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  • 1.
    Andrijauskas, T.
    et al.
    Vilnius State University.
    Shylau, Artsem
    Linköping University, Department of Science and Technology, Physics and Electronics. Linköping University, The Institute of Technology.
    Zozoulenko, Igor
    Linköping University, Department of Science and Technology, Physics and Electronics. Linköping University, The Institute of Technology.
    Thomas-Fermi and Poisson modeling of gate electrostatics in graphene nanoribbon2012In: Lithuanian Journal of Physics, ISSN 1648-8504, Vol. 52, no 1, p. 63-69Article in journal (Refereed)
    Abstract [en]

    We describe a simple graphene nanoribbon and bottom gate system and present numerical algorithms for solving Poissons and Thomas-Fermi equations for electrons in the graphene nanoribbon. The Poissons equation is solved using finite difference and finite element methods. Using the Poisson and Thomas-Fermi equations we calculate an electrostatic potential and surface electron density in the graphene nanoribbon. Finally, the Poisson-Thomas-Fermi model for the graphene nanoribbon is compared to a tight-binding Hartree model. The results show a good correspondence with the tight-binding model. The developed solver of the Poissons equation can be used in the future calculations of more complex graphene and gate systems.

  • 2.
    Klos, J W
    et al.
    Adam Mickiewicz Univ Poznan, Fac Phys, Surface Phys Div, PL-61614 Poznan, Poland.
    Shylau, A A
    Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
    Zozoulenko, Igor
    Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
    Xu, Hengyi
    University Dusseldorf, Condensed Matter Phys Lab, D-40225 Dusseldorf, Germany .
    Heinzel, T
    University Dusseldorf, Condensed Matter Phys Lab, D-40225 Dusseldorf, Germany .
    Transition from ballistic to diffusive behavior of graphene ribbons in the presence of warping and charged impurities2009In: PHYSICAL REVIEW B, ISSN 1098-0121, Vol. 80, no 24, p. 245432-Article in journal (Refereed)
    Abstract [en]

    We study the effects of the long-range disorder potential and warping on the conductivity and mobility of graphene ribbons using the Landauer formalism and the tight-binding p-orbital Hamiltonian. We demonstrate that as the length of the structure increases the system undergoes a transition from the ballistic to the diffusive regime. This is reflected in the calculated electron-density dependencies of the conductivity and the mobility. In particular, we show that the mobility of graphene ribbons varies as mu(n)similar to n(-lambda), with 0 andlt;lambda less than or similar to 0.5. The exponent lambda depends on the length of the system with lambda=0.5 corresponding to short structures in the ballistic regime, whereas the diffusive regime lambda=0 (when the mobility is independent on the electron density) is reached for sufficiently long structures. Our results can be used for the interpretation of experimental data when the value of lambda can be used to distinguish the transport regime of the system (i.e., ballistic, quasiballistic, or diffusive). Based on our findings we discuss available experimental results.

  • 3.
    Radchenko, T. M.
    et al.
    Linköping University, Department of Science and Technology. Linköping University, Faculty of Health Sciences.
    Shylau, Artsem
    Linköping University, Department of Science and Technology, Physics and Electronics. Linköping University, The Institute of Technology.
    Zozoulenko, Igor
    Linköping University, Department of Science and Technology, Physics and Electronics. Linköping University, The Institute of Technology.
    Influence of correlated impurities on conductivity of graphene sheets: Time-dependent real-space Kubo approach2012In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 86, no 3, p. 035418-Article in journal (Refereed)
    Abstract [en]

    Numerical calculations of the conductivity of graphene sheets with random and correlated distributions of disorders have been performed using the time-dependent real-space Kubo formalism. The disorder was modeled by the long-range Gaussian potential describing screened charged impurities and by the short-range potential describing neutral adatoms both in the weak and strong scattering regimes. Our central result is that correlation in the spatial distribution for the strong short-range scatterers and for the long-range Gaussian potential do not lead to any enhancement of the conductivity in comparison to the uncorrelated case. Our results strongly indicate that the temperature enhancement of the conductivity reported in the recent study [J. Yan and M. S. Fuhrer, Phys. Rev. Lett. 107, 206601 (2011)] and attributed to the effect of dopant correlations was most likely caused by other factors not related to the correlations in the scattering potential.

  • 4.
    Shylau, A A
    et al.
    Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
    Klos, J W
    Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
    Zozoulenko, Igor
    Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
    Capacitance of graphene nanoribbons2009In: PHYSICAL REVIEW B, ISSN 1098-0121, Vol. 80, no 20, p. 205402-Article in journal (Refereed)
    Abstract [en]

    We present an analytical theory for the gate electrostatics and the classical and quantum capacitance of the graphene nanoribbons (GNRs) and compare it with the exact self-consistent numerical calculations based on the tight-binding p-orbital Hamiltonian within the Hartree approximation. We demonstrate that the analytical theory is in a good qualitative (and in some aspects quantitative) agreement with the exact calculations. There are however some important discrepancies. In order to understand the origin of these discrepancies we investigate the self-consistent electronic structure and charge density distribution in the nanoribbons and relate the above discrepancy to the inability of the simple electrostatic model to capture the classical gate electrostatics of the GNRs. In turn, the failure of the classical electrostatics is traced to the quantum mechanical effects leading to the significant modification of the self-consistent charge distribution in comparison to the noninteracting electron description. The role of electron-electron interaction in the electronic structure and the capacitance of the GNRs is discussed. Our exact numerical calculations show that the density distribution and the potential profile in the GNRs are qualitatively different from those in conventional split-gate quantum wires; at the same time, the electron distribution and the potential profile in the GNRs show qualitatively similar features to those in the cleaved-edge overgrown quantum wires. Finally, we discuss an experimental extraction of the quantum capacitance from experimental data.

  • 5.
    Shylau, Artsem
    Linköping University, Department of Science and Technology, Physics and Electronics. Linköping University, The Institute of Technology.
    Electron transport, interaction and spin in graphene and graphene nanoribbons2012Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Since the isolation of graphene in 2004, this novel material has become the major object of modern condensed matter physics. Despite of enormous research activity in this field, there are still a number of fundamental phenomena that remain unexplained and challenge researchers for further investigations. Moreover, due to its unique electronic properties, graphene is considered as a promising candidate for future nanoelectronics. Besides experimental and technological issues, utilizing graphene as a fundamental block of electronic devices requires development of new theoretical methods for going deep into understanding of current propagation in graphene constrictions.

    This thesis is devoted to the investigation of the effects of electron-electron interactions, spin and different types of disorder on electronic and transport properties of graphene and graphene nanoribbons.

    In paper I we develop an analytical theory for the gate electrostatics of graphene nanoribbons (GNRs). We calculate the classical and quantum capacitance of the GNRs and compare the results with the exact self-consistent numerical model which is based on the tight-binding p-orbital Hamiltonian within the Hartree approximation. It is shown that electron-electron interaction leads to significant modification of the band structure and accumulation of charges near the boundaries of the GNRs.

    It's well known that in two-dimensional (2D) bilayer graphene a band gap can be opened by applying a potential difference to its layers.  Calculations based on the one-electron model with the Dirac Hamiltonian predict a linear dependence of the energy gap on the potential difference. In paper II we calculate the energy gap in the gated bilayer graphene nanoribbons (bGNRs) taking into account the effect of electron-electron interaction. In contrast to the 2D bilayer systems the energy gap in the bGNRs depends non-linearly on the applied gate voltage. Moreover, at some intermediate gate voltages the energy gap can collapse which is explained by the strong modification of energy spectrum caused by the electron-electron interactions.

    Paper III reports on conductance quantization in grapehene nanoribbons subjected to a perpendicular magnetic field. We adopt the recursive Green's function technique to calculate the transmission coefficient which is then used to compute the conductance according to the Landauer approach. We find that the conductance quantization is suppressed in the magnetic field. This unexpected behavior results from the interaction-induced modification of the band structure which leads to formation of the compressible strips in the middle of GNRs. We show the existence of the counter-propagating states at the same half of the GNRs. The overlap between these states is significant and can lead to the enhancement of backscattering in realistic (i.e. disordered) GNRs.

    Magnetotransport in GNRs in the presence of different types of disorder is studied in paper IV. In the regime of the lowest Landau level there are spin polarized states at the Fermi level which propagate in different directions at the same edge. We show that electron interaction leads to the pinning of the Fermi level to the lowest Landau level and subsequent formation of the compressible strips in the middle of the nanoribbon. The states which populate the compressible strips are not spatially localized in contrast to the edge states. They are manifested through the increase of the conductance in the case of the ideal GNRs. However due to their spatial extension these states are very sensitive to different types of disorder and do not significantly contribute to conductance of realistic samples with disorder. In contrast, the edges states are found to be very robust to the disorder. Our calculations show that the edge states can not be easily suppressed and survive even in the case of strong spin-flip scattering.

    In paper V we study the effect of spatially correlated distribution of impurities on conductivity in 2D graphene sheets. Both short- and long-range impurities are considered. The bulk conductivity is calculated making use of the time-dependent real-space Kubo-Greenwood formalism which allows us to deal with systems consisting of several millions of carbon atoms. Our findings show that correlations in impurities distribution do not significantly influence the conductivity in contrast to the predictions based on the Boltzman equation within the first Born approximation.

    In paper VI we investigate spin-splitting in graphene in the presence of charged impurities in the substrate and calculate the effective g-factor. We perform self-consistent Thomas-Fermi calculations where the spin effects are included within the Hubbard approximation and show that the effective g-factor in graphene is enhanced in comparison to its one-electron (non-interacting) value. Our findings are in agreement to the recent experimental observations.

    List of papers
    1. Capacitance of graphene nanoribbons
    Open this publication in new window or tab >>Capacitance of graphene nanoribbons
    2009 (English)In: PHYSICAL REVIEW B, ISSN 1098-0121, Vol. 80, no 20, p. 205402-Article in journal (Refereed) Published
    Abstract [en]

    We present an analytical theory for the gate electrostatics and the classical and quantum capacitance of the graphene nanoribbons (GNRs) and compare it with the exact self-consistent numerical calculations based on the tight-binding p-orbital Hamiltonian within the Hartree approximation. We demonstrate that the analytical theory is in a good qualitative (and in some aspects quantitative) agreement with the exact calculations. There are however some important discrepancies. In order to understand the origin of these discrepancies we investigate the self-consistent electronic structure and charge density distribution in the nanoribbons and relate the above discrepancy to the inability of the simple electrostatic model to capture the classical gate electrostatics of the GNRs. In turn, the failure of the classical electrostatics is traced to the quantum mechanical effects leading to the significant modification of the self-consistent charge distribution in comparison to the noninteracting electron description. The role of electron-electron interaction in the electronic structure and the capacitance of the GNRs is discussed. Our exact numerical calculations show that the density distribution and the potential profile in the GNRs are qualitatively different from those in conventional split-gate quantum wires; at the same time, the electron distribution and the potential profile in the GNRs show qualitatively similar features to those in the cleaved-edge overgrown quantum wires. Finally, we discuss an experimental extraction of the quantum capacitance from experimental data.

    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-52823 (URN)10.1103/PhysRevB.80.205402 (DOI)
    Available from: 2010-01-12 Created: 2010-01-12 Last updated: 2012-08-28
    2. Interactions and screening in gated bilayer graphene nanoribbons
    Open this publication in new window or tab >>Interactions and screening in gated bilayer graphene nanoribbons
    2010 (English)In: PHYSICAL REVIEW B, ISSN 1098-0121, Vol. 82, no 11, p. 115311-Article in journal (Refereed) Published
    Abstract [en]

    The effects of Coulomb interactions on the electronic properties of bilayer graphene nanoribbons (BGNs) covered by a gate electrode are studied theoretically. The electron-density distribution and the potential profile are calculated self-consistently within the Hartree approximation. A comparison to their single-particle counterparts reveals the effects of interactions and screening. Due to the finite width of the nanoribbon in combination with electronic repulsion, the gate-induced electrons tend to accumulate along the BGN edges where the potential assumes a sharp triangular shape. This has a profound effect on the energy gap between electron and hole bands, which depends nonmonotonously on the gate voltage and collapses at intermediate electric fields. We interpret this behavior in terms of interaction-induced warping of the energy dispersion.

    Place, publisher, year, edition, pages
    American Physical Society, 2010
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-59954 (URN)10.1103/PhysRevB.82.115311 (DOI)000281845700005 ()
    Note
    Original Publication: Hengyi Xu, T Heinzel, Artsem A Shylau and Igor Zozoulenko, Interactions and screening in gated bilayer graphene nanoribbons, 2010, PHYSICAL REVIEW B, (82), 11, 115311. http://dx.doi.org/10.1103/PhysRevB.82.115311 Copyright: American Physical Society http://www.aps.org/ Available from: 2010-10-01 Created: 2010-10-01 Last updated: 2012-08-28
    3. Generic suppression of conductance quantization of interacting electrons in graphene nanoribbons in a perpendicular magnetic field
    Open this publication in new window or tab >>Generic suppression of conductance quantization of interacting electrons in graphene nanoribbons in a perpendicular magnetic field
    2010 (English)In: PHYSICAL REVIEW B, ISSN 1098-0121, Vol. 82, no 12, p. 121410-Article in journal (Refereed) Published
    Abstract [en]

    The effects of electron interaction on the magnetoconductance of graphene nanoribbons (GNRs) are studied within the Hartree approximation. We find that a perpendicular magnetic field leads to a suppression instead of an expected improvement of the quantization. This suppression is traced back to interaction-induced modifications of the band structure leading to the formation of compressible strips in the middle of GNRs. It is also shown that the hard-wall confinement combined with electron interaction generates overlaps between forward and backward propagating states, which may significantly enhance backscattering in realistic GNRs. The relation to available experiments is discussed.

    Place, publisher, year, edition, pages
    American Physical Society, 2010
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-60230 (URN)10.1103/PhysRevB.82.121410 (DOI)000281846000002 ()
    Note
    Original Publication: Artsem Shylau, Igor Zozoulenko, H Xu and T Heinzel, Generic suppression of conductance quantization of interacting electrons in graphene nanoribbons in a perpendicular magnetic field, 2010, PHYSICAL REVIEW B, (82), 12, 121410. http://dx.doi.org/10.1103/PhysRevB.82.121410 Copyright: American Physical Society http://www.aps.org/ Available from: 2010-10-08 Created: 2010-10-08 Last updated: 2012-08-28
    4. Interacting electrons in graphene nanoribbons in the lowest Landau level
    Open this publication in new window or tab >>Interacting electrons in graphene nanoribbons in the lowest Landau level
    2011 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 84, no 7, p. 075407-Article in journal (Refereed) Published
    Abstract [en]

    e study the effect of electron-electron interaction and spin on electronic and transport properties of gated graphene nanoribbons (GNRs) in a perpendicular magnetic field in the regime of the lowest Landau level (LL). The electron-electron interaction is taken into account using the Hartree and Hubbard approximations, and the conductance of GNRs is calculated on the basis of the recursive Greens function technique within the Landauer formalism. We demonstrate that, in comparison to the one-electron picture, electron-electron interaction leads to the drastic changes in the dispersion relation and structure of propagating states in the regime of the lowest LL showing a formation of the compressible strip and opening of additional conductive channels in the middle of the ribbon. We show that the latter are very sensitive to disorder and get scattered even if the concentration of disorder is moderate. In contrast, the edge states transport is very robust and cannot be suppressed even in the presence of a strong spin-flipping.

    Place, publisher, year, edition, pages
    American Physical Society, 2011
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-70105 (URN)10.1103/PhysRevB.84.075407 (DOI)000293374700003 ()
    Note
    Original Publication: Artsem Shylau and Igor Zozoulenko, Interacting electrons in graphene nanoribbons in the lowest Landau level, 2011, Physical Review B. Condensed Matter and Materials Physics, (84), 7, 075407. http://dx.doi.org/10.1103/PhysRevB.84.075407 Copyright: American Physical Society http://www.aps.org/ Available from: 2011-08-19 Created: 2011-08-19 Last updated: 2017-12-08
    5. Influence of correlated impurities on conductivity of graphene sheets: Time-dependent real-space Kubo approach
    Open this publication in new window or tab >>Influence of correlated impurities on conductivity of graphene sheets: Time-dependent real-space Kubo approach
    2012 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 86, no 3, p. 035418-Article in journal (Refereed) Published
    Abstract [en]

    Numerical calculations of the conductivity of graphene sheets with random and correlated distributions of disorders have been performed using the time-dependent real-space Kubo formalism. The disorder was modeled by the long-range Gaussian potential describing screened charged impurities and by the short-range potential describing neutral adatoms both in the weak and strong scattering regimes. Our central result is that correlation in the spatial distribution for the strong short-range scatterers and for the long-range Gaussian potential do not lead to any enhancement of the conductivity in comparison to the uncorrelated case. Our results strongly indicate that the temperature enhancement of the conductivity reported in the recent study [J. Yan and M. S. Fuhrer, Phys. Rev. Lett. 107, 206601 (2011)] and attributed to the effect of dopant correlations was most likely caused by other factors not related to the correlations in the scattering potential.

    Place, publisher, year, edition, pages
    American Physical Society, 2012
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-79666 (URN)10.1103/PhysRevB.86.035418 (DOI)000306410300005 ()
    Available from: 2012-08-14 Created: 2012-08-13 Last updated: 2017-12-07
    6. Interaction-induced enhancement of g-factor in graphene
    Open this publication in new window or tab >>Interaction-induced enhancement of g-factor in graphene
    2012 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 86, no 15, p. 155440-Article in journal (Refereed) Published
    Abstract [en]

    We study the effect of electron interaction on the spin-splitting and the g-factor in graphene in perpendicular magnetic field using the Hartree and Hubbard approximations within the Thomas-Fermi model. We found that the g-factor is enhanced in comparison to its free electron value g = 2 and oscillates as a function of the filling factor ѵ in the range 2 ≤ g < 4 reaching maxima at even ѵ and minima at odd ѵ. We outline the role of charged impurities in the substrate, which are shown to suppress the oscillations of the g-factor. This effect becomes especially pronounced with the increase of the impurity concentration, when the effective g-factor becomes independent of the filling factor reaching a value of g ≈ 2.3. A relation to the recent experiment is discussed.

    Place, publisher, year, edition, pages
    American Physical Society, 2012
    National Category
    Natural Sciences
    Identifiers
    urn:nbn:se:liu:diva-80620 (URN)10.1103/PhysRevB.86.155440 (DOI)000310130800005 ()
    Available from: 2012-08-28 Created: 2012-08-28 Last updated: 2017-12-07Bibliographically approved
  • 6.
    Shylau, Artsem
    et al.
    Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
    Zozoulenko, Igor
    Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
    Interacting electrons in graphene nanoribbons in the lowest Landau level2011In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 84, no 7, p. 075407-Article in journal (Refereed)
    Abstract [en]

    e study the effect of electron-electron interaction and spin on electronic and transport properties of gated graphene nanoribbons (GNRs) in a perpendicular magnetic field in the regime of the lowest Landau level (LL). The electron-electron interaction is taken into account using the Hartree and Hubbard approximations, and the conductance of GNRs is calculated on the basis of the recursive Greens function technique within the Landauer formalism. We demonstrate that, in comparison to the one-electron picture, electron-electron interaction leads to the drastic changes in the dispersion relation and structure of propagating states in the regime of the lowest LL showing a formation of the compressible strip and opening of additional conductive channels in the middle of the ribbon. We show that the latter are very sensitive to disorder and get scattered even if the concentration of disorder is moderate. In contrast, the edge states transport is very robust and cannot be suppressed even in the presence of a strong spin-flipping.

  • 7.
    Shylau, Artsem
    et al.
    Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
    Zozoulenko, Igor
    Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
    Xu, H
    University of Dusseldorf.
    Heinzel, T
    University of Dusseldorf.
    Generic suppression of conductance quantization of interacting electrons in graphene nanoribbons in a perpendicular magnetic field2010In: PHYSICAL REVIEW B, ISSN 1098-0121, Vol. 82, no 12, p. 121410-Article in journal (Refereed)
    Abstract [en]

    The effects of electron interaction on the magnetoconductance of graphene nanoribbons (GNRs) are studied within the Hartree approximation. We find that a perpendicular magnetic field leads to a suppression instead of an expected improvement of the quantization. This suppression is traced back to interaction-induced modifications of the band structure leading to the formation of compressible strips in the middle of GNRs. It is also shown that the hard-wall confinement combined with electron interaction generates overlaps between forward and backward propagating states, which may significantly enhance backscattering in realistic GNRs. The relation to available experiments is discussed.

  • 8.
    Volkov, A. V.
    et al.
    Nizhny Novgorod State University, Russia.
    Shylau, Artsem
    Linköping University, Department of Science and Technology, Physics and Electronics. Linköping University, The Institute of Technology.
    Zozoulenko, Igor
    Linköping University, Department of Science and Technology, Physics and Electronics. Linköping University, The Institute of Technology.
    Interaction-induced enhancement of g-factor in graphene2012In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 86, no 15, p. 155440-Article in journal (Refereed)
    Abstract [en]

    We study the effect of electron interaction on the spin-splitting and the g-factor in graphene in perpendicular magnetic field using the Hartree and Hubbard approximations within the Thomas-Fermi model. We found that the g-factor is enhanced in comparison to its free electron value g = 2 and oscillates as a function of the filling factor ѵ in the range 2 ≤ g < 4 reaching maxima at even ѵ and minima at odd ѵ. We outline the role of charged impurities in the substrate, which are shown to suppress the oscillations of the g-factor. This effect becomes especially pronounced with the increase of the impurity concentration, when the effective g-factor becomes independent of the filling factor reaching a value of g ≈ 2.3. A relation to the recent experiment is discussed.

  • 9.
    Xu, Hengyi
    et al.
    University of Dusseldorf.
    Heinzel, T
    University of Dusseldorf.
    Shylau, Artsem A
    Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
    Zozoulenko, Igor
    Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
    Interactions and screening in gated bilayer graphene nanoribbons2010In: PHYSICAL REVIEW B, ISSN 1098-0121, Vol. 82, no 11, p. 115311-Article in journal (Refereed)
    Abstract [en]

    The effects of Coulomb interactions on the electronic properties of bilayer graphene nanoribbons (BGNs) covered by a gate electrode are studied theoretically. The electron-density distribution and the potential profile are calculated self-consistently within the Hartree approximation. A comparison to their single-particle counterparts reveals the effects of interactions and screening. Due to the finite width of the nanoribbon in combination with electronic repulsion, the gate-induced electrons tend to accumulate along the BGN edges where the potential assumes a sharp triangular shape. This has a profound effect on the energy gap between electron and hole bands, which depends nonmonotonously on the gate voltage and collapses at intermediate electric fields. We interpret this behavior in terms of interaction-induced warping of the energy dispersion.

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