The Properties Of Polaron State In Momolayer Graphene

Using the method of combining the linear combination operator,the Lee–Low–Pines(LLP)transformation,variational method and Pekar variational method to research the properties of stong-coupling polaron,weak-coupling polaron,strong-coupiling bound polaron and weak-coupling bound polaron in momolayer graphene at the limiting low temperature.The mainly results are:Firstly,by using linear combination operator and Pekar variational method,the relations of between the ground state energy,the first exited state energy and magnetic field strength,Debye cut-off wavenumbers are studied in the case of considering the el-ectron-surface acoustic phonon(SA)strong coupling system.The calculations indicate that Polaron ground-state energy and the magnetic field strength increase with increasing debye cut-off wave number,the ground-state energy of the polaron near the Dirac point will be split into two large reverse band;the first excited state energy increase with increasing the magnetic field strength and debye cut-off wave Numbers of logarithmic.Secondly,in the case of considering electron-SA weak-coupling system,the LLP transformation method and pekar variational method are used to study the relation between the ground state energy,the first exited state energy of the polaron and magnetic field strength,debye cut-off wave number in the monolayer graphene.Calculations show that the the energy of the ground state and the first exited state is an increasing function with magnetic field strength and logarithm of debey cut-off wave numbers,meanwhile,near the Dirac point the ground state energy is splitted into two big reverse energy band,and the value of these energy is agreement with the result of weak-coupling case,which can also prove that the ground state energy has no obvious relationship with coupling strength.Thirdly,on the basis of the research about weak coupling properties in the monolayer graphene,linear combination operator and LLP transformation method are applied to study the properties of the strong coupling polaron in the case of considering coulomb interaction,and the relationship of the ground state energy and the magnetic field strength,the coulomb bound potential,the cut-off wave number,the distance of single layer graphene and the four different substrates.The numerical calculations indicate that the ground state energy and the energy of the first excited state will increase with increasing of magnetic field strength and the coulomb bound potential,and the ground state energy will increase with increasing of the cut-off wave number untile eventually reaches a stable value,while the first excited state energy will increase with the increasing of the cut-off wave number first,then reduce with the increasing of the cut-off wave number and eventually reach a stable value.Both the ground state energy and the energy of the first excited state will reduce with the increasing of the distance between the graphene and three different substrates.Meanwhile near the Dirac point the ground state energy will still split into two large reverse band,but the energy of the first exited state will not.Fourthly,under considering the coulomb interaction the properties of the weak coupling polaron are researched by using Pekar variational method and LLP transformation.The variable relationships of the ground-state energy with the magnetic field strength,the coulomb bound potential,the cut-off wave number,the distances of between the graphene and three different substrates are calculated.The results show the ground state energy and the energy of the first excited state will increase with increasing of magnetic field strength and the coulomb bound potential,and the ground state energy will increase with increasing of the cut-off wave number untile eventually reaches a stable value,while the first excited state energy will increase with the increasing of the cut-off wave number,then reduce with the increasing of the cut-off wave number and eventually reach a stable value.Both the ground state energy and the energy of the first excited state will reduce with the increasing of the distance between the graphene and three different substrates.Meanwhile near the Dirac point the ground state energy will still split into two large reverse band,but the energy of the first exited state will not.