Off-plane Impurity Effects in Graphene Quantum Dots

Defne Akay; Bekir Sıtkı Kandemir

doi:10.17776/csj.14715

Off-plane Impurity Effects in Graphene Quantum Dots

Year 2016, Volume: 37 Issue: 1, 20 - 29, 19.01.2016

Defne Akay Bekir Sıtkı Kandemir

https://doi.org/10.17776/csj.14715

Abstract

Abstract. Within the continuum model of graphene, we study the properties of energy spectrum of graphene quantum dots in the presence of an off-plane donor/acceptor Coulomb impurities as a function of their positions. We propose a variational scheme in which the trial wave functions take into account the confinement of the carriers of graphene quantum dot together with the influence of magnetic field. The dependence of graphene quantum dot states on the location of impurity is investigated in the presence of magnetic field. We show that the off-plane donor/acceptor hydrogenic impurity removes the degeneracy of the relativistic Fock-Darwin states, and modifies the valley splitting due to the spatial confinement.

Keywords: Graphene quantum dots, Hydrogenic impurity

Özet. Grafenin sürekli modeli çerçevesinde, grafen kuantum noktalarının enerji spektrumu konumlarının bir fonksiyonu olarak düzlem dışı donör/akseptor Coulomb safsızlıklarının varlığında çalışılmıştır. Manyetik alanın etkisi altındaki grafen kuantum noktasının yük taşıyıcılarının sınırlanması göz önüne alınarak, varyasyonel yöntemde kullanılacak dalga fonksiyonu önerilmiştir. Grafen kuantum nokta durumlarının safsızlığın konumuna bağlılığı manyetik alanın varlığında incelenmiştir. Düzlem dışı donör/akseptör hidrojenik safsızlığın, göreli Fock-Darwin durumlarının dejenereliğini kaldırdığı ve uzaysal sınırlamadan dolayı vadi dejenereliğinin değiştiği görülmüştür.

Anahtar Kelimeler: Grafen kuantum noktaları, Hidrojenik safsızlık

References

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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, P. M. Ostrovsky, I. V. Gornyi, and A. D. Mirlin, “Electron transport in disordered graphene ”, Phys. Rev. B, vol. 74, pp. 235443, 2006.
M. I. Katsnelson, “Nonlinear screening of charge impurities in graphene”, Phys. Rev. B, vol. 74, pp. 201401, 2006.
Vitor M. Pereira, Johan Nilsson, and A. H. Castro Neto,“Coulomb impurity problem in graphene ”, Phys. Rev. Lett. vol. 99, pp. 166802, 2007.
M. M. Fogler, D. S. Novikov, and B. I. Shklovskii, “Screening of a hypercritical charge in graphene”, Phys. Rev. B, 76, 233402, 2007.
A. V. Shytov, M. I. Katsnelson, and L. S. Levitov, “Vacuum polarization and screening of supercritical impurities in graphene”, Phys. Rev. Lett. vol. 99, pp. 236801, 2007.
A. V. Shytov, M. I. Katsnelson, and L. S. Levitov “Atomic collapse and quasi–Rydberg states in graphene”, Phys. Rev. Lett. 99, 246802, 2007.
D. S. Novikov, “Numbers of donors and acceptors from transport measurements in graphene”, Appl. Phys. Lett. vol. 91, pp. 102102, 2007.
D. S. Novikov , “Elastic scattering theory and transport in graphene”, Phys. Rev. B, vol. 76, pp. , 2007.
Ivan S. Terekhov, Alexander I. Milstein, Valeri N. Kotov, and Oleg P. Sushkov, “Screening of Coulomb impurities in graphene”, Phys. Rev. Lett., vol. 100, pp. 076803, 2008.
Valeri N. Kotov, Vitor M. Pereira, and Bruno Uchoa, “Polarization charge distribution in gapped graphene: Perturbation theory and exact diagonalization analysis”, Phys. Rev. B 78, 075433 ,
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Vitor M. Pereira, Valeri N. Kotov, and A. H. Castro Neto, “Supercritical Coulomb impurities in gapped graphene”, Phys. Rev. B, vol.78, pp. 085101, 2008.
M. I. Katsnelson and A.K Geim, “Electron scattering on microscopic corrugations in graphene”, Trans. R. Soc. A vol. 366, pp. 195, 2008.
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B. S. Kandemir and A. Mogulkoc, “Variational approach for the effects of periodic modulations on the spectrum of massless Dirac fermion”, Eur. Phys. J. B vol. 74, pp. 391-396, 2010.
T. Altanhan and B. Kozal, “Impurity effects in graphene”, Eur. Phys. J. B, vol. 85, pp. 222, 2012.
Jia-Lin Zhu, Songyang Sun, and Ning Yang, “Dirac donor states controlled by magnetic field in gapless and gapped graphene”, Phys. Rev. B, vol. 85, pp. 035429 , 2012.
Gordon W. Semenoff, “Condensed-Matter Simulation of a Three-Dimensional Anomaly”, Phys. Rev. Lett. vol. 53, pp. 2449, 1984.
P. R. Wallace, “The band theory of graphite”, Phys. Rev. vol. 71, pp. 622, 1947.
P. G. Silvestrov and K. B. Efetov, “Quantum dots in graphene”, Phys. Rev. Lett. vol. 98, pp. ,2007.
Hong-Yi Chen, Vadim Apalkov, and Tapash Chakraborty “Fock-Darwin electrons in graphene-based artificial atoms”, Phys. Rev. Lett. vol. 98, pp.186803, 2007.
A. Rycerz, J. Twozydlo, C. W. J. Beenakker, “Valley filter and valley valve in graphene ”, Nat. Phys. vol. 3, pp. 172-175, 2007.
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. states of Dirac
F. Sols, F. Guinea, and A. H. Castro Neto, “Coulomb blockade in graphene nanoribbons”, Phys. Rev. Lett. vol. 99, pp. 166803, 2007.
P. Recher, B. Trauzettel, A. Rycerz, Ya. M. Blanter, C. W. J. Beenakker, and A. F. Morpurgo, “Aharonov-Bohm effect and broken valley degeneracy in graphene rings”, Phys. Rev. B vol.76, pp. , 2007.
B.Trauzettel, D. V. Bulaev, D. Loss, and Guido Burkard, “Spin qubits in graphene quantum dots”, Nature Physics 3, 192 - 196 (2007).
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.
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.
A. Matulis and F. M. Peeters, “Quasibound states of quantum dots in single and bilayer graphene”, Phys. Rev. B, vol. 77, pp. 115423, 2008.
M. I. Kastnelson and F. Guinea, “Transport through evanescent waves in ballistic graphene quantum dots”, Phys. Rev. B vol. 78, pp. 075417, 2008.
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.
P. Hewageegana and V. Apalkov, “Electron localization in graphene quantum dots”, Phys. Rev. B vol. 77, pp. 245426, 2008.
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.
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.
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. , pp. 075311, 2009.
N. Stander, B. Huard, and D. Goldhaber-Gordon, “Evidence for Klein tunneling in graphene p−n junctions”, Phys. Rev. Lett. vol. 102, pp. 026807, 2009.
Andrea F. Young, and Philip Kim, “Quantum interference and Klein tunnelling in graphene heterojunctions”, Nature Physics vol. 5, pp. 222 – 226, 2009.
Jürgen Wurm, Adam Rycerz, İnanç Adagideli, Michael Wimmer, Klaus Richter, and Harold U. Baranger, “Symmetry Classes in Graphene Quantum Dots: Universal Spectral Statistics, Weak Localization, and Conductance Fluctuations”, Phys. Rev. Lett. vol. 102, pp. 056806, 2009.
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.
D.Wang and G. Jin, “Magnetically confined states of Dirac electrons in a graphene-based quantum annulus”, Europhys. Lett. Assoc. , vol. 88, no. 1, 2009.
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.
N. M. R. Peres, J. N. B. Rodrigues, T. Stauber and J. M. B. Lopes dos Santos, “Dirac electrons in graphene-based quantum wires and quantum dots”, J. Phys.: Condens. Matter, vol. 21,pp. 344202,
Dali Wang, Guojun Jin, “Bound states of Dirac electrons in a graphene-based magnetic quantum dot”, Dali Wang, Guojun Jin, Phys. Lett. A, vol. 373, pp. 4082, 2009.
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.
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.
P. Recher and B. Trauzettel “Quantum dots and spin qubits in graphene”, Nanotechnology, vol. 21, pp. 302001, 2010.
G. Giavaras, P. A. Maksyma, M. Roy, “Electron confinement in single layer graphene quantum dots: Semiclassical approach”, Physica E, vol. 42, pp. 715, 2010.
Cong-Hua Yan and Lian-Fu Wei, “Size effects in Aharonov-Bohm graphene rings”, J. Phys.: Condens. Matter, vol. 22, pp. 295503, 2010.
N. J. M. Horing and S. Y. Liu, “Energy spectrum and density of states for a graphene quantum dot in a magnetic field”, J. Phys.: Condens. Matter, vol. 22, pp. 025502, 2010.
N. J. M. Horing and S. Y. Liu, “Energy spectrum and density of states for a graphene quantum dot in a magnetic field”, J. Phys.: Condens. Matter, vol. 22, pp. 159801, 2010.
J. W. Gonz´alez, M. Pacheco, L. Rosales and P. A. Orellana, “Bound states in the continuum in graphene quantum dot structures” Europhys. Lett., vol. 91, pp. 66001, 2010.
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.
F. Libich, S. Rotter, J. Guttinger, C. Stampfer, J.Burgdörfer, “Transition to Landau levels in graphene quantum dots”, Phys. Rev. B, vol. 81, pp. 245411, 2010.
M. Wimmer, A. R. Akhmerov, and F. Guinea, “Robustness of edge states in graphene quantum dots”, Phys. Rev. B, vol. 82, pp. 045409, 2010.
G. Giavaras and F. Nori, “Dirac gap-induced graphene quantum dot in an electronic potential”, Phys. Rev. B, vol. 83, pp. 165427, 2011.
M. Ramezani Masir, P. Vasilopoulos and F. M. Peeters, J. “Graphene in inhomogeneous magnetic fields: bound, quasi-bound and scattering states”, Phys.: Condens. Matter, vol. 23, pp. 315301,
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.
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.
G. Pal, W. Apel, and L. Schweitzer, “Electric transport through circular graphene quantum dots: Presence of disorder”, Phys. Rev. B, vol. 84, pp. 075446 2011.
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.
M. Tahir and K. Sabeeh, “Gap opening in the zeroth Landau level in gapped graphene: pseudo- Zeeman splitting in an angular magnetic field”, J. Phys.: Condens. Matter, vol. 24, pp. 135005,
S. C. Kim, J. W. Lee and S-R Eric Yang, “Resonant, non-resonant, and anomalous states of Dirac electrons in a parabolic well in the presence of magnetic fields”, J. Phys.: Condens. Matter, vol. 24, pp. 495302, 2012.
M Gruji ́, M Zarenia, M Tadi ́ and F. M. Peeters, “Interband optical absorption in a circular graphene quantum dot” Phys. Scr. T, vol. 149, pp. 014056, 2012.
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Grafen Kuantum Noktalarında Düzlem Dışı Safsızlık Etkileri

Year 2016, Volume: 37 Issue: 1, 20 - 29, 19.01.2016

Defne Akay Bekir Sıtkı Kandemir

https://doi.org/10.17776/csj.14715

Abstract

Grafenin sürekli modeli çerçevesinde, grafen kuantum noktalarının enerji spektrumu konumlarının bir fonksiyonu olarak düzlem dışı donör/akseptor Coulomb safsızlıklarının varlığında çalışılmıştır. Manyetik alanın etkisi altındaki grafen kuantum noktasının yük taşıyıcılarının sınırlanması göz önüne alınarak, varyasyonel yöntemde kullanılacak dalga fonksiyonu önerilmiştir. Grafen kuantum nokta durumlarının safsızlığın konumuna bağlılığı manyetik alanın varlığında incelenmiştir. Düzlem dışı donör/akseptör hidrojenik safsızlığın, göreli Fock-Darwin durumlarının dejenereliğini kaldırdığı ve uzaysal sınırlamadan dolayı vadi dejenereliğinin değiştiği görülmüştür

Keywords

Grafen kuantum noktaları, Hidrojenik safsızlık

References

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.
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, P. M. Ostrovsky, I. V. Gornyi, and A. D. Mirlin, “Electron transport in disordered graphene ”, Phys. Rev. B, vol. 74, pp. 235443, 2006.
M. I. Katsnelson, “Nonlinear screening of charge impurities in graphene”, Phys. Rev. B, vol. 74, pp. 201401, 2006.
Vitor M. Pereira, Johan Nilsson, and A. H. Castro Neto,“Coulomb impurity problem in graphene ”, Phys. Rev. Lett. vol. 99, pp. 166802, 2007.
M. M. Fogler, D. S. Novikov, and B. I. Shklovskii, “Screening of a hypercritical charge in graphene”, Phys. Rev. B, 76, 233402, 2007.
A. V. Shytov, M. I. Katsnelson, and L. S. Levitov, “Vacuum polarization and screening of supercritical impurities in graphene”, Phys. Rev. Lett. vol. 99, pp. 236801, 2007.
A. V. Shytov, M. I. Katsnelson, and L. S. Levitov “Atomic collapse and quasi–Rydberg states in graphene”, Phys. Rev. Lett. 99, 246802, 2007.
D. S. Novikov, “Numbers of donors and acceptors from transport measurements in graphene”, Appl. Phys. Lett. vol. 91, pp. 102102, 2007.
D. S. Novikov , “Elastic scattering theory and transport in graphene”, Phys. Rev. B, vol. 76, pp. , 2007.
Ivan S. Terekhov, Alexander I. Milstein, Valeri N. Kotov, and Oleg P. Sushkov, “Screening of Coulomb impurities in graphene”, Phys. Rev. Lett., vol. 100, pp. 076803, 2008.
Valeri N. Kotov, Vitor M. Pereira, and Bruno Uchoa, “Polarization charge distribution in gapped graphene: Perturbation theory and exact diagonalization analysis”, Phys. Rev. B 78, 075433 ,
J.-H. Chen, C. Jang, S. Adam, M. S. Fuhrer, E. D. Williams, and M. Ishigami, “Charged-impurity scattering in graphene ”, Nature Physic, vol. 4, pp. 377 – 381, 2008.
Vitor M. Pereira, Valeri N. Kotov, and A. H. Castro Neto, “Supercritical Coulomb impurities in gapped graphene”, Phys. Rev. B, vol.78, pp. 085101, 2008.
M. I. Katsnelson and A.K Geim, “Electron scattering on microscopic corrugations in graphene”, Trans. R. Soc. A vol. 366, pp. 195, 2008.
W. Zhu, Z.Wang, Q. Shi, K. Y. Szeto, J. Chen, and J. G. Hou, “Electronic structure in gapped graphene with a Coulomb potential”, Phys. Rev. B, vol. 79, pp. 155430 , 2009.
B. S. Kandemir and A. Mogulkoc, “Variational approach for the effects of periodic modulations on the spectrum of massless Dirac fermion”, Eur. Phys. J. B vol. 74, pp. 391-396, 2010.
T. Altanhan and B. Kozal, “Impurity effects in graphene”, Eur. Phys. J. B, vol. 85, pp. 222, 2012.
Jia-Lin Zhu, Songyang Sun, and Ning Yang, “Dirac donor states controlled by magnetic field in gapless and gapped graphene”, Phys. Rev. B, vol. 85, pp. 035429 , 2012.
Gordon W. Semenoff, “Condensed-Matter Simulation of a Three-Dimensional Anomaly”, Phys. Rev. Lett. vol. 53, pp. 2449, 1984.
P. R. Wallace, “The band theory of graphite”, Phys. Rev. vol. 71, pp. 622, 1947.
P. G. Silvestrov and K. B. Efetov, “Quantum dots in graphene”, Phys. Rev. Lett. vol. 98, pp. ,2007.
Hong-Yi Chen, Vadim Apalkov, and Tapash Chakraborty “Fock-Darwin electrons in graphene-based artificial atoms”, Phys. Rev. Lett. vol. 98, pp.186803, 2007.
A. Rycerz, J. Twozydlo, C. W. J. Beenakker, “Valley filter and valley valve in graphene ”, Nat. Phys. vol. 3, pp. 172-175, 2007.
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. states of Dirac
F. Sols, F. Guinea, and A. H. Castro Neto, “Coulomb blockade in graphene nanoribbons”, Phys. Rev. Lett. vol. 99, pp. 166803, 2007.
P. Recher, B. Trauzettel, A. Rycerz, Ya. M. Blanter, C. W. J. Beenakker, and A. F. Morpurgo, “Aharonov-Bohm effect and broken valley degeneracy in graphene rings”, Phys. Rev. B vol.76, pp. , 2007.
B.Trauzettel, D. V. Bulaev, D. Loss, and Guido Burkard, “Spin qubits in graphene quantum dots”, Nature Physics 3, 192 - 196 (2007).
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.
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.
A. Matulis and F. M. Peeters, “Quasibound states of quantum dots in single and bilayer graphene”, Phys. Rev. B, vol. 77, pp. 115423, 2008.
M. I. Kastnelson and F. Guinea, “Transport through evanescent waves in ballistic graphene quantum dots”, Phys. Rev. B vol. 78, pp. 075417, 2008.
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.
P. Hewageegana and V. Apalkov, “Electron localization in graphene quantum dots”, Phys. Rev. B vol. 77, pp. 245426, 2008.
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.
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.
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. , pp. 075311, 2009.
N. Stander, B. Huard, and D. Goldhaber-Gordon, “Evidence for Klein tunneling in graphene p−n junctions”, Phys. Rev. Lett. vol. 102, pp. 026807, 2009.
Andrea F. Young, and Philip Kim, “Quantum interference and Klein tunnelling in graphene heterojunctions”, Nature Physics vol. 5, pp. 222 – 226, 2009.
Jürgen Wurm, Adam Rycerz, İnanç Adagideli, Michael Wimmer, Klaus Richter, and Harold U. Baranger, “Symmetry Classes in Graphene Quantum Dots: Universal Spectral Statistics, Weak Localization, and Conductance Fluctuations”, Phys. Rev. Lett. vol. 102, pp. 056806, 2009.
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.
D.Wang and G. Jin, “Magnetically confined states of Dirac electrons in a graphene-based quantum annulus”, Europhys. Lett. Assoc. , vol. 88, no. 1, 2009.
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.
N. M. R. Peres, J. N. B. Rodrigues, T. Stauber and J. M. B. Lopes dos Santos, “Dirac electrons in graphene-based quantum wires and quantum dots”, J. Phys.: Condens. Matter, vol. 21,pp. 344202,
Dali Wang, Guojun Jin, “Bound states of Dirac electrons in a graphene-based magnetic quantum dot”, Dali Wang, Guojun Jin, Phys. Lett. A, vol. 373, pp. 4082, 2009.
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.
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.
P. Recher and B. Trauzettel “Quantum dots and spin qubits in graphene”, Nanotechnology, vol. 21, pp. 302001, 2010.
G. Giavaras, P. A. Maksyma, M. Roy, “Electron confinement in single layer graphene quantum dots: Semiclassical approach”, Physica E, vol. 42, pp. 715, 2010.
Cong-Hua Yan and Lian-Fu Wei, “Size effects in Aharonov-Bohm graphene rings”, J. Phys.: Condens. Matter, vol. 22, pp. 295503, 2010.
N. J. M. Horing and S. Y. Liu, “Energy spectrum and density of states for a graphene quantum dot in a magnetic field”, J. Phys.: Condens. Matter, vol. 22, pp. 025502, 2010.
N. J. M. Horing and S. Y. Liu, “Energy spectrum and density of states for a graphene quantum dot in a magnetic field”, J. Phys.: Condens. Matter, vol. 22, pp. 159801, 2010.
J. W. Gonz´alez, M. Pacheco, L. Rosales and P. A. Orellana, “Bound states in the continuum in graphene quantum dot structures” Europhys. Lett., vol. 91, pp. 66001, 2010.
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.
F. Libich, S. Rotter, J. Guttinger, C. Stampfer, J.Burgdörfer, “Transition to Landau levels in graphene quantum dots”, Phys. Rev. B, vol. 81, pp. 245411, 2010.
M. Wimmer, A. R. Akhmerov, and F. Guinea, “Robustness of edge states in graphene quantum dots”, Phys. Rev. B, vol. 82, pp. 045409, 2010.
G. Giavaras and F. Nori, “Dirac gap-induced graphene quantum dot in an electronic potential”, Phys. Rev. B, vol. 83, pp. 165427, 2011.
M. Ramezani Masir, P. Vasilopoulos and F. M. Peeters, J. “Graphene in inhomogeneous magnetic fields: bound, quasi-bound and scattering states”, Phys.: Condens. Matter, vol. 23, pp. 315301,
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.
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.
G. Pal, W. Apel, and L. Schweitzer, “Electric transport through circular graphene quantum dots: Presence of disorder”, Phys. Rev. B, vol. 84, pp. 075446 2011.
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.
M. Tahir and K. Sabeeh, “Gap opening in the zeroth Landau level in gapped graphene: pseudo- Zeeman splitting in an angular magnetic field”, J. Phys.: Condens. Matter, vol. 24, pp. 135005,
S. C. Kim, J. W. Lee and S-R Eric Yang, “Resonant, non-resonant, and anomalous states of Dirac electrons in a parabolic well in the presence of magnetic fields”, J. Phys.: Condens. Matter, vol. 24, pp. 495302, 2012.
M Gruji ́, M Zarenia, M Tadi ́ and F. M. Peeters, “Interband optical absorption in a circular graphene quantum dot” Phys. Scr. T, vol. 149, pp. 014056, 2012.
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There are 66 citations in total.

Details

Journal Section	Natural Sciences Research Article
Authors	Defne Akay Bekir Sıtkı Kandemir This is me
Publication Date	January 19, 2016
Published in Issue	Year 2016 Volume: 37 Issue: 1

Cite

APA	Akay, D., & Kandemir, B. S. (2016). Off-plane Impurity Effects in Graphene Quantum Dots. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, 37(1), 20-29. https://doi.org/10.17776/csj.14715
AMA	Akay D, Kandemir BS. Off-plane Impurity Effects in Graphene Quantum Dots. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. April 2016;37(1):20-29. doi:10.17776/csj.14715
Chicago	Akay, Defne, and Bekir Sıtkı Kandemir. “Off-Plane Impurity Effects in Graphene Quantum Dots”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 37, no. 1 (April 2016): 20-29. https://doi.org/10.17776/csj.14715.
EndNote	Akay D, Kandemir BS (April 1, 2016) Off-plane Impurity Effects in Graphene Quantum Dots. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 37 1 20–29.
IEEE	D. Akay and B. S. Kandemir, “Off-plane Impurity Effects in Graphene Quantum Dots”, Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, vol. 37, no. 1, pp. 20–29, 2016, doi: 10.17776/csj.14715.
ISNAD	Akay, Defne - Kandemir, Bekir Sıtkı. “Off-Plane Impurity Effects in Graphene Quantum Dots”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 37/1 (April 2016), 20-29. https://doi.org/10.17776/csj.14715.
JAMA	Akay D, Kandemir BS. Off-plane Impurity Effects in Graphene Quantum Dots. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. 2016;37:20–29.
MLA	Akay, Defne and Bekir Sıtkı Kandemir. “Off-Plane Impurity Effects in Graphene Quantum Dots”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, vol. 37, no. 1, 2016, pp. 20-29, doi:10.17776/csj.14715.
Vancouver	Akay D, Kandemir BS. Off-plane Impurity Effects in Graphene Quantum Dots. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. 2016;37(1):20-9.

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