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

Du, Long; Wang, Yong-Long; Liang, Guo-Hua; Kang, Guang-Zhen; Liu, Xiaojun; Zong, Hong-Shi

doi:10.1016/j.physe.2015.10.011

Cited by 10 publications

(6 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Later on, an approach which does not suffer from this ambiguity was devised by Jensen and Koppe [4] in the 1970s and by Da Costa [5,6] in the 1980s, showing that a geometry-induced potential (GIP) acts upon the dynamics 1 . Since then, some research on the subject has been reported, such as a path integral formulation [13,14], effects on the eigenstates of nanostructures [15,16], interaction with an electromagnetic potential [17,18,19,20], modeling of bound states on conical surfaces [21,22,23], spinorbit interaction [24,25,26], electronic transport in nanotubes [27,28], and bent waveguides [11,29,30,31], just to name a few.…”

Section: Introductionmentioning

confidence: 99%

Quantum mechanics of a constrained particle and the problem of prescribed geometry-induced potential

2017

View full text Add to dashboard Cite

The experimental techniques have evolved to a stage where various examples of nanostructures with nontrivial shapes have been synthesized, turning the dynamics of a constrained particle and the link with geometry into a realistic and important topic of research. Some decades ago, a formalism to deduce a meaningful Hamiltonian for the confinement was devised, showing that a geometry-induced potential (GIP) acts upon the dynamics. In this work we study the problem of prescribed GIP for curves and surfaces in Euclidean space R 3 , i.e., how to find a curved region with a potential given a priori. The problem for curves is easily solved by integrating Frenet equations, while the problem for surfaces involves a non-linear 2nd order PDE. Here, we explore the GIP for surfaces invariant by a 1-parameter group of isometries of R 3 , which turns the PDE into an ODE and leads to cylindrical, revolution, and helicoidal surfaces. Helicoidal surfaces are particularly important, since they are natural candidates to establish a link between chirality and the GIP. Finally, for the family of helicoidal minimal surfaces, we prove the existence of geometryinduced bound and localized states and the possibility of controlling the change in the distribution of the probability density when the surface is subjected to an extra charge.

show abstract

Section: Introductionmentioning

confidence: 99%

Quantum mechanics of a constrained particle and the problem of prescribed geometry-induced potential

2017

View full text Add to dashboard Cite

show abstract

“…In consequence, the commutators

[p_{i}, p_{j}]

turn out to satisfy the following relation with

f,_{k} \equiv \partial f / \partial x_{k}

false[p_{i}, p_{j} false] = \frac{i ℏ}{2} ((n_{j} n_{i, l} - n_{i} n_{j, l}) p_{l} + p_{l} (n_{j} n_{i, l} - n_{i} n_{j, l})),

and the Hamiltonian operator turns out to be,

H = \frac{p^{2}}{2 μ} - \frac{ℏ^{2}}{8 μ} M^{2} + V_{G} .

The second and key finding of this Letter is: With the quantum condition being imposed, the curvature‐induced potential

V_{G}

proves to be the geometric potential what has been expected for more than three and a half decades. Being

K \equiv \nabla_{N} n : \nabla_{N} n = {(n_{i, j})}^{2}

in fact the trace of square of the extrinsic curvature tensor, the geometric potential is

V_{G} = - \frac{ℏ^{2}}{4 μ} K + \frac{ℏ^{2}}{8 μ} M^{2}

…”

Section: Dirac Brackets and Quantization Conditionsmentioning

confidence: 99%

“…This CPF has a distinct feature for no presence of any ambiguity. It is thus a powerful tool to examine various curvature‐induced consequences in two‐dimensional curved surfaces or curved wires . Experimental confirmations of the geometric potential include: an optical realization in 2010 and an observation of its effects in an uneven periodic caged peanut‐shaped nanostructure in 2012 .…”

Section: Introductionmentioning

confidence: 99%

Geometric Potential and Dirac Quantization

Lian

Liu

2018

Annalen der Physik

View full text Add to dashboard Cite

A fundamental problem regarding the Dirac quantization of a free particle on an N − 1 (N ≥ 2) curved hypersurface embedded in N flat space is the impossibility to give the same form of the curvature-induced quantum potential, the geometric potential as commonly called, as that given by the Schrödinger equation method where the particle moves in a region confined by a thin-layer sandwiching the surface. This problem is resolved by means of a previously proposed scheme that hypothesizes a simultaneous quantization of positions, momenta, and Hamiltonian, among which the operator-ordering-free section is identified and is then found sufficient to lead to the expected form of geometric potential.

show abstract

“…Quantum transmission is a natural property of nanostructure devices, in which the topological effect is considerable. Recently, the geometric effects on the coherent electron transport have been investigated in bent cylindrical surfaces [28], and in the surface of a truncated cone [29]. Additionally, the curvature effects on vitrification behavior has been discussed for polymer nanotubes [30].…”

Section: Introductionmentioning

confidence: 99%

Coherent electron transport in a helical nanotube

Liang

Wang

et al. 2016

Physica E: Low-dimensional Systems and Nanostructures

Self Cite

View full text Add to dashboard Cite

The quantum dynamics of carriers bound to helical tube surfaces is investigated in a thin-layer quantization scheme. By numerically solving the open-boundary Schrödinger equation in curvilinear coordinates, geometric effect on the coherent transmission spectra is analysed in the case of single propagating mode as well as multimode. It is shown that, the coiling endows the helical nanotube with different transport properties from a bent cylindrical surface. Fano resonance appears as a purely geometric effect in the conductance, the corresponding energy of quasibound state is obviously influenced by the torsion and length of the nanotube. We also find new plateaus in the conductance. The transport of double-degenerate mode in this geometry is reminiscent of the Zeeman coupling between the magnetic field and spin angular momentum in quasi-one-dimensional structure.

show abstract

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

Cited by 10 publications

References 35 publications

Quantum mechanics of a constrained particle and the problem of prescribed geometry-induced potential

Quantum mechanics of a constrained particle and the problem of prescribed geometry-induced potential

Geometric Potential and Dirac Quantization

Coherent electron transport in a helical nanotube

Contact Info

Product

Resources

About