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Mott Transition in Ordered and Disordered Honeycomb Lattice Using Strong-coupling Perturbation Theory

Adibi, Elaheh | 2018

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 51313 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Jafari, Akbar
  7. Abstract:
  8. The ability to determine the nature of the low temperature state of the interacting quantum system is one of the main goals of condensed matter theory. Nevertheless, despite ongoing efforts, no single method has proved to work perfectly for interacting systems. In this thesis, we employ the strong-coupling perturbation theory which corresponds to an expansion in powers of the hopping t around the atomic limit. So, first the strong-coupling perturbation theory is introduced. Next we apply this approach to the half-filled Hubbard model on honeycomb lattice. Within this approach, we are able to obtain an analytical form for single-particle gap, extracted from density of state, as a function of interaction strength. In the presence of electron-electron interaction, the system undergoes a phase transition to the Mott insulator at critical interaction strength Uc ≈ 2.38t . Also, the half-filled ionic Hubbard model on honeycomb lattice by strong-coupling perturbation theory is studied. Owing to interplay between ionic potential ∆ and interaction U, a semimetallic phase is appeared at interaction strength U = 2∆, sandwiched between two band and Mott insulating states. We investigate the Anderson disordered Hubbard model on the honeycomb lattice by strong-coupling perturbation theory. For uniformly distributed random potential, our findings rule out the possibility of metallic phase in between the Mott and Anderson insulating phases. We therefore find a direct transition between Anderson and Mott insulator. For al- loy Hubbard model which two different atoms randomly distributed on the lattice, we found the band, Mott and Anderson insulators as well as metallic phase arising from competition between interaction and disorder
  9. Keywords:
  10. Hubbard Model ; Strongly Correlated Electron Systems ; Strong Coupling ; Mott Transition ; Honeycomb Lattice

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