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Chapter 6 Sample Clauses

Chapter 6. Data presentation, analysis and discussion
Sample 1
Chapter 6. In the Sixth Chapter the discussion about the role of flat bands in mag- netic properties of 2D crystals is extended to the case of high-order van Hove singularities. As it was shown in the literature, the usual van Hove singularities lead to paramagnetic response of the system [50], the exactly flat bands in the dice lattice lead to very strong paramagnetic response [13]. The corresponding paramagnetic response is manifestedvi a Dirac delta-function shape of the orbital susceptibility as function of chemical potential. Notably, in dice lattice this paramagnetic response dominates the diamagnetic Delta-like response of Dirac cones, which was present in graphene [51]. The focus of the Chapter is concentrated on studying the role of not perfectly flat bands - high-order van Hove singulatiries, in orbital suscepti- bility. As an example, the square-octagon lattice is analyzed. Such lattice was expected to occur as a stable 2D graphene allotrope - T-graphene, [52], but now is studied in connection with transition-metal dichalcogenides [53]. The chapter contains detailed characterization of tight-binding model describing square-octagon lattice, effective models that have form of 1) relativistic pseudospin-1 type and 2) second-order that capture precisely dispersion of high-order saddle point. Based on these models it is shown that paramagnetic contribution from van Hove singularity is weaker than that of flat band. The numerical calculations of orbital susceptibility show that the para-to-diamagnetic phase transition is possible if the parameters of the system are tuned. The results on orbital susceptibility presented in the chapter show that magnetic properties of van Hove singularities of different kinds are more complicated that for exactly flat bands, and the full analysis of their role in orbital susceptibility for the novel 2D materials should be performed in future. Next follow the additional chapters that are not focused on flat bands, but are related to zero-energy modes.
Sample 1

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