Curvature-induced bound states and coherent electron transport on the surface of a truncated cone

Abstract

We study the curvature-induced bound states and the coherent transport properties for a particle constrained to move on a truncated cone-like surface. With longitudinal hard wall boundary condition, the probability densities and spectra energy shifts are calculated, and are found to be obviously affected by the surface curvature. The bound-state energy levels and energy differences decrease as increasing the vertex angle or the ratio of axial length to bottom radius of the truncated cone. In a two-dimensional (2D) GaAs substrate with this geometric structure, an estimation of the ground-state energy shift of ballistic transport electrons induced by the geometric potential (GP) is addressed, which shows that the fraction of the ground-state energy shift resulting from the surface curvature is unnegligible under some region of geometric parameters. Furthermore, we model a truncated cone-like junction joining two cylinders with different radii, and investigate the effect of the GP on the transmission properties by numerically solving the open-boundary 2D Schrödinger equation with GP on the junction surface. It is shown that the oscillatory behavior of the transmission coefficient as a function of the injection energy is more pronounced when steeper GP wells appear at the two ends of the junction. Moreover, at specific injection energy, the transmission coefficient is oscillating with the ratio of the cylinder radii at incoming and outgoing sides.

8pages, 9figures

References in corpus (5)

• Quantum mechanics on curved 2D systems with electric and magnetic fields
• Quantum mechanics of a spin-orbit coupled electron constrained to a space curve
• Pauli equation for a charged spin particle on a curved surface in an electric and magnetic field
• Nonrelativistic quantum dynamics on a cone with and without a constraining potential
• Curvature effects on surface electron states in ballistic nanostructures

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• Geometric Potential Resulting from Dirac Quantization
• Fermionic fields in a four-dimensional Bonnor-Melvin-Lambda space-time
• Coherent electron transport in a helical nanotube
• Generalized Centripetal Force Law and Quantization of Motion Constrained on 2D Surfaces
• Geometric effects on the electronic structure and the bound states in annular corrugated wires
• Geometry-induced wavefunction collapse
• Dynamics and transport of Bose-Einstein condensates in bent potentials