锂的卤化物LiX(X=F,Cl,Br,I)的镜像势态
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摘要
基于局域密度近似的密度泛函理论,运用多体摄动理论的GW近似,计算了碱金属锂的卤族化合物LiF (001)-(1X1)、LiCl (001)-(1X1)、LiBr (001)-(1X1)、LiI (001)-(1X1)表面的准粒子能带结构.GW近似改进了密度泛函理论对于电子交换关联的处理,计算出的带隙与实验值吻合.由GW近似计算得出的LiF、LiCl和LiBr的(001)表面能带具有负亲和能,由于绝缘体表面外真空中电子与绝缘体表面极化电荷的相互作用,在真空中产生了镜像势态.利用GW近似研究了镜像势态波函数沿表面法线方向的分布,并将由GW近似计算得到的镜像势态的单粒子势能与经典的镜像势能进行了比较.但是,从GW近似给出的表面能带结构可看出,LiI(001)表面具有正亲和能,因而不存在镜像势态.
Based on density functional theory concerning the local-density approximation(LDA), the multiplebody perturbation theory regarding the GW approximation(GWA) is used to calculate the band structures for the surfaces of alkali metal halides including LiF(001)-(1X1), LiCl(001)-(1X1), LiBr(001)-(1X1) and LiI(001)-(1X1). Since the GWA improves the electronic exchange-correlation within the LDA, the obtained GWA band gaps are in good agreement with the corresponding experimental results. It is found that the surface of LiF(001)-(1X1), LiCl(001)-(1X1), and LiBr(001)-(1X1) has negative electron affinity, and the image-potential state exists in the vacuum outside the surface, which results from the electrostatic interaction between an electron outside the surface and the polarizability in the insulator. The distributions of the wave functions for the image-potential states along the directions perpendicular to the surfaces are investigated, and the calculated local potentials using the GWA are compared with the corresponding classical image potentials. It is worth noting that since LiI(001) is not a negative electron affinity surface, there is no image-potential state existing in the vacuum outside the LiI(001) surface.
Based on density functional theory concerning the local-density approximation(LDA), the multiplebody perturbation theory regarding the GW approximation(GWA) is used to calculate the band structures for the surfaces of alkali metal halides including LiF(001)-(1X1), LiCl(001)-(1X1), LiBr(001)-(1X1) and LiI(001)-(1X1). Since the GWA improves the electronic exchange-correlation within the LDA, the obtained GWA band gaps are in good agreement with the corresponding experimental results. It is found that the surface of LiF(001)-(1X1), LiCl(001)-(1X1), and LiBr(001)-(1X1) has negative electron affinity, and the image-potential state exists in the vacuum outside the surface, which results from the electrostatic interaction between an electron outside the surface and the polarizability in the insulator. The distributions of the wave functions for the image-potential states along the directions perpendicular to the surfaces are investigated, and the calculated local potentials using the GWA are compared with the corresponding classical image potentials. It is worth noting that since LiI(001) is not a negative electron affinity surface, there is no image-potential state existing in the vacuum outside the LiI(001) surface.
引文
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[37]Aguado A,Lopez J M,Alonso T A,et al.Calculation of the band gap energy of ionic crystals[J].Revista Mexicana de Fisica,1998,44:550-558.
[2]Shockley W.On the surface states associated with a periodic potential[J].Physical Review,1939,56:317-323.
[3]Cole M,Cohen M H.Image-potential-induced surface bands in insulators[J].Physical Review Letters,1969,23:1238-1241.
[4]Echenique P M,Pendry J B.The existence and detection of Rydberg states at surfaces[J].Journal of Physics C,1978,11:2065-2075.
[5]Giesen K,Hage F,Himpsel F J,et al.Two-photon photoemission via image-potential states[J].Physical Review Letters,1985,55:300-303.
[6]H?fer U,Shumay I L,Reu?C,et al.Time-resolved coherent photoelectron spectroscopy of quantized electronic states on metal surfaces[J].Science,1997,277:1480-1482.
[7]Smith N V.Inverse photoemission[J].Reports on Progress in Physics,1988,51:1227-1294.
[8]Jung T,Mo Y W,Himpsel F J.Identification of metals in scanning tunneling microscopy via image states[J].Physical Review Letters,1995,74:1641-1644.
[9]Ruffieux P,A?t-Mansour K,Bendounan A,et al.Mapping the electronic surfaces potential of nanostructured surfaces[J/OL].Physical Review Letters,2009,102:086807[2017-07-13].https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.102.086807.
[10]Bobrov K,Mayne A,Dujardin G.Atomic-scale imaging of insulating diamond through resonant electron injection[J].Nature,2001,413:616-619.
[11]Platzman P,Dykman M.Spontaneous bubble domain formation in a Laye red ferromagnetic crystal[J].Science,1999,284:1967-1969.
[12]Schouteden K,Van Haesendonck C.Quantum confinement of hot image-potential states electrons[J/OL].Physical Review Letters,2009,103:266805[2017-12-05].https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.103.266805.
[13]Pascual J I,Corriol C,Ceballos G,et al.Role of the electric field in surface electron dynamics above the vacuum level[J/OL].Physical Review B,2007,75:165326[2018-01-21].https://journals.aps.org/prb/abstract/10.1103/PhysRevB.75.165326.
[14]Zhang H,Hu H,Pan Y,et al.Graphene based quantum dots[J/OL].Journal of Physics:Condensed Matter,2010,22:302001[2018-03-16].https://iopscience.iop.org/article/10.1088/0953-8984/22/30/302001/pdf.
[15]Manghi F,Perfetti P,Reihl B.Experimental and theoretical evidence of image states at semiconductor surface:the case of GaP(110)[J].Solid State Communication,1990,76:1371-1373.
[16]Rohlfing M,Wang N P,Krüger P,et al.Image states at insulator surface with negative electron affinity[J/OL].Physical Review Letters,2003,91:256802[2018-04-22].https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.91.256802.
[17]Baumeier B,Krüger P,Pollmann J.Bulk and surface electronic structures of alkaline-earth metal oxides:Bound surface and image-potential states from first principles[J/OL].Physical Review B,2007,76:205404[2018-03-16].https://journals.aps.org/prb/abstract/10.1103/PhysRevB.76.205404.
[18]Mabuchi T,Watanabe H,Onaka R.Surface phonons of Na F and LiF films[J].Journal of the Physical Society of Japan,1987,56:2124-2135.
[19]Chulkov E V,Silkin V M,Echenique P M.Image potential states on lithium,copper and silver surfaces[J].Surface Science,1997,391:L1217-L1223.
[20]Chulkov E V,Silkin V M,Echenique P M.Image potential states on metal surfaces:Binding energies and wave functions[J].Surface Science,1999,437:330-352.
[21]White I D,Needs R J,Rieger M M,et al.Dynamic image potential at an Al(111)surface[J].Physical Review Letters,1998,80:4265-4268.
[22]Kohn W,Sham L J.Self-consistent equations including exchange and corelation effects[J].Physical Review,1965,140:A1133-A1138.
[23]Ceperley D M,Alder B I.Ground state of the electron gas by a stochastic method[J].Physical Review Letters,1980,45:566-569.
[24]Bachelet G B,Hamann D R,Schlüter M.Pseudopotentials that work:From H to Pu[J].Physical Review B,1982,26:4199-4228.
[25]Hamann D R.Generalized norm-conserving pseudopotential[J].Physical Review B,1989,40:2980-2987.
[26]Rohlfing M,Krüger P,Pollmann J.Efficient scheme for GW quasiparticle band-structure calculations with applications[J].Physical Review B,1995,52:1905-1917.
[27]Hedin L.New method for calculating the one-particle Green’s function with application to the electron-gas problem[J].Physical Review,1965,139:A796-A823.
[28]Hedin L,Lundqvist S.Effects of Electron-Electron and Electron-Phonon Interactions on the One-Electron States of Solids[M]//Seitz F,Turnbull D,Ehrenreich H.Solid State Physics:Advances in Research and Application.New York:Academic,1969:1.
[29]Rohlfing M,Krüger P,Pollmann J.Quasiparticle bandstructure calculations for C,Si,Ge,GaAs,and SiC using Gaussian-orbital basis sets[J].Physical Review B,1993,48:17791-17805.
[30]Jiang Y F,Wang N P,Rohlfing M.Electronic excitations of bulk LiCl from many-body perturbation theory[J/OL].The Journal of Chemical Physics,2013,139:214710[2018-05-08].https://doi.org/10.1063/1.4835695.
[31]Hybertsen M S,Louie S G.Model dielectric matrices for quasiparticle self-energy calculation[J].Physical Review B,1988,37:2733-2736.
[32]Landau L D,Lifshitz E M.Electrodynamics-of-ContinuousMedia[M].London:Pergamon Press,1960:40.
[33]Rohlfing M.The GW calculation code[Z].Münster:Universit?t Münster,2004.
[34]Gopikrishnan C R,Jose D,Datta A.Electronic structure,lattice energies and Born exponents for alkali halides from first principles[J/OL].AIP Advances,2012,2:012131[2018-06-14].https://doi.org/10.1063/1.3684608.
[35]Piacentini M,Lynch D W,Olson C G.Thermoreflectance of LiF between 12 and 30 eV[J].Physical Review B,1976,13:5530-5543.
[36]Pemmaraju C D,Archer T,Sanvito S,et al.Atomicorbital-based approximate self-interaction correction scheme for molecules and solids[J/OL].Physical Review B,2007,75:045101[2018-07-20].https://journals.aps.org/prb/abstract/10.1103/PhysRevB.75.045101.
[37]Aguado A,Lopez J M,Alonso T A,et al.Calculation of the band gap energy of ionic crystals[J].Revista Mexicana de Fisica,1998,44:550-558.