A Curved Noninteracting 2D Electron Gas with Anisotropic Mass

Souza, Pedro H.; Silva, Edilberto O.; Rojas, M.; Filgueiras, Cleverson

doi:10.1002/andp.201800112

Cited by 11 publications

(5 citation statements)

References 45 publications

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“…We emphasize that the 3D Minkowski geometry is suggested by the unusual dispersion relation characteristic of hyperbolic metamaterials, which makes possible a description in terms of an effective geometry as an alternative to the conventional concept of an effective mass as recently done in Ref. 10 , where the background geometry is still Euclidean.…”

Section: Introductionmentioning

confidence: 86%

Schrödinger formalism for a particle constrained to a surface in $\mathbb{R}_1^3$

Teixeira,

Leandro,

da Silva

et al. 2018

Preprint

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In this work it is studied the Schrödinger equation for a non-relativistic particle restricted to move on a surface S in a three-dimensional Minkowskian medium R 3 1 , i.e., the space R 3 equipped with the metric diag(−1, 1, 1). After establishing the consistency of the interpretative postulates for the new Schrödinger equation, namely the conservation of probability and the hermiticity of the new Hamiltonian built out of the Laplacian in R 3 1 , we investigate the confining potential formalism in the new effective geometry. Like in the well-known Euclidean case, it is found a geometryinduced potential acting on the dynamics V S = − 2 2m (εH 2 − K) which, besides the usual dependence on the mean (H) and Gaussian (K) curvatures of the surface, has the remarkable feature of a dependence on the signature of the induced metric of the surface: ε = +1 if the signature is (−, +), and ε = 1 if the signature is (+, +).Applications to surfaces of revolution in R 3 1 are examined, and we provide examples where the Schrödinger equation is exactly solvable. It is hoped that our formalism will prove useful in the modeling of novel materials such as hyperbolic metamaterials, which are characterized by a hyperbolic dispersion relation, in contrast to the usual spherical (elliptic) dispersion typically found in conventional materials.

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Section: Introductionmentioning

confidence: 86%

Schrödinger formalism for a particle constrained to a surface in $\mathbb{R}_1^3$

Teixeira,

Leandro,

da Silva

et al. 2018

Preprint

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“…Consider the case that S is the Euclidean plane. Then the Hamiltonian (3) reduces to (21), and in the position representation the time-independent Schrödinger equation reads…”

Section: Scattering By Parallel Line Defects In a Planementioning

confidence: 99%

“…The study of physical systems described by the Hamiltonian operator (2) have been a focus of attention for decades [11,15,16,17,18]. The generalizations of this Hamiltonian to particles interacting with electromagnetic fields, spin 1/2 particles, particles with position-dependent and anisotropic effective masses, and thin layers with small but finite thickness have been considered in [7,19,20,21,22,23].…”

Section: Introductionmentioning

confidence: 99%

Geometric scattering in the presence of line defects

Bui,

Mostafazadeh,

Seymen

2020

Preprint

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A non-relativistic scalar particle moving on a curved surface undergoes a geometric scattering whose behavior is sensitive to the theoretically ambiguous values of the intrinsic and extrinsic curvature coefficients entering the expression for the quantum Hamiltonian operator. This suggests using the scattering data to settle the ambiguity in the definition of the Hamiltonian. It has recently been shown that the inclusion of point defects on the surface enhances the geometric scattering effects. We perform a detailed study of the geometric scattering phenomenon in the presence of line defects for the case that the particle is confined to move on a Gaussian bump and the defect(s) are modeled by delta-function potentials supported on a line or a set of parallel lines normal to the scattering axis. In contrast to a surface having point defects, the scattering phenomenon associated with this system is generically geometric in nature in the sense that for a flat surface the scattering amplitude vanishes for all scattering angles θ except θ = θ 0 and π − θ 0 , where θ 0 is the angle of incidence. We show that the presence of the line defects amplifies the geometric scattering due to the Gaussian bump. This amplification effect is particularly strong when the center of the bump is placed between two line defects.

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“…( 7) depends on the position-dependence of the effective mass function m * . In general, the effective mass may be anisotropic, as a result of a non-symmetric energy band [34,35]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Position-dependent mass effects on a bilayer graphene catenoid bridge

Silva,

Furtado,

Ramos

2021

Preprint

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A Curved Noninteracting 2D Electron Gas with Anisotropic Mass

Cited by 11 publications

References 45 publications

Schrödinger formalism for a particle constrained to a surface in $\mathbb{R}_1^3$

Schrödinger formalism for a particle constrained to a surface in $\mathbb{R}_1^3$

Geometric scattering in the presence of line defects

Position-dependent mass effects on a bilayer graphene catenoid bridge

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