Effect of vacancy defects on the Josephson current in zigzag graphene narrow strips

Document Type : Original Article

Authors

1 Department of Physics, Alzahra University, Tehran, Iran

2 Department of Physics, Alzahra University​, Tehran, Iran

3 Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran

Abstract

We investigate the Josephson current in a superconductor/zigzag graphene narrow strip/superconductor (Sc-ZGNS-Sc) junction, with vacancy defects. For this purpose, we extend a recursive Green’s function based numerical method to ZGNSs and take into account the effect of vacancies including random single vacancy distributions and also chain-like linear defects. We investigate how the Josephson current is affected by the length and the width of the strip and the concentration of the vacancies. We find that the Josephson current exhibits an exponentially dependence on the vacancy concentration. The exponent coefficient is a nonlinear function of the length of the lattice and the vacancy concentration. For the width dependence we find a linear relation between the Josephson current and the width of the ZGNS which propose a semi classical treatment of the electron transport in this system. Finally, we study the effect of chain-like linear defects and compare them with randomly distributed single vacancies.

Keywords

Article Title [فارسی]

اثر عیوب تهی جائی بر جریان جوزفسونی در نانوریبون زیگزاگی

Authors [فارسی]

  • سمیه زارعی 1
  • وحید دادمهر 2
  • حسین حکیمی پژوه 1
  • زهرا فرائی 3

1 گروه فیزیک، دانشگاه الزهرا، تهران، ایران

2 گروه فیزیک، دانشگاه الزهرا، تهران، ایران

3 گروه فیزیک، دانشگاه تحصیلات تکمیلی علوم پایه گاوازنگ، زنجان، ایران

Abstract [فارسی]

ما جریان جوزفسون را در یک اتصال ابررسانا/نوار باریک زیگزاگ گرافن/ابررسانا (Sc-ZGNS-Sc) با نقص های تهی جائی بررسی می کنیم. برای این منظور ، ما روش عددی مبتنی بر تابع بازگشتی را به ZGNS ها بسط داده و تأثیر تهی جاها شامل توزیع های تک تهی جای تصادفی و نقص های خطی زنجیره ای از تهی جاها را در نظر می گیریم. ما چگونگی تغییر جریان جوزفسون تحت تأثیر طول و عرض نوار و غلظت تحت موقعیت های تهی جاها بررسی می کنیم. دریافتیم که جریان جوزفسون وابستگی نمایی به غلظت تهی جائی دارد. ضریب توان یک تابع غیر خطی از طول شبکه و غلظت تهی جاها است. برای وابستگی جریان جوزفسون به عرض ZGNR ما یک رابطه خطی بین جریان جوزفسون پیدا کردیم که یک سازوکار نیمه کلاسیک از انتقال الکترون در این سیستم پیشنهاد می کند. در نهایت، ما اثر عیوب خطی زنجیره ای را مطالعه می کنیم و آنها را با موقعیت های تهی جائی منفرد به طور تصادفی مقایسه می کنیم.

Keywords [فارسی]

  • نوار باریک گرافن
  • جریان جوزفسون
  • عیب تهی جا
  • الگوی شبکه
[1]
A.K. Geim, "Graphene: Status and Prospects." Science, 324 (2009) 1530.
[2]
D. Jariwala, V.K. Sangwan, L.J. Lauhon, T. J. Marks, M.C. Hersam, "Carbon nanomaterials for electronics, optoelectronics, photovoltaics, and sensing." Chemical Society Reviews, 42 (2013) 2824.
[3]
Y. Zhu , et al, "Graphene and Graphene Oxide: Synthesis, Properties, and Applications." Advanced Materials, 22 (2010) 3906.
[4]
A.K. Geim, K.S. Novoselov, "The rise of graphene." Nature Materials, 6 (2007) 183.
[5]
A.H. Castro Neto, F. Guinea, N.M. R. Peres, K.S. Novoselov, and A.K. Geim, "The electronic properties of graphene." Reviews of Modern Physics, 81 (2009) 109.
[6]
C.W. J.Beenakker, M. Titov , "Josephson effect in ballistic graphene." Physical Review B, 74 (2006) 041401.
[7]
C. Ojeda-Aristizabal, M. Ferrier, S. Guéron, and H. Bouchiat, "Tuning the proximity effect in a superconductor-graphene-superconductor junction." Physical Review B, 79 (2009) 165436.
[8]
M. Wilson, "Electrons in atomically thin carbon sheets behave like massless particles." Physics Today, 59 (2006)21.
[9]
V. Eswaraiah, et al, "Top down method for synthesis of highly conducting graphene by exfoliation of graphite oxide using focused solar radiation." Journal of Materials Chemistry, 21 (2011) 6800.
[10]
L. Tang, et al, "Bottom-up synthesis of large-scale graphene oxide nanosheets/" Journal of Materials Chemistry, 22 (2012) 5676.
[11]
Y. Kim, J. Ihm, E.Yoon, G.D. Lee, "Dynamics and stability of divacancy defects in graphene." Physical Review B, 84 (2011) 075445.
[12]
J. Kotakoski, A.V. Krasheninnikov, U. Kaiser, and J.C. Meyer, "From Point Defects in Graphene to Two-Dimensional Amorphous Carbon." Physical Review Letters, 106 (2011) 105505.
[13]
A. Hashimoto, K. Suenaga, A. Gloter, K. Urita, S. Iijima, "Direct evidence for atomic defects in graphene layers." Nature, 430 (2004) 870.
[14]
K. Brenner, R. Murali, "In situ doping of graphene by exfoliation in a nitrogen ambient." Applied Physics Letters, 98 (2011) 13115.
[15]
C. Zhang, L. Fu, N. Liu, M. Liu, Y. Wang, Z. Liu, "Synthesis of Nitrogen‐Doped Graphene Using Embedded Carbon and Nitrogen Sources." Advanced Materials, 23 (2011) 1020.
[16]
L. Li, S. Reich, J. Robertson, "Defect energies of graphite: Density-functional calculations." Physical Review B, 72 (2005) 184109.
[17]
C. Ataca, E. Akturk, H. Şahin, S. Ciraci, "Adsorption of carbon adatoms to graphene and its nanoribbons." Journal of Applied Physics, 109 (2011) 013704.
[18]
M. Terrones, A.R. Botello-Méndez, J. Campos-Delgado, F. López-Urías, Y.I. Vega-Cantú, F.J. Rodríguez-Macías, A.L. Elias, E. Munoz-Sandoval, A.G. Cano-Marquez, J. Charlier, "Graphene and graphite nanoribbons: Morphology, properties, synthesis, defects and applications." Nano Today, 5 ( 2010) 351.
[19]
P.T. Araujo, M. Terrones, M.S. Dresselhaus, "Defects and impurities in graphene-like materials." Materials Today, 15 (2012) 98.
[20]
C.Ö. Girit, et al, "Graphene at the Edge: Stability and Dynamics." Science, 323 ( 2009) 1705.
[21]
M.M. Ugeda, I. Brihuega, F. Guinea, J.M. Gómez-Rodríguez, "Missing Atom as a Source of Carbon Magnetism." Physical Review Letters, 104 (2010) 096804.
[22]
Y. Wang,Y. Wu, "Disorder enhanced conductance in graphene." Physica B, 478 (2015) 84.
[23]
L. Nanshu, Z. Si, Z. Jijun, "Electrical Conductance of Graphene with Point Defects." Acta Physico-Chimica Sinica, 35 (2018) 1142.
[24]
W.A. Mu˜noz, L. Covaci and F.M. Peeters, "Disordered graphene Josephson junctions." Physical Review B, 91 (2015) 054506.
[25]
M. Gokhan Sensoy, "The influence of vacancy-induced local strain on the transport properties in armchair and zigzag graphene nanoribbons." Materials Research Express, 6 ( 2019) 045057.
[26]
S. Zareei,V. Daadmehr, H. Hakimipajouh, Z. Faraei, "Josephson current for a Graphene nanoribbon using a lattice model." Journal of Interfaces, Thin films, and Low dimensional systems, 2 (2019)113.
[27]
A. Furusaki, "DC Josephson effect in dirty SNS junctions: Numerical study." Physica B: Condensed Matter, 203 (1994) 214.
[28]
W. Hou, J.M. Chen, "Hidden symmetry and protection of Dirac points on the honeycomb lattice." Scientific Reports, 5 (2014) 17571.
[29]
K. Wakabayashi, M. Fujita, H. Ajiki and M. Sigrist, "Electronic and magnetic properties of nanographite ribbons." Physical Review B, 59  (1999) 8271.
[30]
Y. Asano, "Numerical method for dc Josephson current between d-wave superconductors," Physical Review B, 63 (2001) 052512.
[31]
M.P. López Sancho, J.M. López Sancho, and J. Rubio, "Quick iterative scheme for the calculation of transfer matrices: application to Mo (100)." Journal of Physics F: Metal Physics, 14 (1984) 1205.
[32]
A.V. Krasheninnikov, P.O. Lehtinen, A.S. Foster, R.M. Nieminen, "Bending the rules: contrasting vacancy energetics and migration in graphite and carbon nanotubes." Chemical Physics Letter, 418 (2006) 1205.
[33]
A.A. El-Barbary, R.H. Telling, C.P. Ewels, M.I. Heggie, P.R. Briddon, "Structure and energetics of the vacancy in graphite." Physical Review B, 68 (2003) 144107.
[34]
F. Banhart, J. Kotakoski, A.V. Krasheninnikov, "Structural Defects in Graphene." ACS Nano, 5 (2011) 26.
[35]
C.W.J. Beenakker, "Specular Andreev Reflection in Graphene." Physical Review Letters, 97 (2006) 067007.
[36]
G. Nanda, et al,, "Current-Phase Relation of Ballistic Graphene Josephson Junctions." Nano Letters, 17 ( 2017) 3396.
[37]
A.M. Black-Schaffer and S. Doniach, "Self-consistent solution for proximity effect and Josephson current in ballistic graphene SNS Josephson junctions." Physical Review B, 78 (2008) 024504.
[38]
M. Jamaati, A. Namiranian, "Random vacancy effect on the electronic transport of zigzag graphene nanoribbon using recursive Green’s function." Computational Materials Science, 101 (2015) 156.
[39]
Z. Chen, Y. Lin, M.J. Rooks, P. Avouris, "Graphene Nano-Ribbon Electronics." Physica E, 40 (2007) 228.
[40]
Z. Xiao, C. Durkan, "Unravelling the electrical properties of epitaxial Graphene nanoribbons." Advanced Materials Interfaces, 6 (2019) 1801794.
[41]
M. Büttiker, R. Landauer, "Diffusive traversal time: Effective area in magnetically induced interference." Physical Review B, 36 (1987) 6255.
[42]
C. Durkan, Current at the nanoscale: An introduction to nanoelectronics, second edition, World Scientific Publishing Company (2013).
[43]
J.H. Warner, G.Do Lee, K. He, A.W. Robertson, "Bond Length and Charge Density Variations within Extended Arm Chair Defects in Graphene." ACS Nano, 7 (2013) 9860.
[44]
A.W. Robertson, G. Do Lee, K. He, Y. Fan, Ch.S. Allen, "Partial dislocations in graphene and their atomic level migration dynamics." Nano letters, 15 (2015) 5950.