深圳大学学报理工版

基于非平衡格林函数(non-equilibrium Green's function, NEGF)和密度泛函理论(density functional theory, DFT),从第一性原理出发研究Armchair型和Zigzag型的石墨烯带正常-超导结的电子输运性质,计算了缺陷对这两种正常-超导结输运性质的影响.计算表明,对无缺陷正常-超导石墨烯带,在超导能隙内,Andreev反射系数TA恰好等于正常石墨烯带的电子透射系数TN. 当石墨烯带存在缺陷时,Andreev反射系数TA不再是一个常数,而在超导能隙边缘出现两个尖锐的峰,其峰值大于正常系统的电子透射系数.在超导能隙之外,Andreev反射系数TA逐渐减小为0,准粒子的正常隧穿几率T1逐渐增大,且趋于无超导下的正常系统的电子透射系数TN. 不同缺陷构型对石墨烯带中载流子的输运过程影响不同.如果缺陷的存在对正常石墨烯带电子散射过程影响越大,则其对正常-超导体系中的Andreev反射和准粒子散射影响也越大.

The first principles calculation has been carried out to investigate the quantum transport properties of normal-superconducting graphene nanoribbons(GNRs)within the combination of non-equilibrium Green's function(NEGF)and density functional theory(DFT). The Andreev reflection coefficient TA and quasi-particle transmission probability T1 of normal-superconducting system of a series of defective configurations were investigated in detail.As a comparison, the electric transmission coefficient TN of normal system was also calculated. In the pristine graphene nanoribbons, The Andreev reflection coefficient TA is a constant and exactly equals to electric transmission coefficient TN of the normal system in the superconducting energy gap, which indicates that the Andreev conductance is twice of the normal electric conductance. In the defective configurations of graphene nanoribbons, TA shows two sharp peaks at E=±Δ, and the peak values are larger than the electric conductance of normal system.Outside the superconducting energy gap, Andreev conductance decays to zero, and quasi-particle transmission probability increases to the normal electric transmission coefficient gradually. Different defective configurations give different influence to the Andreev reflection of the normal-superconducting graphene nanoribbons.

引言
1 系统结构和计算方法
2 结果和讨论
3 结语

图1 Andreev反射示意图<br/>Fig.1 Schematic diagrams of Andreev reflection

图1 Andreev反射示意图
Fig.1 Schematic diagrams of Andreev reflection

图2 不同缺陷的石墨烯构型示意图<br/>Fig.2 Schematic structures of graphene with different defect configurations

图2 不同缺陷的石墨烯构型示意图
Fig.2 Schematic structures of graphene with different defect configurations

图3 无限长Armchair型和Zigzag型的正常-超导石墨烯带结构示意图(图中非阴影为向左无限延长的正常导线区域,阴影部分为向右无限延长的超导区域)<br/>Fig.3 Schematic structures of normal-superconductor GNRs with Armchair and Zigzag edges. (The non-shadow region and shadow region represent the normal and superconductor leads which extend to left and right infinitely, respectively.)

图3 无限长Armchair型和Zigzag型的正常-超导石墨烯带结构示意图(图中非阴影为向左无限延长的正常导线区域,阴影部分为向右无限延长的超导区域)
Fig.3 Schematic structures of normal-superconductor GNRs with Armchair and Zigzag edges. (The non-shadow region and shadow region represent the normal and superconductor leads which extend to left and right infinitely, respectively.)

图4 单边被单个氢原子饱和,另一边不饱和的Armchair型(N=11)石墨烯带及两边都被单个氢原子饱和的Zigzag型(N=8)石墨烯带的能带结构和正常透射系数(各图中绿色虚线对应费米能)<br/>Fig.4 Band structure and normal transmission coefficients of Armchair GNR(N=11)and Zigzag GNR(N=8). Armchair GNR is mono-hydrogenated on one

图4 单边被单个氢原子饱和,另一边不饱和的Armchair型(N=11)石墨烯带及两边都被单个氢原子饱和的Zigzag型(N=8)石墨烯带的能带结构和正常透射系数(各图中绿色虚线对应费米能)
Fig.4 Band structure and normal transmission coefficients of Armchair GNR(N=11)and Zigzag GNR(N=8). Armchair GNR is mono-hydrogenated on one

图5 无缺陷石墨烯带的正常电子透射系数TN(E)(黑色点线)、正常-超导Andreev反射系数TA(E)(红色实线)和准粒子透射率T1(E)(蓝色虚线)随能量变化<br/>Fig.5 Transmission coefficient TN(E) of pure normal GNR(black dot line), Andreev reflection coefficient TA(E)(red solid line)and quasi-particle tunneling probability T1(E)(blue dashed line)of pristine normal-superconductor GNR versus electron energy.

图5 无缺陷石墨烯带的正常电子透射系数TN(E)(黑色点线)、正常-超导Andreev反射系数TA(E)(红色实线)和准粒子透射率T1(E)(蓝色虚线)随能量变化
Fig.5 Transmission coefficient TN(E) of pure normal GNR(black dot line), Andreev reflection coefficient TA(E)(red solid line)and quasi-particle tunneling probability T1(E)(blue dashed line)of pristine normal-superconductor GNR versus electron energy.

图6 存在缺陷的石墨烯带正常透射系数TN(E)、正常-超导Andreev反射系数TA(E)及准粒子隧穿几率T1(E)<br/>Fig.6 Transmission coefficient TN(E) of defective normal GNR(black dot line), Andreev reflection coefficient TA(E)(red solid line)and quasi-particle tunneling probability T1(E)(blue dashed line)of defective normal-superconductor GNR versus electron energy.

图6 存在缺陷的石墨烯带正常透射系数TN(E)、正常-超导Andreev反射系数TA(E)及准粒子隧穿几率T1(E)
Fig.6 Transmission coefficient TN(E) of defective normal GNR(black dot line), Andreev reflection coefficient TA(E)(red solid line)and quasi-particle tunneling probability T1(E)(blue dashed line)of defective normal-superconductor GNR versus electron energy.

[1] Novoselov K S, Geim A K, Morozov S V, et al. Electric field effect in atomically thin carbon films[J].Science, 2004,306(5696):666- 669.
[2] Novoselov K S,Geim A K,Morozov S V,et al.Two-dimensional gas of massless dirac fermions in graphene[J].Nature,2005,438(10):197-200.
[3] Zhang Yuanbo,Tan Yanwen,Stormer H L,et al.Experimental observation of the quantum hall effect and Berry's phase in grapheme[J].Nature,2005, 438(10):201-204.
[4] Katsnelson M I,Novoselov K S,Geim A K.Chiral tunnelling and the Klein paradox in grapheme[J].Nature Physics,2006,2(10):620- 625.
[5] Song H S,Li S L,Miyazaki H,et al.Origin of the relatively low transport mobility of graphene grown through chemical vapor deposition[J].Scientific Reports,2012,2(337):1- 6.
[6] Wang Zi, Guo Hong, Bevan K H. First principles modeling of disorder scattering in graphene[J].Journal of Computational Electronics, 2013, 12(2):104-114.
[7] Ugeda M M,Brihuega I,Hiebel F,et al.Electronic and structural characterization of divacancies in irradiated graphene[J].Physical Review B,2012,85(12):121402-1-121402-5.
[8] Chen Zhihong,Lin YuMing,Michael J,et al.Graphene nano-ribbon electronics[J].Physica E,2007,40(2): 228-232.
[9] Wang Bin, Wang Jian, Guo Hong. Ab initio calculation of transverse spin current in graphene nanostructures[J].Physics Review B, 2009, 79(16): 165417-1-165417-5.
[10] Wan Langhui, Yu Yunjin, Wang Bin. Spin filter of graphene nanoribbon based structure[J]. Chinese Physics Letters, 2010, 27(8): 087205-1- 087205- 4.
[11] Yu Yunjin, Wei Yadong, Wan Langhui. Ab initio study of carbon chain parametric pump[J].Journal of Shenzhen University Science and Engineering, 2007, 24(3):313-316.(in Chinese)
[12] Wan Langhui, Wang Bin, Wei Yadong. Nonlinear thermoelectric transport of carbon nanotube[J].Journal of Shenzhen University Science and Engineering, 2009, 26(4):356-359.(in Chinese)
[13] Amorim R G,Fazzio A,Antonelli A,et al.Divacancies in graphene and carbon nanotubes[J].Nano Letters, 2007,7(8):2459-2462.
[14] Kim Y,Ihm J,Yoon E,et al.Dynamics and stability of divacancy defects in graphene[J].Physics Review B, 2011,84(7):075445-1- 075445-5.
[15] Wei Yadong, Wang Jian, Guo Hong, et al. Resonant Andreev reections in superconductor-carbon-nanotube devices[J].Physics Review B,2001,63(19):195412-1-195412-5.
[16] Wang Jian, Wei Yadong, Sun Qingfeng, et al. Nonlinear transport theory for hybrid normal-superconducting devices[J].Physics Review B,2001,64(10):104508-1-104508-5.
[17] Cheng Shuguang,Xing Yanxia,Wang Jian.Contro-llable andreev retroreflection and specular andreev reflection in a four-terminal graphene-superconductor hybrid system[J].Physics Review Letters,2009, 103(16):167003-1-167003- 4.
[18] Sun Qingfeng,Xie Xiaoyi.Quantum transport through a graphene nanoribbon-superconductor junction[J].Journal of Physics:Condensed Matter, 2009, 21(34):344204-1-344204-9.
[19] Beenakker C W J.Specular andreev reflection in graphene[J].Physics Review Letters,2006,97(6):067007-1- 067007- 4.
[20] Mizuno N,Nielsen B,Xu Du.Suspended graphene ballistic josephson weak links[EB/OL].(2013- 05- 09)[2014- 01- 01]. http: //arxiv.org//abs/1305.2180.
[21] Cayssol J.Crossed andreev reflection in a graphene bipolar transistor[J].Physics Review Letters,2008,100(14):147001-1-147001-3.
[22] Stone A J,Wales D J.Theoretical studies of icosahedral C60 and some related species[J].Chemical Physics Letters, 1986,128(5/6):501-503.
[23] Kresse G, Furthmuller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[J].Physics Review B,1996, 54(16):11169-11186.
[24] Perdew J P,Wang Yue.One-dimensional extended lines of divacancy defects in graphene[J].Nanoscale,2011, 3(28):2868-2872.
[25] Taylor J,Guo Hong,Wang Jian.Ab initio modeling of quantum transport properties of molecular electronic devices[J].Physics Review B,2001,63(24):245407-1-245407-13.
[26] Sun Qingfeng,Wang Jian,Lin Tsunghan.Resonant Andreev reflection in a normal-metal-quantum-dot-superconductor system[J].Physics Review B,1999, 59(5):3831-3840.
[27] Wang Bin,Wei Yadong,Wang Jian.First-principles calculation of the andreev conductance of carbon wires[J].Physics Review B,2012,86(3):035414-1- 035414-5.
[28] Gennes P G DE.Superconductivity of metals and alloys[M].New York: Westview Press,1999.

备注

引言

1 系统结构和计算方法

2 结果和讨论

3 结语

期刊信息

备注

引言

1 系统结构和计算方法

2 结果和讨论

3 结 语

期刊信息

3 结语