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

TL;DR

This paper investigates how surface curvature affects bound states and electron transport on a truncated cone surface, revealing significant energy shifts and transmission oscillations influenced by geometric parameters.

Contribution

It provides a detailed analysis of curvature-induced bound states and transport properties on truncated cone surfaces, including estimations of energy shifts and the impact of geometric potential on transmission.

Findings

Bound-state energy levels decrease with increasing vertex angle.

Surface curvature causes notable energy shifts in electron states.

Transmission coefficients exhibit oscillatory behavior influenced by geometric parameters.

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 Schr\"odinger 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.