磁场对石墨烯中弱耦合极化子性质的影响
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摘要
研究了磁场作用下石墨烯中电子与表面光学声子弱耦合情况下的极化子的性质。采用线性组合算符和Pekar变分法分别推导出了石墨烯中弱耦合极化子的基态能量E_0、第一激发态能量E_1和跃迁频率ω随磁场强度B和德拜截止波数k_d之间的变化关系。数值计算结果表明,极化子的基态能量E_0随磁场强度B变化的曲线(k_d一定时)和E_0随k_d的变化曲线(B一定时)均会分裂成对称的两条,并且当B一定时E0的绝对值随k_d的增加而增加。在k_d一定时,极化子的第一激发态能量E_1和跃迁频率ω均为磁场B的增函数;在B一定时,E_1和ω均随kd的增加而增大。
The influence of magnetic field on the polaron properties in the weak coupling of electron and surface optical phonons in monolayer graphene was investigated by using the improved linear combination operator method and the Pekar variational method. The dependences of the energies of the ground state E_0,the first excited state E_1 and the transition frequency ω of weak-coupling polaron on magnetic field B and Debye cut-off wavenumber kdwere derived. Numerical calculations show that the ground state energy E_0 of weak-coupling polaron near the Dirac point is an increasing function of strength of magnetic field B and Debye cut-off wavenumber kd,the curves of the polaron's ground state energy E_0 of weak-coupling polaron will split into two equal and opposite band; both the first excited state energy E_1 and the transition frequency ω are also an increasing function with strength of magnetic field B and Debye cutoff wavenumbers kd.
The influence of magnetic field on the polaron properties in the weak coupling of electron and surface optical phonons in monolayer graphene was investigated by using the improved linear combination operator method and the Pekar variational method. The dependences of the energies of the ground state E_0,the first excited state E_1 and the transition frequency ω of weak-coupling polaron on magnetic field B and Debye cut-off wavenumber kdwere derived. Numerical calculations show that the ground state energy E_0 of weak-coupling polaron near the Dirac point is an increasing function of strength of magnetic field B and Debye cut-off wavenumber kd,the curves of the polaron's ground state energy E_0 of weak-coupling polaron will split into two equal and opposite band; both the first excited state energy E_1 and the transition frequency ω are also an increasing function with strength of magnetic field B and Debye cutoff wavenumbers kd.
引文
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[2]HENRIKSEN E A,CADDEN Z P,JIANG Z,et al..Interaction-induced shift of the cyclotron resonance of graphene using infrared spectroscopy[J].Phys.Rev.Lett.,2010,104(6):067404.
[3]ZHAO Y,CADDEN Z P,JIANG Z,et al..Symmetry breaking in the zero-energy landau level in bilayer graphene[J].Phys.Rev.Lett.,2010,104(6):066801.
[4]WANG Z W,LI S S.Lattice relaxation of the graphene under high magnetic field[J].J.Phys.:Condens.Matter,2012,24:265302.
[5]ZHU J,BADALYAN S M,PEETERS F M.Plasmonic excitations in coulomb-coupled N-layer graphene structures[J].Phys.Rev.B,2013,87(8):085401.
[6]LI W P,WANG Z W,YIN J W.The effects of the magnetopolaron on the energy gap opening in graphene[J].J.Phys.:Condens.Matter,2012,24(13):135301-1-5.
[7]WANG Z W,LIU L,LI Z.Energy gap induced by the surface optical polaron in graphene on polar substrates[J].Appl.Phys.Lett.,2015,106(10):1016011-1-4.
[8]DING Z H,ZHAO Y,XIAO J L.The magnetic effect of polaron in monolayer graphene[J].J.Low Temp.Phys.,2016,182(5):162-169.
[9]DING Z H,ZHAO Y,XIAO J L.The properties of strong couple bound polaron in monolayer graphene[J].Superlatt.Microstruct.,2016,97:298-302.
[10]杨杨,吴丽娜,祁立娜,等.自旋对量子线中强耦合磁极化子的影响[J].内蒙古民族大学学报(自然科学版),2014,29(1):7-10.YANG Y,WU L N,QI L N,et al..Effect of spin of strong-coupled magnetopolaron in quantum wire[J].J.Inner Mongolia Univ.Nation.,2014,29(1):7-10.(in Chinese)
[11]FUCHS J N,LEDER P.Spontaneous parity breaking of graphene in the quantum Hall regime[J].Phys.Rev.Lett.,2007,98(1):016803.
[12]LI W P,WANG Z W,YIN J W.The effects of the magnetopolaron on the energy gap opening in graphene[J].J.Phys.:Condens.Matter,2012,24(13):135301-135305.
[13]HUYBRECHTS W J.Internal excited state of the optical polaron[J].J.Phys.C:Solid State Phys.,1977,10(19):3761-3768.
[14]LEE T D,LOW F E,PINES D.The motion of slow electrons in a polar crystal[J].Phys.Rev.,1953,90(2):297-302.
[15]VILJAS J K,HEIKKILA T T.Electron-phonon heat transfer in monolayer and bilayer graphene[J].Phys.Rev.B,2010,81(24):245404.
[16]MILLER D L,KUBISTA K D,RUTTER G M,et al..Observing the quantization of zero mass carriers in graphene[J].Sci.Mag.,2009,324(5929):924-927.