Curved non-interacting two-dimensional electron gas with anisotropic mass

Abstract

In the da Costa's thin-layer approach, a quantum particle moving in a 3D sample is confined on a curved thin interface. At the end, the interface effects are ignored and such quantum particle is localized on a curved surface. A geometric potential arises and, since it manifests due to this confinement procedure, it depends on the transverse to the surface mass component. This inspired us to consider, in this paper, the effects due to an anisotropic effective mass on a non-interacting two dimensional electron gas confined on a curved surface, a fact not explored before in this context. By tailoring the mass, many investigations carried out in the literature can be improved which in turns can be useful to better designing electronic systems without modifying the geometry of a given system. Some examples are examined here, as a particle on helicoidal surface, on a cylinder, on a catenoid and on a cone, with some possible applications briefly discussed.

arXiv comment10 pages, 9 figures

References in corpus (25)

• Hyperbolic metamaterials: fundamentals and applications
• Transport of Dirac quasiparticles in graphene: Hall and optical conductivities
• Quantum mechanics on curved 2D systems with electric and magnetic fields
• Fractional Quantum Hall Effect in a Curved Space: Gravitational Anomaly and Electromagnetic Response
• Entanglement versus Quantum Discord in Two Coupled Double Quantum Dots
• Giant asymmetry of the longitudinal magnetoresistance in high-mobility two-dimensional electron gas on a cylindrical surface
• Pauli equation for a charged spin particle on a curved surface in an electric and magnetic field
• Geometry induced charge separation on a helicoidal ribbon
• Emergent Conformal Symmetry of Quantum Hall States on Singular surfaces
• Geometric influences of a particle confined to a curved surface embedded in three-dimensional Euclidean space
• Geometry induced potential on a 2D-section of a wormhole: catenoid
• Quantum particle confined to a thin-layer volume: Non-uniform convergence toward the curved surface
• Geometric effects in the electronic transport of deformed nanotubes
• Can the canonical quantization be accomplished within the intrinsic geometry?
• Landau levels, self-adjoint extensions and Hall conductivity on a cone
• Geometric effects resulting from square and circular confinements for a particle constrained to a space curve
• On the dynamics of a particle on a cone
• Metamaterials for Ballistic Electrons
• Signature of snaking states in the conductance of core-shell nanowires
• Modeling Kleinian cosmology with electronic metamaterials
• Electronic structure of helicoidal graphene: massless Dirac particles on a curved surface with a screw symmetry
• Geometric Potential Resulting from Dirac Quantization
• A Metamaterial-Inspired Model for Electron Waves in Bulk Semiconductors
• Transmission gaps from corrugations
• Generalized Centripetal Force Law and Quantization of Motion Constrained on 2D Surfaces

Cited by in corpus (6)

• Position-dependent mass effects in the electronic transport of two-dimensional quantum systems
• Position-dependent mass effects on a bilayer graphene catenoid bridge
• Schrödinger formalism for a particle constrained to a surface in ${\mathbb{R}}_1^3$
• Thermodynamic properties of an electron gas in a two-dimensional quantum dot: an approach using density of states
• Geometric scattering in the presence of line defects
• Quantum heat machines enabled by twisted geometry