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考虑到原子的非简谐振动和电子-声子相互作用，建立了金属基外延石墨烯的物理模型，用固体物理理论和方法，得到金属基外延石墨烯的电导率和费米速度随温度变化的解析式.以碱金属基底为例，探讨了基底材料和非简谐振动对外延石墨烯电导率和费米速度的影响.结果表明：1）零温情况下，碱金属基外延石墨烯的电导率和费米速度均随基底元素原子序数的增大而增大；2）外延石墨烯的电导率随温度升高而减小，其中，温度较低时时变化较快，而温度较高时则变化很慢，费米速度随温度升高而增大，其变化率随基底材料原子序数的增大而增大；3）原子非简谐振动对外延石墨烯的电导率和费米速度有重要的影响，简谐近似下，费米速度为常数，电导率的温度变化率较大；考虑到原子非简谐项后，费米速度随温度升高而增大，电导率的温度变化率减小；温度愈高，原子振动的非简谐效应愈明显.The atomic anharmonic vibration and the electron-phonon interaction are considered, and then a physical model about the metal-based epitaxial graphene is built. Variations of the electrical conductivity and the Fermi velocity with temperature for the metal-based epitaxial graphene are given based on the solid state physics theory or method. The alkali-metal epitaxial graphene is selected as the substrate, and then the influences of substrate material, electron-phonon interaction and the anharmonic vibration on the electrical conductivity and the Fermi velocity of epitaxial graphene are discussed. Some results are shown as follows. Firstly, at zero temperature, the electrical conductivity and the Fermi velocity of the alkali-metal-base epitaxial graphene increase with the number of the atoms in substrate material increasing. Secondly, the electrical conductivity of epitaxial graphene decreases with temperature rising. Furthermore, the variation rate also decreases with temperature rising. Generally, the electrical conductivity originates mainly from electrons and phones. The electronic contribution to the electrical conductivity varies with temperature slowly, but the phone contribution to electrical conductivity varies with temperature evidently. Therefore, the contribution of phonons to electrical conductivity is much larger than that of electrons. Furthermore, the contribution increases with the number of atoms in basal elements. The phonon contribution to conductivity decreases with temperature rising, but it is unrelated to the basal elements. Thirdly, the Fermi velocity of the epitaxial graphene increases with temperature slowly. The variation of the Fermi velocity with temperature decreases with the increase of interaction between the graphene and the basal atoms. However, it increases with the number of atoms of the basal materials. The anharmonic effect causes important influences on the electrical conductivity and the Fermi velocity. Under the harmonic approximation the velocity is constant. However, the conductance increases rapidly with temperature. With considering the atomic anharmonic terms, the Fermi velocity increases with temperature. The variation of the electrical conductivity with temperature increasing becomes slower. If the temperature is higher, the anharmonic effects become more evident.
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Keywords:
- epitaxial graphene /
- anharmonic vibration /
- electrical conductivity /
- Fermi velocity
[1] Davydov S Yu 2013 Phys. Stat. Sol. 55 813 （in Russian)
[2] Tian W, Yuan P F, Yu Z L 2015 Acta Phys. Sin. 64 046102 （in Chinese)[田文, 袁鹏飞, 禹卓良2015 64 046102]
[3] Wei C, Li J, Liu Q B, Cai S J, Feng Z H 2015 Acta Phys. Sin. 64 038102 （in Chinese)[蔚翠, 李佳, 刘庆彬, 蔡树均, 冯值红2015 64 038102]
[4] Tang J, Liu Z L, Kang C Y, Yan W S, Xu P S, Pan H B, Wei S Q, Gao Y Q, Xu X G 2010 Acta Phys.-Chim. Sin. 26 253 （in Chinese)[唐军, 刘忠良, 康朝阳, 闫文盛, 徐彭寿, 潘海斌, 韦世强, 高压强, 徐现刚2010物理化学学报26 253]
[5] Davydov S Yu 2012 Phys. Stat. Sol. 54 821(in Russian)
[6] Wang L, Tian L H, Wei G D, Gao F M, Zheng J J, Yang W Y 2011 J. Inorganic Mater. 26 1009 （in Chinese)[王霖, 田林海, 尉国栋, 高凤梅, 郑金桔, 杨为佑2011无机材料学报26 1009]
[7] Tetlow H, Posthuma de Boer J, Ford I J, Vvedensky D D, Coraux J, Kantorovich L 2014 Phys. Reports 542 195
[8] Grneis A 2013 J. Phys.:Condens. Matter 25 043001
[9] Sutter P, Albrecht P, Albrecht P, Sutter E 2010 Appl. Phys. Lett. 97 213101
[10] Wang R, Hao Y, Wang Z, Gong H, Tho J T 2010 Nano Lett. 10 4844
[11] Hu B, Ago H, Ito Y, Kawahara K, Tsuji M, Mogome E, Sumitani K, Mizuta N, Ikeda K, Seigi Mizuno S 2012 Carbon 50 57
[12] Davydov S Yu 2011 Tech. Phys. Lett. 37 64
[13] Alisultanov Z Z 2013 Tech. Phys. Lett. 39 32 （in Russian)
[14] Larciprete R, Ulstrup S, Lacovig P, et al. 2012 Acs Nano 6 9551
[15] Davydov S Yu, Sabinowa G Y 2011 Phys. Stat. Sol. 53 608(in Russian)
[16] Alisultanov Z Z, Kamilov Y K 2014 Phys. Stat. Sol. 56 821(in Russian)
[17] Davydov S Yu 2014 Phys. Stat. Sol. 56 816 （in Russian)
[18] Fang X Y,Yu X X, Zheng H M, Jin H B, Wang L, Cao M S 2015 Phys. Lett. A 379 2245
[19] Cheng Z F, Zheng R L 2016 Chin. Phys. Lett. 33 046501
[20] Cheng Z F, Zheng R L 2016 Acta Phys. Sin. 65 104701 （in Chinese)[程正富, 郑瑞伦2016 65 104701]
[21] Davydov S Yu 2011 Tech. Phys. 37 42(in Russian)
[22] Davydov S Yu 2012 Phys. Solid State 54 875
[23] Huang K, Han R Q 2001 Solid-State Physics（Beijing:China Higher Education Press, CHEP) pp276-282(in Chinese)[黄昆, 韩汝琦2001固体物理学(北京:高等教育出版社)第276–282页]
[24] Zheng R L, Hu X Q, Yang G X 1996 Solid Theory and Application（Chongqing:Southwest Normal University Press) pp267-271(in Chinese)[郑瑞伦, 胡先权, 杨国祥1996固体理论及其应用(重庆:西南师范大学出版社)第267–271页]
[25] Davydov S Yu, Tikhonov S K 1996 Phys. Semicond. Technol. 30 968(in Russian)
[26] Kittel C 1968 Am. J. Phys. 35 547
[27] Yu S, Davydov S Yu 2012 Phys. Semicond. Technol. 46 204(in Russian)
[28] Reina A, Jia X T, Ho J, Nezich D, Son H B, Bulovic V, Dresselhaus M S, Kong J 2009 Nano Lett. 9 30
[29] Ma Q F, Fang R S, Xiang L C, Guo Y 1986 Handbook of Thermo-Physical Properties（Beijing:China Agricultural Machinery Press) pp42-54(in Chinese)[马庆方, 方荣生, 项立成, 郭预1986实用热物理性质手册(北京:中国农业机械出版社)第42–54页]
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[1] Davydov S Yu 2013 Phys. Stat. Sol. 55 813 （in Russian)
[2] Tian W, Yuan P F, Yu Z L 2015 Acta Phys. Sin. 64 046102 （in Chinese)[田文, 袁鹏飞, 禹卓良2015 64 046102]
[3] Wei C, Li J, Liu Q B, Cai S J, Feng Z H 2015 Acta Phys. Sin. 64 038102 （in Chinese)[蔚翠, 李佳, 刘庆彬, 蔡树均, 冯值红2015 64 038102]
[4] Tang J, Liu Z L, Kang C Y, Yan W S, Xu P S, Pan H B, Wei S Q, Gao Y Q, Xu X G 2010 Acta Phys.-Chim. Sin. 26 253 （in Chinese)[唐军, 刘忠良, 康朝阳, 闫文盛, 徐彭寿, 潘海斌, 韦世强, 高压强, 徐现刚2010物理化学学报26 253]
[5] Davydov S Yu 2012 Phys. Stat. Sol. 54 821(in Russian)
[6] Wang L, Tian L H, Wei G D, Gao F M, Zheng J J, Yang W Y 2011 J. Inorganic Mater. 26 1009 （in Chinese)[王霖, 田林海, 尉国栋, 高凤梅, 郑金桔, 杨为佑2011无机材料学报26 1009]
[7] Tetlow H, Posthuma de Boer J, Ford I J, Vvedensky D D, Coraux J, Kantorovich L 2014 Phys. Reports 542 195
[8] Grneis A 2013 J. Phys.:Condens. Matter 25 043001
[9] Sutter P, Albrecht P, Albrecht P, Sutter E 2010 Appl. Phys. Lett. 97 213101
[10] Wang R, Hao Y, Wang Z, Gong H, Tho J T 2010 Nano Lett. 10 4844
[11] Hu B, Ago H, Ito Y, Kawahara K, Tsuji M, Mogome E, Sumitani K, Mizuta N, Ikeda K, Seigi Mizuno S 2012 Carbon 50 57
[12] Davydov S Yu 2011 Tech. Phys. Lett. 37 64
[13] Alisultanov Z Z 2013 Tech. Phys. Lett. 39 32 （in Russian)
[14] Larciprete R, Ulstrup S, Lacovig P, et al. 2012 Acs Nano 6 9551
[15] Davydov S Yu, Sabinowa G Y 2011 Phys. Stat. Sol. 53 608(in Russian)
[16] Alisultanov Z Z, Kamilov Y K 2014 Phys. Stat. Sol. 56 821(in Russian)
[17] Davydov S Yu 2014 Phys. Stat. Sol. 56 816 （in Russian)
[18] Fang X Y,Yu X X, Zheng H M, Jin H B, Wang L, Cao M S 2015 Phys. Lett. A 379 2245
[19] Cheng Z F, Zheng R L 2016 Chin. Phys. Lett. 33 046501
[20] Cheng Z F, Zheng R L 2016 Acta Phys. Sin. 65 104701 （in Chinese)[程正富, 郑瑞伦2016 65 104701]
[21] Davydov S Yu 2011 Tech. Phys. 37 42(in Russian)
[22] Davydov S Yu 2012 Phys. Solid State 54 875
[23] Huang K, Han R Q 2001 Solid-State Physics（Beijing:China Higher Education Press, CHEP) pp276-282(in Chinese)[黄昆, 韩汝琦2001固体物理学(北京:高等教育出版社)第276–282页]
[24] Zheng R L, Hu X Q, Yang G X 1996 Solid Theory and Application（Chongqing:Southwest Normal University Press) pp267-271(in Chinese)[郑瑞伦, 胡先权, 杨国祥1996固体理论及其应用(重庆:西南师范大学出版社)第267–271页]
[25] Davydov S Yu, Tikhonov S K 1996 Phys. Semicond. Technol. 30 968(in Russian)
[26] Kittel C 1968 Am. J. Phys. 35 547
[27] Yu S, Davydov S Yu 2012 Phys. Semicond. Technol. 46 204(in Russian)
[28] Reina A, Jia X T, Ho J, Nezich D, Son H B, Bulovic V, Dresselhaus M S, Kong J 2009 Nano Lett. 9 30
[29] Ma Q F, Fang R S, Xiang L C, Guo Y 1986 Handbook of Thermo-Physical Properties（Beijing:China Agricultural Machinery Press) pp42-54(in Chinese)[马庆方, 方荣生, 项立成, 郭预1986实用热物理性质手册(北京:中国农业机械出版社)第42–54页]
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