Chapter 3 Sample Clauses
Chapter 3. The literature review on co-operatives
Chapter 3. In the Third Chapter the role of flat band in dynamical generation of excitonic gap is studied. Excitons are bound states of electron and holes tied by an attractive Coulomb interaction. The excitonic gap in the spec- trum appears when it is energetically favorable to create excitons out of electrons and holes that have energies close to charge-neutrality point. Experimentally and theoretically it was found that the excitonic gap is generated in multilayer graphene (see Refs.[35–44]) and the more softer dispersion is - the larger gap is generated. Such picture is in agreement with simple considerations about the role of kinetic and potential energies discussed in the Preface (1.1) of this Introduction. As the flat bands represent the most soft type of kinetic energy, it is expected that the dynamical excitonic gap generation should be favor- able. In the Chapter 3 several possible gap parameters for dice lattice are studied that satisfy symmetries and correspond to different pairings in sublattice spaces. It is shown that among several possible scenarios one dominates as energetically more favorable. The excitonic gap in such case has an intervalley type (pairing happens for quasiparticles from different valleys). For the formation of corresponding order parameter (excitonic gap) the flat band plays a role of catalyst. Similarly to chemical reac- tions, where the catalyst does not disappear during reaction but helps it to proceed more efficiently, the excitonic gap formation splits flat band into two but leaves both of them perfectly flat. But, the flat band enor- mously enhances the energy gap size. These predictions suggest that such mechanism might compete with superconductivity in flat band systems and dominate in their transport properties at intermediate temperatures leading to insulating state. In addition, it is important to underline that the type of excitonic gap that is favorable due to flat band catalysis has particular type of symmetry. In other words, not every type of excitonic order parameter is enhanced in the presence of flat band. The studies of such valley-mixing order parameters in more complicated systems such as twisted bilayer graphene are very active ongoing topic [45, 46].