The mass effects on two-dimensional relativistic fermions

Li, M.K.; Lee, S.J.; Kang, Tae Won

doi:10.1016/j.cap.2008.07.012

Cited by 5 publications

(4 citation statements)

References 10 publications

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“…It is worth pointing out that graphene (single atomic layer of graphite), a recently discovered material [19,20] which is receiving a lot of attention, exhibits several properties whose explanation involve the Dirac equation for massless fermions. For a comprehensive review see for example [21] Recent reports studying these effects [22,23] attest the use of the Dirac equation in explaining the properties of single-layer graphene .…”

Section: Introductionmentioning

confidence: 99%

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New exact solution of the one-dimensional Dirac equation for the Woods–Saxon potential within the effective mass case

Panella¹,

Biondini²,

Arda³

2010

J. Phys. A: Math. Theor.

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We study the one-dimensional Dirac equation in the framework of a position dependent mass under the action of a Woods-Saxon external potential. We find that constraining appropriately the mass function it is possible to obtain a solution of the problem in terms of the hypergeometric function. The mass function for which this turns out to be possible is continuous. In particular we study the scattering problem and derive exact expressions for the reflection and transmission coefficients which are compared to those of the constant mass case. For the very same mass function the bound state problem is also solved, providing a transcendental equation for the energy eigenvalues which is solved numerically.

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Section: Introductionmentioning

confidence: 99%

“…For a comprehensive review, see for example [21]. Recent reports studying these effects [22,23] attest the use of the Dirac equation in explaining the properties of single-layer graphene.…”

Section: Introductionmentioning

confidence: 99%

New exact solution of the one-dimensional Dirac equation for the Woods–Saxon potential within the effective mass case

Panella¹,

Biondini²,

Arda³

2010

J. Phys. A: Math. Theor.

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“…They found the system to be less sensitive to the temperature and more sensitive to the magnetic field, as compared to 2DEG. Li et al [10] calculated the chemical potential, total energy and specific heat as functions of the temperature, carrier concentration and the effective mass at low temperatures with relativistic effects. They evaluated and discussed the density distribution of massive Dirac fermions as functions of the effective mass and the carrier density, which could be varied in doped or gated graphene systems.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic properties of graphene using the static fluctuation approximation (SFA)

et al. 2017

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The thermodynamic properties of two-dimensional graphene nanosystems are investigated using the static fluctuation approximation (SFA). These properties are analyzed using both extensive and nonextensive statistical mechanics. It is found that these properties are less sensitive to temperature when using nonextensive — in contrast to extensive — statistical mechanics. It is also noted that the mean internal energy and the specific heat behave as a power law, Tα, at T < 8 eV; whereas they go to the classical limit for the two-dimensional ideal gas at T > 8 eV. The results are presented in a set of figures and one table. The roles played by the number of particles and the entropy parameter q are underlined. Whenever possible, comparisons are made to previous studies. It is concluded that Boltzmann–Gibbs statistics are not valid for some cases, and that SFA results are in good agreement with those obtained within other formalisms.

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“…However, its unusual material and physical properties have already captured the interest of many researchers working in condensedmatter physics [3][4][5][6]. This two-dimensional material is of very high quality, extremely strong, exhibits ballistic electronic transport on the micrometer scale at room temperature, can be chemically doped and its conductivity can be controlled with an electric field [7][8][9][10]. Graphene has a linear gapless spectrum, and therefore exhibits metallic conductivity even in the limit of nominally zero carrier concentration [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Graphene-based modulation-doped superlattice structures

Bolmatov

Mou

2011

J. Exp. Theor. Phys.

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The electronic transport properties of graphene-based superlattice structures are investigated. A graphene-based modulation-doped superlattice structure geometry is proposed and consist of periodically arranged alternate layers: InAs/graphene/GaAs/graphene/GaSb. Undoped graphene/GaAs/graphene structure displays relatively high conductance and enhanced mobilities at elevated temperatures unlike modulation-doped superlattice structure more steady and less sensitive to temperature and robust electrical tunable control on the screening length scale. Thermionic current density exhibits enhanced behaviour due to presence of metallic (graphene) mono-layers in superlattice structure. The proposed superlattice structure might become of great use for new types of wide-band energy gap quantum devices.Comment: 5 figure

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The mass effects on two-dimensional relativistic fermions

Cited by 5 publications

References 10 publications

New exact solution of the one-dimensional Dirac equation for the Woods–Saxon potential within the effective mass case

New exact solution of the one-dimensional Dirac equation for the Woods–Saxon potential within the effective mass case

Thermodynamic properties of graphene using the static fluctuation approximation (SFA)

Graphene-based modulation-doped superlattice structures

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