Curvature-induced toroidal bound states

Encinosa, M.; Mott, Lonnie

doi:10.1103/physreva.68.014102

Cited by 63 publications

(70 citation statements)

References 16 publications

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“…The β i are compared to those found in [25] where V C was included in the T 2 Hamiltonian and in [26] where it was not. These results indicate the soft constraint quantities are relatively insensitive to differing L and ω, and are better matched by the spectra of [25]. In tables II and III the ground and first excited state wave functions for the six cases described above are shown.…”

Section: Resultsmentioning

confidence: 99%

“…A procedure for determining the low-lying eigenvalues and eigenfunctions of H 0 has been given in [26] and applied to H C in [25] so the focus here may be placed on the method employed for solving Eq. (5).…”

Section: Methodsmentioning

confidence: 99%

“…The symmetry of the torus reduces computational intensiveness, but, because a torus has non-trivial mean and Gaussian curvatures, curvature effects remain important [25].…”

Section: Introductionmentioning

confidence: 99%

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Wave Functions in the Neighborhood of a Toroidal Surface; Hard vs. Soft Constraint

2005

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The curvature potential arising from confining a particle initially in three-dimensional space onto a curved surface is normally derived in the hard constraint q → 0 limit, with q the degree of freedom normal to the surface. In this work the hard constraint is relaxed, and eigenvalues and wave functions are numerically determined for a particle confined to a thin layer in the neighborhood of a toroidal surface. The hard constraint and finite layer (or soft constraint) quantities are comparable, but both differ markedly from those of the corresponding two dimensional system, indicating that the curvature potential continues to influence the dynamics when the particle is confined to a finite layer. This effect is potentially of consequence to the modelling of curved nanostructures.

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Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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Wave Functions in the Neighborhood of a Toroidal Surface; Hard vs. Soft Constraint

2005

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“…With the advent and development of nanostructure and quantum waveguide technology [8,9], the geometric effects were observed experimentally in some nano-devices [6,10]. For the constrained systems with novel geometries, a great deal of theoretical works have been reported [11][12][13][14][15][16]. Furthermore,in the presence of electromagnetic (EM) field with a proper choice of gauge, Giulio Ferrari and Giampaolo Cuoghi derived the surface Schrödinger equation (SSE) for a spinless charged particle constrained on a general curved surface without source current perpendicular to the thinfilm surface.…”

Section: Introductionmentioning

confidence: 99%

“…Several studies have dis-cussed the effect of the geometric potential to the electronic states [12,[19][20][21]. Geometric actions were investigated on some special surfaces of revolution [16,[22][23][24].…”

Section: Introductionmentioning

confidence: 99%

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

Wang

Liang

et al. 2016

Physica E: Low-dimensional Systems and Nanostructures

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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.

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Spin Interference Effects in Rashba Quantum Rings

Ortix

2018

NanoScience and Technology

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Quantum interference effects in rings provide suitable means to control spins at the mesoscopic scale. In this chapter we present the theory underlying spin-induced modulations of unpolarized currents in quantum rings subject to the Rashba spin-orbit interaction. We discuss explicitly the connection between the conductance modulations and the geometric phase acquired by the spin during transport, as well as pathways to directly control them.arXiv:1810.03843v1 [cond-mat.mes-hall]

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Curvature-induced toroidal bound states

Cited by 63 publications

References 16 publications

Wave Functions in the Neighborhood of a Toroidal Surface; Hard vs. Soft Constraint

Wave Functions in the Neighborhood of a Toroidal Surface; Hard vs. Soft Constraint

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

Spin Interference Effects in Rashba Quantum Rings

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