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Plasmon Modes in Borophene and Graphene: Ladder Corrections

Jalali-Mola, Zahra | 2019

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 51880 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Jafari, Akbar
  7. Abstract:
  8. In this thesis, we have investigated the plasmon dispersion on the Dirac matter. The Dirac matters which we consider to this end are graphene and borophene allotrope.The borophene allotrope has smaller anisotropic Fermi velocity and tilted Dirac cone in comparison with graphene. We briefly give a short introduction to these materials and then we study the propagation of electromagnetic modes in them. We begin with graphene as a well known two dimensional Dirac material. It has been found that two kinds of plasmon modes named as plasmon mode and transverse electric filed mode are allowed to propagate in graphene but just the plasmon mode can be affected by interaction. As the correlated Hubbard interaction in graphene is big enough then the role of spin fluctuation and it is the effect on the plasmon mode will be important. Our result shows that this kind of fluctuation within fluctuation exchange approximation and using ladder diagrams causes the propagation of plasmon in undoped graphene possible and moreover put the plasmon dispersion down to lower energy. Next, in the case of tilted Dirac cone in the borophene layer we calculate the complete analytical density response function which due to the linear dispersion dependence on the direction of the wave vector, it has angular and tilt dependent characteristic. Our results show that not only plasmon mode can be affected by angular characteristic but also by increasing the tilt parameter they disperse at higher energy and the most important they show the kink in the boundary of inter-band particle hole continuum.Moreover, for a large amount of tilt parameter, another overdamped mode will appear which has linear properties and propagate in intra-band particle hole continuum.Finally, we have investigated the plasmon dispersions namely in-phase with square root dispersion and out-of-phase with linear dispersion in double layer structures of Dirac materials. Our result for double layer borophene shows that by increasing layer spacing two modes be degenerate with single layer plasmon moreover two plasmon
    modes have kink properties. Then by increasing tilt parameter, it can be seen that plasmon mode dispersion propagate at higher energy and out-of-phase mode strongly affected by decreasing density carrier in one layer in which it propagates in lower energy and in undoped case out-of-phase mode will be removed and in-phase mode will be damped totally. In addition in the case of borophene-graphene layer as a result of different Fermi velocity the damping structure will be different but two modes which are eigenstate modes of the system show kink in their dispersion. In the end, in the double layer structure, there is an overdamped mode which in the long wavelength limit has linear properties
  9. Keywords:
  10. Plasmons ; Spin Fluctuation ; Dirac Materials ; Tilted Dirac Cone ; Kinky Plasmon

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