Plasmon In 2D Tilted Dirac Materials

This thesis reports a research about plasmons in two dimensional(2D)tilted Dirac materials,including 2D tilted Dirac semimetals(DSM)and 2D tilted topological insulators(TI).Using the linear response theory,we calculate numerically the dielectric function of system described by the low energy effective Hamiltonian,within random phase approximation(RPA).We find that tilted energy band has a deep influence on plasmons in 2D DSM.In 2D untilted DSM,only one isotropic plasmon permitted with q1/2 law in long-wave approximation,which is the typical dispersion of plasmon in 2D metallic systems.By contrast,in 2D tilted Dirac semimetal,several anisotropic plasmons could be probed due to anisotropic Fermi surface caused by tilted energy bands.To be specific,for one thing,only one plasmon could be probed along the untilted direction of energy bands while two plasmons could be detected along the tilted direction of energy bands in 2D under-tilted DSM.And for another,three branches of plasmons could be detected along untilted direction of energy bands as well as along the over-tilted direction of energy bands in 2D over-tilted DSM.Compared with that the only one traditional q1/2-law plasmon in 2D untilted DSM,those additional plasmonic modes in 2D tilted DSM do not obey q1/2 law but linear law.In order to reveal origin of plasmons in 2D tilted DSM,and also to elucidate the difference between plasmons in 2D under-tilted DSM and plasmons in over-tilted DSM,we analyze the Fermi surface of DSM under finite n-doped case.We find that different hoping progresses in energy bands of 2D tilted DSM with distinct types of tilt determine the difference between plasmons in 2D under-tilted DSM and plasmons in over-tilted DSM,due to various Fermi surfaces provided by 2D under-tilted and over-tilted DSM.(Fermi surface in 2D under-tilted DSM is only constructed by electron pockets while it is concreted by electron and hole pockets in 2D over-tilted DSM)Furthermore,under background of the research mentioned above,we also pay attention to modulation of energy gap for plasmon in order to take a survey of plasmon in 2D tilted TI.In this work,we have a systematical understanding about plasmons in 2D tilted Dirac materials and some predictions on plasmons' detection.This work also propose an auxiliary method for distinguishing 2D over-tilted Dirac materials from the under-tilted,experimentally.