Edge effects in graphene nanostructures: From multiple reflection expansion to density of states

Wurm, Juergen; Richter, Klaus; Adagideli, İnanç

doi:10.1103/physrevb.84.075468

Cited by 55 publications

(53 citation statements)

References 79 publications

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“…(19) we expect the susceptibility contribution χ T for a zigzag triangular quantum dot to be smaller than for the corresponding armchair system at the same temperature corresponding to Eq. (20). This behavior is also confirmed in Ref.…”

Section: B Comparability Of Numerical Results With Analytical Bulk Dsupporting

confidence: 86%

“…[20,21,57] the authors show in a general way how the trace formulas for "Schrödinger billiards" with classically regular or chaotic dynamics can be extended to an arbitrary shaped, field-free graphene flake including the most common types of boundaries, i.e., zigzag, armchair, and infinite-masstype edges. Resembling Eq.…”

Section: A General Semiclassical Frameworkmentioning

confidence: 99%

“…[20,57]. In order to compute its magnetic properties within semiclassical approximation, we combine these results with results adapted from Ref.…”

Section: Circular Billiard With Infinite-mass-type Edgesmentioning

confidence: 99%

“…The trace over the pseudospin propagator for an orbit family characterized by the tupel (w,v) can be calculated from Eq. (66) and reads [20,57] …”

Section: Circular Billiard With Infinite-mass-type Edgesmentioning

confidence: 99%

“…As recently shown, such an approach is suitable for the quantitative description and interpretation of the density of states [20] and conductance [21] of graphenebased cavities. This approach allows for the incorporation of graphene-specific boundary effects (zigzag, armchair, and infinite mass).…”

Section: Introductionmentioning

confidence: 99%

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Orbital magnetism of graphene nanostructures: Bulk and confinement effects

Heße

Richter

2014

Phys. Rev. B

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We consider the orbital magnetic properties of noninteracting charge carriers in graphene-based nanostructures in the low-energy regime. The magnetic response of such systems results both from bulk contributions and from confinement effects that can be particularly strong in ballistic quantum dots. First we provide a comprehensive study of the magnetic susceptibility χ of bulk graphene in a magnetic field for the different regimes arising from the relative magnitudes of the energy scales involved, i.e., temperature, Landau-level spacing, and chemical potential. We show that for finite temperature or chemical potential, χ is not divergent although the diamagnetic contribution χ 0 from the filled valance band exhibits the well-known −B −1/2 dependence. We further derive oscillatory modulations of χ , corresponding to de Haas-van Alphen oscillations of conventional two-dimensional electron gases. These oscillations can be large in graphene, thereby compensating the diamagnetic contribution χ 0 and yielding a net paramagnetic susceptibility for certain energy and magnetic field regimes. Second, we predict and analyze corresponding strong, confinement-induced susceptibility oscillations in graphene-based quantum dots with amplitudes distinctly exceeding the corresponding bulk susceptibility. Within a semiclassical approach we derive generic expressions for orbital magnetism of graphene quantum dots with regular classical dynamics. Graphene-specific features can be traced back to pseudospin interference along the underlying periodic orbits. We demonstrate the quality of the semiclassical approximation by comparison with quantum-mechanical results for two exemplary mesoscopic systems, a graphene disk with infinite mass-type edges, and a rectangular graphene structure with armchair and zigzag edges, using numerical tight-binding calculations in the latter case.

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Section: B Comparability Of Numerical Results With Analytical Bulk Dsupporting

confidence: 86%

Section: A General Semiclassical Frameworkmentioning

confidence: 99%

“…[20,57]. In order to compute its magnetic properties within semiclassical approximation, we combine these results with results adapted from Ref.…”

Section: Circular Billiard With Infinite-mass-type Edgesmentioning

confidence: 99%

“…The trace over the pseudospin propagator for an orbit family characterized by the tupel (w,v) can be calculated from Eq. (66) and reads [20,57] …”

Section: Circular Billiard With Infinite-mass-type Edgesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Orbital magnetism of graphene nanostructures: Bulk and confinement effects

Heße

Richter

2014

Phys. Rev. B

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Klein paradox in chaotic Dirac billiards

et al. 2019

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We investigate the Schrödinger (non-relativistic) and the Dirac ("relativistic") billiards in the universal regime. The study is based on a non-ideal quantum resonant scattering numerical simulation. We show universal results that reveal anomalous behavior on the conductance, on the shot-noise power and on the respective eigenvalues distributions. In particular, we demonstrate the Klein's paradox in the graphene and tunable suppression/amplification transitions on the typical observables of the quantum dots.

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