Finite Temperature Mean-Field Theory Of The Interaction Induced Band Gap Of The Trilayer Graphene

Because of the novel properties of the electricity,optics,thermal physics and mechanics,the graphene has drawn great research interest in last decade.The band gap of the monolayer graphene is zero which limit its application.The theoretical calculation shows that the interaction will induce a gap of the multilayer graphene energy band.Recently,the research of the band gap of the multilayer graphene has attracted much more attention.Experiment shows that the band gap of the multilayer graphene decreases when increasing the temperature.The band gap will close completely when the temperature approaches to a critical value.However,at finite temperature the theoretical researchers have no yet considered the band gap of the multilayer graphene.In this thesis,we use mean-field method to calculate the change of the band gap of the trilayer graphene at the finite temperature based on the Hubbard model.We first determine the value of Hubbard U of the system based on the experimentally obtained the band gap at low temperature.Then,using the determined Hubbard U,we calculate the band gap of the multilayer graphene at different temperature.The trend of our calculation result is consistent with the experiment.That is,as the temperature increase,the band gap decrease.Subsequently,we compare the critical temperature which was obtained by the experiments,the first principles and the mean-field theory.We find the critical temperature is different from the experiment,but it is basically consistent with the results of the first principle calculation.We think that the qualitative difference between the experiment and the theory(our result and the result of the first principles calculation)is due to practical factors such as impurity or nonuniform potential distribution in the experiment,and these factors are not reflected in the theoretical model.Subsequently,We also calculated the critical doping that closes the band gap of the trilayer graphene at zero temperate,and our results are consistent with the experiment in the order of magnitude.The calculation results in this thesis improve the theoretical understanding of the ground state of the multilayer graphene,and point out the inconsistency between the experiment and the existing theory.Besides,our work points out the direction for further experimental and theoretical research.