Electronic band structure of magnetic bilayer graphene superlattices

Pham, C. Huy; Nguyen, Thanh; Nguyen, Van-Cuong

doi:10.1063/1.4896530

Cited by 12 publications

(6 citation statements)

References 29 publications

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“…For the finite bilayer-graphene-based superlattices we are only able to calculate T n numerically. Remarkably, numerical calculations performed for two potential models, the electric potential studied in [23] and the magnetic potential studied in [24], show seemingly the (n − 1)-fold resonance splitting similar to that presented above for single-layer graphene superlattices.…”

Section: Discussionsupporting

confidence: 75%

Tunneling through finite graphene superlattices: resonance splitting effect

Pham

Nguyen²

2015

J. Phys.: Condens. Matter

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An exact expression of the transmission probability through a finite graphene superlattice with an arbitrary number of potential barriers n is derived in two cases of the periodic potential: rectangular electric potential and δ-function magnetic potential. Obtained transmission probabilities show two types of resonance energy: barrier-induced resonance energies unchanged as n varies and well-induced resonance energies that have undergone the (n - 1)-fold splitting as n increases. Supported by numerical calculations for various types of graphene superlattices, these analytical findings are assumed to be equally applied to all of the finite graphene superlattices regardless of their potential nature (electric or magnetic) and potential barrier shapes.

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Section: Discussionsupporting

confidence: 75%

Tunneling through finite graphene superlattices: resonance splitting effect

Pham

Nguyen²

2015

J. Phys.: Condens. Matter

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“…We note that the basic coefficient C can be considered as the spinor represented in a basis that depends on r according to Eq. (6). Then, Eq.…”

Section: General Considerationmentioning

confidence: 99%

“…We note that the basic coefficient C can be considered as the spinor represented in a basis that depends on r according to equation (6). Then, equation ( 5) actually describes a (nonunitary) basis transformation of the spinor.…”

Section: General Considerationmentioning

confidence: 99%

“…For the graphene nanostructures induced by one-dimensional (1D) potentials, such as the multi-barrier structures or the n-p-n-junctions, the T-matrix calculations have been developed to study the energy spectrum [3] as well as the dynamical characteristics [4]. In particular, the T-matrix approach was successfully used to calculate the electronic band structure and the transport properties of various single-/bi-layer graphene superlattices induced by periodic electrostatic and/ or magnetic potentials (see, for example, [5,6] and references therein). Note that, traditionally, the T-matrix approach was just suggested for (quasi) 1D potential problems.…”

Section: Introductionmentioning

confidence: 99%

“…Appendix A: W-matrix for E = Ū ± ν∆ As was mentioned above, the W( Ū , r)-matrix as defined in (6) diverges as E → Ū ± ν∆. Note that the basic solutions are always defined up to constant factors that do not depend on r. To cure this divergence, we introduce the regularization factors to the basic solutions so that they remain finite in the limit of E → Ū ± ν∆.…”

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confidence: 99%

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The transfer matrix approach to circular graphene quantum dots

Nguyen¹,

Nguyen²,

Nguyen³

2016

J. Phys.: Condens. Matter

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We adapt the transfer matrix (T-matrix) method originally designed for one-dimensional quantum mechanical problems to solve the circularly symmetric two-dimensional problem of graphene quantum dots. In similarity to one-dimensional problems, we show that the generalized T-matrix contains rich information about the physical properties of these quantum dots. In particular, it is shown that the spectral equations for bound states as well as quasi-bound states of a circular graphene quantum dot and related quantities such as the local density of states and the scattering coefficients are all expressed exactly in terms of the T-matrix for the radial confinement potential.As an example, we use the developed formalism to analyse physical aspects of a graphene quantum dot induced by a trapezoidal radial potential. Among the obtained results, it is in particular suggested that the thermal fluctuations and electrostatic disorders may appear as an obstacle to controlling the valley polarization of Dirac electrons.

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Strain impacts on commensurate bilayer graphene superlattices: Distorted trigonal warping, emergence of bandgap and direct-indirect bandgap transition

Khatibi

Namiranian

Parhizgar

2019

Diamond and Related Materials

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Due to low dimensionality, the controlled stacking of the graphene films and their electronic properties are susceptible to environmental changes including strain. The strain-induced modification of the electronic properties such as the emergence and modulation of bandgaps crucially depends on the stacking of the graphene films. However, to date, only the impact of strain on electronic properties of Bernal and AA-stacked bilayer graphene has been extensively investigated in theoretical studies. Exploiting density functional theory and tight-binding calculation, we investigate the impacts of in-plane strain on two different class of commensurate twisted bilayer graphene (TBG) which are even/odd under sublattice exchange (SE) parity. We find that the SE odd TBG remains gapless whereas the bandgap increases for the SE even TBG when applying equibiaxial tensile strain. Moreover, we observe that for extremely large mixed strains both investigated TBG superstructures demonstrate direct-indirect bandgap transition. arXiv:1809.08555v1 [cond-mat.mes-hall]

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Electronic band structure of magnetic bilayer graphene superlattices

Cited by 12 publications

References 29 publications

Tunneling through finite graphene superlattices: resonance splitting effect

Tunneling through finite graphene superlattices: resonance splitting effect

The transfer matrix approach to circular graphene quantum dots

Strain impacts on commensurate bilayer graphene superlattices: Distorted trigonal warping, emergence of bandgap and direct-indirect bandgap transition

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