The combined effects of an asymmetric (square or V-shaped) notch and uniaxial strain are studied in a zigzag graphene nanoribbon (ZGNR) device using a generalized tight-binding model. The spin-polarization and conductance-gap properties, calculated within the Landauer–B¨uttiker formalism, were found to be tunable for uniaxial strain along the ribbon-length and ribbon-width for an ideal ZGNR and square (V-shaped) notched ZGNR systems. Uniaxial strain along the ribbon-width for strains 10% initiated significant notch-dependent reductions to the conduction-gap. For the V-shaped notch, such strains also induced spin-dependent changes that result, at 20% strain, in a semi-conductive state and metallic state for each respective spin-type, thus demonstrating possible quantum mechanisms for spin-filtration.
References
[1]
Huang, B.; Liu, F.; Wu, J.; Gu, B.L.; Duan, W. Suppression of spin polarization in graphene nanoribbons by edge defects and impurities. Phys. Rev. B 2008, 77, 153411:1–153411:10.
[2]
Areshkin, D.A.; Gunlycke, D.; White, C.T. Ballistic transport in graphene nanostrips in the presence of disorder: Importance of edge effects. Nano Lett. 2007, 7, 204–210, doi:10.1021/nl062132h.
[3]
Li, T.C.; Lu, S.P. Quantum conductance of graphene nanoribbons with edge defects. Phys. Rev. B 2008, 77, 085408:1–085408:8.
[4]
Mucciolo, E.R.; Neto, A.H.C.; Lewenkopf, C.H. Conductance quantization and transport gaps in disordered graphene nanoribbons. Phys. Rev. B 2009, 79, 075407:1–075407:5.
[5]
Cresti, A.; Nemec, N.; Biel, B.; Niebler, G.; Triozon, F.; Cuniberti, G.; Roche, S. Charge transport in disordered graphene-based low dimensional materials. Nano Res. 2008, 1, 361–394, doi:10.1007/s12274-008-8043-2.
[6]
Cresti, A.; Roche, S. Range and correlation effects in edge disordered graphene nanoribbons. NewJ. Phys. 2009, 11, 095004:1–095004:11.
[7]
Saloriutta, K.; Hancock, Y.; K？rkk？inen, A.; K？rkk？inen, L.; Puska, M.J.; Jauho, A-P. Electron transport in edge-disordered graphene nanoribbons. Phys. Rev. B 2011, 83, 205125:1–205125:6.
[8]
Wimmer, M.; Adagideli, I.; Berber, S.; Tománek, D.; Richter, K. Spin currents in rough graphene nanoribbons: Universal fluctuations and spin injection. Phys. Rev. Lett. 2008, 100, 177207:1–177207:4.
[9]
Zhang, X.J.; Chen, K.Q.; Tang, L.M.; Long, M.Q. Electronic transport properties on V-shaped-notched zigzag graphene nanoribbons junctions. Phys. Lett. A. 2011, 375, 3319–3324.
[10]
Niimi, Y.; Matsui, T.; Kambara, H.; Tagami, K.; Tsukada, M.; Fukuyama, H. Scanning tunneling microscopy and spectroscopy of the electronic local density of states of graphite surfaces near monoatomic step edges. Phys. Rev. B 2006, 73, 085421:1–085421:20.
[11]
Nakada, K.; Fujita, M.; Dresselhaus, G.; Dresselhaus, M.S. Edge state in graphene ribbons: Nanometer size effect and edge shape dependence. Phys. Rev. B 1996, 54, 17954–17961.
[12]
Dutta, S.; Pati, S.K. Edge reconstructions induce magnetic and metallic behavior in zigzag graphene nanoribbons. Carbon 2010, 48, 4409–4413, doi:10.1016/j.carbon.2010.07.057.
[13]
Hancock, Y.; Uppstu, A.; Saloriutta, K.; Harju, A.; Puska, M.J. Generalized tight-binding transport model for graphene nanoribbon-based systems. Phys. Rev. B 2010, 81, 245402:1–245402:6.
Lian, C.; Tahy, K.; Fang, T.; Li, G.; Xing, H.G.; Jena, D. Quantum transport in graphene nanoribbons patterned by metal masks. Appl. Phys. Lett. 2010, 96, 103109:1–103109:3.
Fischbein, M.D.; Drndic, M. Electron beam nanosculpting of suspended graphene sheets. Appl.Phys. Lett. 2008, 93, 113107:1–113107:3.
[18]
Pereira, V.M.; Neto, A.H.C. Strain engineering of graphene’s electronic structure. Phys. Rev. Lett. 2009, 103, 046801–046801:4, doi:10.1103/PhysRevLett.103.046801.
[19]
Sun, L.; Li, Q.; Ren, H.; Su, H.; Shi, Q.W.; Yang, J. Strain effect on electronic structures of graphene nanoribbons: A first-principles study. J. Chem. Phys. 2008, 129, 074704:1–074704:6.
[20]
Poetschke, M.; Rocha, C.G.; Torres, L.E.F.F.; Roche, S.; Cuniberti, G. Modeling graphene-based nanoelectromechanical devices. Phys. Rev. B 2010, 81, 193404:1–193404:4.
[21]
Ni, Z.H.; Yu, T.; Lu, Y.H.; Wang, Y.Y.; Feng, Y.P.; Shen, Z.X. Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening. ACS Nano 2008, 2, 2301–2305, doi:10.1021/nn800459e.
[22]
Han, M.; Zhang, Y.; Zheng, H-B. Effect of uniaxial strain on band gap of armchair-edge graphene nanoribbons. Chin. Phys. Lett. 2010, 27, 266–269.
[23]
Lu, Y.; Guo, J. Band gap of strained graphene nanoribbons. Nano Res. 2010, 3, 189–199.
[24]
Su, W.S.; Wu, B.R.; Leung, T.C. A first-principles study on the electromechanical effect of graphene nanoribbon. Comput. Phys. Commun. 2011, 182, 99–102, doi:10.1016/j.cpc.2010.07.019.
[25]
Viana-Gomes, J.; Pereira, V.M.; Peres, N.M.R. Magnetism in strained graphene dots. Phys. Rev. B 2009, 80, 245436:1–245436:11.
[26]
Pellegrino, F.M.D.; Angilella, G.G.N.; Pucci, R. Dynamical polarization of graphene under strain. Phys. Rev. B 2010, 82, 115434:1–115434:9.
[27]
Lee, S.H.; Chiu, C.W.; Ho, Y.H.; Lin, M.F. Uniaxial-stress effects on electronic structures of monolayer and bilayer graphenes. Synth. Met. 2010, 160, 2435–2441, doi:10.1016/j.synthmet.2010.09.023.
[28]
Zhang, X.H. Coherent transport in strained zigzag graphene nanoconstriction. Eur. Phys. J. B 2012, 85, 228–234, doi:10.1140/epjb/e2012-21056-9.
[29]
Pereira, V.M.; Neto, A.H.C.; Peres, N.M.R. Tight-binding approach to uniaxial strain in graphene. Phys. Rev. B. 2009, 80, 045401:1–045401:8.
[30]
Rostami, H.; Asgari, R. Electronic ground-state properties of strained graphene. Phys. Rev. B 2012, 86, 155435:1–155435:7.
[31]
Bruna, M.; Vaira, A.; Battiato, A.; Vittone, E.; Borini, S. Graphene strain tuning by control of the substrate surface chemistry. Appl. Phys. Lett. 2010, 97, 021911:1–021911:3.
[32]
Tsoukleri, G.; Parthenios, J.; Papagelis, K.; Jalil, R.; Ferrari, A.C.; Geim, A.K.; Novoselov, K.S.; Galiotis, C. Subjecting a graphene monolayer to tension and compression. Small 2009, 5, 2397–2402, doi:10.1002/smll.200900802.
[33]
Liu, F.; Ming, P.; Li, J. Ab initio calculation of ideal strength and phonon instability of graphene under tension. Phys. Rev. B. 2007, 76, 064120:1–064120:7.
[34]
Lee, C.; Wei, X.; Kysar, J.W.; Hone, J. Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 2008, 321, 385–388, doi:10.1126/science.1157996.
[35]
Xu, P.; Yang, Y.; Barber, S.D.; Ackerman, M.L.; Schoelz, J.K.; Qi, D.; Kornev, I.A.; Dong, L.; Bellaiche, L.; Barraza-Lopez, S.; Thibado, P.M. Atomic control of strain in freestanding graphene. Phys. Rev. B. 2012, 85, 121406:1–121416:5.
[36]
Frank, I.W.; Tanenbaum, D.M.; van der Zande, A.M.; McEuen, P.L. Mechanical properties of suspended graphene sheets. J. Vac. Sci. Technol. B 2007, 25, 2558–2561, doi:10.1116/1.2789446.
[37]
Palacios, T.; Hsu, A.; Wang, H. Applications of graphene devices in RF communications. IEEE Commun. Mag. 2010, 48, 122–128, doi:10.1109/MCOM.2010.5473873.
[38]
Kim, K.S.; Zhao, Y.; Jang, H.; Lee, S.Y.; Kim, J.M.; Kim, K.S.; Ahn, J.H.; Kim, P.; Choi, J.Y.; Hong, B.H. Large-scale pattern growth of graphene films for stretchable transparent electrodes. Nature 2009, 457, 706–710, doi:10.1038/nature07719.
[39]
Geim, A.K. Graphene: Status and prospects. Science 2009, 324, 1530–1534, doi:10.1126/science.1158877.
[40]
Hubbard, J. Electron correlations in narrow energy bands. Proc. R. Soc. A 1963, 276, 238–257, doi:10.1098/rspa.1963.0204.
[41]
Hancock, Y.; Smith, A.E. Local and interfacial magnetic properties of inhomogeneous finite linear chains. Phys. E 2003, 18, 383–392, doi:10.1016/S1386-9477(02)01103-7.
[42]
Datta, S. Electronic Transport in Mesoscopic Systems; Cambridge University Press: Cambridge, UK, 1997.
[43]
Guinea, F.; Tejedor, C.; Flores, F.; Louis, E. Effective two-dimensional Hamiltonian at surfaces. Phys. Rev. B 1983, 28, 4397–4402.
[44]
Brandbyge, M.; Mozos, J.L.; Ordejón, P.; Taylor, J.; Stokbro, K. Density-functional method for nonequilibrium electron transport. Phys. Rev. B 2002, 65, 165401:1–165401:17.
[45]
Soler, J.M.; Artacho, E.; Gale, J.D.; García, A.; Junquera, J.; Ordejón, P.; Sánchez-Portal, D. The SIESTA method for ab initio order-N materials simulation. J. Phys. Condens. Matter 2002, 14, 2745–2779, doi:10.1088/0953-8984/14/11/302.
[46]
Ordejón, P.; Artacho, E.; Soler, J.M. Self-consistent order-N density-functional calculations for very large systems. Phys. Rev. B 1996, 53, R10441–R10444, doi:10.1103/PhysRevB.53.R10441.
[47]
Ashcroft, N.; Mermin, M. Solid State Physics; Holt, Rinehart and Winston: New York, NY, USA, 1976.
[48]
Son, Y.W.; Cohen, M.L.; Louie, S.G. Energy gaps in graphene nanoribbons. Phys. Rev. Lett. 2006, 97, 216803:1–216803:4.
