 Sb_5, where A is one of the elements K , Rb , Cs. Experimental measurements indicate that these compounds remain paramagnetic even at low temperatures. The simultaneous observation of superconductivity and charge ordering has significantly intensified the interest in their study, providing the principal motivation for the present thesis. In this work, we investigate these materials within the framework of the fluctuation exchange approximation. Specifically, we attempt, by employing this approximation, to capture charge-order and superconducting phases in the two-dimensional Hubbard model. We find that in the spin and charge susceptibilities obtained from this approximation, sharp peaks appear at the nesting vectors of the Fermi surface below a critical temperature. Furthermore, we observe that, due to the intrinsic difference between the two Van Hove singularities, the transition temperature into this phase depends on the position of the Fermi level. In an additional analysis, we find that this phase does not occur in proximity to the filling fraction associated with the Dirac cones. In another part of this study, we examine the effect of the Hubbard interaction strength on this phase and observe that this interaction, as expected, enhances the separation between the two susceptibilities. Finally, our preliminary results concerning the emergence of superconductivity are also presented and discussed. Based on the limited calculations performed, we find that d_xy superconductivity is more favorable compared to the other two gap symmetries considered, namely d_(x^2-y^2 ), d+id and f_(x^3-3xy^3 ) . Collectively, these results not only provide a deeper understanding of the mechanisms underlying the stability of emergent phases in kagome materials, but also serve as a foundation for future theoretical and experimental studies in the context of superconductivity and charge ordering in two-dimensional systems
  9. Keywords:
  10. Superconductivity ; Dirac Dispersion ; Charge Order ; Kagome Lattice ; Van-Hove Singularity

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