**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31097

##### Magnetic Field Effects on Parabolic Graphene Quantum Dots with Topological Defects

**Authors:**
Defne Akay,
Bekir S. Kandemir

**Abstract:**

**Keywords:**
coulomb impurity,
graphene cones,
topological defects,
graphene
quantum dots

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1338678

**References:**

[1] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. GrigorievaA. A. Firsov, “Electric field effect in atomically thin carbon films”, Science, vol.306, pp.666-669, 2004.

[2] K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, “Two-dimensional atomic crystals”, Proc. Natl Acad. Sci. USA vol. 102, pp. 10 451–10 453, 2005.

[3] K. Geim and K. S. Novoselov, “The rise of graphene”, Nat. Mater. vol. 6, pp. 183–191, 2007.

[4] M. I. Katsnelson, “Graphene: carbon in two dimensions”, Mater. Today, vol. 10, no. 1-2, pp. 20–27, 2007.

[5] P. R. Wallace, “The band theory of graphite”, Phys. Rev. vol. 71, pp. 622, 1946.

[6] G. W. Semenof, “Condensed-Matter Simulation of a Three-Dimensional Anomaly”, Phys. Rev. Lett. vol. 53, pp. 2449, 1984.

[7] P. Recher and B. Trauzettel “Quantum dots and spin qubits in graphene”, Nanotechnology vol. 21, pp. 302001, 2010.

[8] F. Molitor, J. Güttinger, C. Stampfer, S. Dröscher, A. Jacobsen, T. Ihn, K. Ensslin, “Electronic properties of graphene nanostructures”, J. Phys.: Condens. Matter vol. 23, pp. 243201, 2011.

[9] V. Rozhkova, G. Giavaras, Y. P. Bliokh, V. Freilikher, F. Nori, “Electronic properties of mesoscopic graphene structures: Charge confinement and control of spin and charge transport ”, Phys. Rep. vol. 503, pp. 77, 2011.

[10] J. Güttinger, F. Molitor, C. Stampfer, S. Schnez, A. Jacobsen, S. Dröscher, T. Ihn, K. Ensslin, “Transport through graphene quantum dots”, Rep. Prog. Phys. vol. 75, pp. 126502, 2012.

[11] P. G. Silvestrov and K. B. Efetov, “Quantum dots in graphene”, Phys. Rev. Lett. vol. 98, pp. 016802, 2007.

[12] M. I. Kastnelson and K. S. Novoselov, A. K. Geim, “Chiral tunnelling and the Klein paradox in graphene”, vol. 2, pp. 620, 2006.

[13] J. Milton Pereira Jr., P. Vasilopoulos, and F. M. Peeters, “Tunable quantum dots in bilayer graphene”, Appl. Phys. Lett. vol. 90, pp. 132122, 2007.

[14] H. Chen, V. Apalkov, and T. Chakraborty, “Fock-Darwin States of Dirac Electrons in Graphene-Based Artificial Atoms”, Phys. Rev. Lett. vol. 98, pp. 186803, 2007.

[15] A. Rycerz, j. Twozydlo, C. W. J. Beenakker, “Valley filter and valley valve in graphene”, Nat. Phys. vol. 3, pp. 172-175, 2007.

[16] A. De Martino, L. Dell’ Anna, and R. Egger, “Magnetic Confinement of Massless Dirac Fermions in Graphene”, Phys. Rev. Lett. vol. 98, pp. 066802, 2007.

[17] A. De Martino, L. Dell’ Anna, and R. Egger, “Magnetic barriers and confinement of Dirac-Weyl quasiparticles in graphene”, Solid State Comm. vol. 144, pp. 547-550, 2007.

[18] B. Wunsch, T. Stauber, and F. Guinea, “Electron-electron interactions and charging effects in graphene quantum dots”, Phys. Rev. B vol. 77, pp. 035316, 2008.

[19] A. Matulis and F. M. Peeters, “Quasibound states of quantum dots in single and bilayer graphene”, Phys. Rev. B, vol. 77, pp. 115423, 2008.

[20] Z. Z. Zhang, K. Chang, and F. M. Peeters, “Tuning of energy levels and optical properties of graphene quantum dots”, Phys. Rev. B. vol. 77, pp. 235411, 2008.

[21] P. Hewageegana and V. Apalkov, “Electron localization in graphene quantum dots”, Phys. Rev. B vol. 77, pp. 245426, 2008.

[22] M. I. Kastnelson and F. Guinea, “Transport through evanescent waves in ballistic graphene quantum dots”, Phys. Rev. B vol. 78, pp. 075417, 2008.

[23] S. Schnez, K. Ensslin, M. Sigrist, and T. Ihn “Analytic model of the energy spectrum of a graphene quantum dot in a perpendicular magnetic field”, Phys. Rev. B vol. 78, pp. 195427, 2008.

[24] J. H. Bardarson, M. Titov, and P. W. Brouwer, “ Electrostatic Confinement of Electrons in an Integrable Graphene Quantum Dot”, Phys. Rev. Lett. vol.102, pp. 226803, 2009.

[25] M. R. Masir, A. Matulis, and F. M. Peeters, “Quasi states of Schrödinger and Dirac electrons in a magnetic quantum dot”, Phys. Rev. B. vol. 79, pp. 155451, 2009.

[26] G. Giavaras, P. A. Maksym, and M. Roy, “Magnetic field induced confinement-deconfinement transition in graphene quantum dots”, J. Phys.: Condens. Matter vol. 21, pp. 102201, 2009.

[27] P. Recher, , J. Nilsson, G. Burkard, and B. Trauzettel, “Bound states and magnetic field induced valley splitting in gate-tunable graphene quantum dots”, Phys. Rev. B. vol.79, pp.085407, 2009.

[28] I. Romanovsky, C. Yannouleas, and U. Landman, “Edge states in graphene quantum dots: Fractional quantum Hall effect analogies and difference at zero magnetic field”, Phys. Rev. B vol. 79, pp. 075311, 2009.

[29] G. Giavaras and F. Nori, “Graphene quantum dots formed by a spatial modulation of the Dirac gap”, Appl. Phys. Lett. vol. 97, pp. 243106, 2010.

[30] S. C. Kim, P. S. Park, and S.-R. Eric Yang, “States near Dirac points of a rectangular graphene dot in a magnetic field”, Phys. Rev. B vol. 81, pp. 085432, 2010.

[31] S. Maiti and A. V. Chubukov, “Transition to Landau levels in grahene quantum dots”, Phys. Rev. B vol. 81, pp. 245411, 2010.

[32] M. Wimmer, A. R. Akhmerov, and F. Guinea, “Robustness of edge states in graphene quantum dots”, Phys. Rev. B vol. 82, pp. 045409, 2010.

[33] G. Giavaras and F. Nori, “Dirac gap-induced graphene quantum dot in an electronic potential”, Phys. Rev. B vol. 83, pp. 165427, 2011.

[34] M. Zarenia, A. Chaves, G. A. Farias, and F. M. Peeters, “Energy levels of triangular and hexagonal graphene quantum dots: A comparative study between the tight-binding and Dirac Equation approach”, Phys. Rev. B. vol. 84, pp. 245403, 2011.

[35] Jia- Lin Zhu and Songyang Sun, “Dirac donor states controlled by magnetic field in gapless and gapped graphene”, Phys. Rev. B. vol. 85, pp. 035429, 2012.

[36] B. S. Kandemir and G. Ömer, “Variational calculations on the energy levels of graphene quantum antidotes”, Eur. Phys. J. B vol. 86, pp. 299, 2013.

[37] C. Furtado, F. Moraes, A. M. de Carvalho, “Geometric phases in graphitic cones”, Phys. Lett. A, vol. 372, pp. 5368, 2008.

[38] J. K. Pachos, “Manifestations of topological defects in graphene”, Contemp. Phys. vol. 50, pp. 375-389, 2009.

[39] B. S. Kandemir and D. Akay “Tuning the pseudo-Zeeman splitting in graphene cones by magnetic field”, Journal of Magnetism and Magnetic Materials , vol. 384, pp. 101-105, 2015.

[40] F. de Juan, A. Cortijo, and M. A. H. Vozmedia, “Dislocations and torsion in graphene and related systems”, Nucl. Phys. B, vol. 828(PM), pp. 625-637, 2010.

[41] E. A. Kochetov, V. A. Osipov, and R. Pincak, “Electronic properties of disclinated flexible membrane beyond the inextensional limit: application to graphene”, J. Phys.: Condens. Matter, vol. 22(PM), pp. 395502, 2010.

[42] K. Bakke and C. Furtado “On the interaction of the Dirac oscillator with the Aharonov-Casher system in the topological defect background”, Annals of Phys., vol. 336, pp. 489-504, 2013.