Geometric influences of a particle confined to a curved surface embedded in three-dimensional Euclidean space

Abstract

In the spirit of the thin-layer quantization approach, we give the formula of the geometric influences of a particle confined to a curved surface embedded in three-dimensional Euclidean space. The geometric contributions can result from the reduced commutation relation between the acted function depending on normal variable and the normal derivative. According to the formula, we obtain the geometric potential, geometric momentum, geometric orbital angular momentum, geometric linear Rashba and cubic Dresselhaus spin-orbit couplings. As an example, a truncated cone surface is considered. We find that the geometric orbital angular momentum can provide an azimuthal polarization for spin, and the sign of the geometric Dresselhaus spin-orbit coupling can be flipped through the inclination angle of generatrix.

12 pages, 2 figures

References in corpus (5)

• Coupling of Spin and Orbital Motion of Electrons in Carbon Nanotubes
• Two-Dimensional Matter: Order, Curvature and Defects
• Quantum mechanics on curved 2D systems with electric and magnetic fields
• Large spin-orbit coupling in carbon nanotubes
• Nonrelativistic quantum dynamics on a cone with and without a constraining potential

Cited by in corpus (27)

• Geometrical phase and Hall effect associated with the transverse spin of light
• Charged fermion in $(1+2)$-dimensional wormhole with axial magnetic field
• Electronic properties of bilayer graphene catenoid bridge
• Pseudo-magnetic field and effective spin-orbit interaction for a spin-1/2 particle confined to a curved surface
• Geometric effects resulting from square and circular confinements for a particle constrained to a space curve
• Position-dependent mass effects in the electronic transport of two-dimensional quantum systems
• Study of electronic properties, Magnetization and persistent currents in a mesoscopic ring by controlled curvature
• Electromagnetic wave propagating along a space curve
• Modifications of electron states, magnetization and persistent current in a quantum dot by controlled curvature
• Curvature control of the superconducting proximity effect in diffusive ferromagnetic nanowires
• Geometric Potential Resulting from Dirac Quantization
• Effective quantum dynamics in curved thin-layer system with inhomogeneous confinement
• Effective dynamics for a spin-1/2 particle constrained to a space curve in an electric and magnetic field
• The theory of gravitation: A tale of many questions and few answers
• Scattering of charged fermion to two-dimensional wormhole with constant axial magnetic flux
• The geometric potential of a double-frequency corrugated surface
• Curved non-interacting two-dimensional electron gas with anisotropic mass
• Quantum mechanics of fermion confined to a curved surface in Foldy-Wouthuysen representation
• Geometric effects on the electronic structure and the bound states in annular corrugated wires
• Geometric effects of a quarter of corrugated torus
• No existence of the geometric potential for a Dirac fermion on two-dimensional curved surfaces of revolution
• General covariant geometric momentum, gauge potential and a Dirac fermion on a two-dimensional sphere
• Non-constant geometric curvature for tailored spin-orbit coupling and chirality in superconductor-magnet heterostructures
• Spin-deformation coupling in two-dimensional polar materials
• Quantum effective potential from discarded degrees of freedom
• Geometric momentum and angular momentum for charge-monopole system
• Effects of curvature on the electronic states of a two-dimensional mesoscopic ring