Electron transport in a two-terminal Aharonov–Bohm ring with impurities

Kokoreva, M. A.; Margulis, V. A.; Pyataev, M. A.

doi:10.1016/j.physe.2011.05.006

Cited by 9 publications

(10 citation statements)

References 47 publications

(94 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To improve the realism of the boundary approximation, we use the isoparametric version of the Q 2 elements, i.e., both the wave function and the boundary of the ring are approximated by quadratic polynomials. We note in passing that the issue of a piecewise linear boundary should be compared with Kokoreva et al 37 as corners might by interpreted as pointlike scatterers. As Hardy space parameters we use κ 0 = 0.13 exp(0.2iπ) and n H = 10.…”

Section: Aharonov-bohm Effectmentioning

confidence: 87%

Finite-element methods for spatially resolved mesoscopic electron transport

Kramer

2013

Phys. Rev. B

View full text Add to dashboard Cite

A finite-element method is presented for calculating the quantum conductance of mesoscopic two-dimensional electron devices of complex geometry attached to semi-infinite leads. For computational purposes, the leads must be cut off at some finite length. To avoid spurious, unphysical reflections, this is modeled by transparent boundary conditions. We introduce the Hardy space infinite-element technique from acoustic scattering as a way of setting up transparent boundary conditions for transport computations spanning the range from the quantum mechanical to the quasiclassical regime. These boundary conditions are exact even for wave packets and thus are especially useful in the limit of high energies with many excited modes. Yet, they possess a memory-friendly sparse matrix representation. In addition to unbounded domains, Hardy space elements allow us to truncate those parts of the computational domain which are irrelevant for the calculation of the transport properties. Thus, the computation can be done only on the region that is essential for a physically meaningful simulation of the scattering states. The benefits of the method are demonstrated by three examples. The convergence properties are tested on the transport through a quasi-one-dimensional quantum wire. It is shown that higher-order finite elements considerably improve current conservation and establish the correct phase shift between the real and the imaginary parts of the electron wave function. The Aharonov-Bohm effect demonstrates that characteristic features of quantum interference can be assessed. A simulation of electron magnetic focusing exemplifies the capability of the computational framework to study the crossover from quantum to quasiclassical behavior.

show abstract

Section: Aharonov-bohm Effectmentioning

confidence: 87%

Finite-element methods for spatially resolved mesoscopic electron transport

Kramer

2013

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…A rigorous mathematical model of our system of coupled circles is constructed by a conventional way by use of the operator extensions theory (see, e.g., [14][15][16][17][18][19]). We assume that the contacts are located at the opposite points (a, ϕ 1 ) and (a, ϕ 2 ), where ϕ 1 = 0, ϕ 2 = π (see Fig.…”

Section: Chain Of Circlesmentioning

confidence: 99%

Periodic chain of disks in a magnetic field: bulk states and edge states

Grishanov¹,

Eremin²,

Ivanov³

et al. 2015

Nanosist.: fiz. him. mat.

View full text Add to dashboard Cite

An explicitly solvable model for periodic chain of coupled disks in orthogonal magnetic field is considered. The spectrum for the Hamiltonian is compared with the spectrum for the corresponding chain of circles. These models are used for the comparison of the bulk and edge states. It is found that for some range of the magnetic field values the lowest band for the circles system lies below the spectrum for the corresponding disks system, i.e. the edge band is below and is separated from the lowest bulk band.

show abstract

“…The general form of the boundary conditions can be obtained from the current conservation law [7,13,14]. We will restrict ourself by the case of continues wave function that corresponds to equal effective width of rings and connecting wires.…”

Section: Dispersion Relationmentioning

confidence: 99%

“…The interest to the systems is stipulated by the possibility to tune the resistance in a very wide range by application of electric or magnetic field and the possibility to obtain specific transport properties of the system by variation of its geometry. The superlattice made of nanorings is of particular interest because the quantum ring is one of the simplest systems which exhibits quantum interference phenomena such as Aharonov-Bohm oscillations [9] persistent current [10] and Fano resonances [11][12][13][14]. A number of experimental studies have shown that quantum interference effects can be observed at individual quantum rings [15] and two-dimensional arrays [16] of rings.…”

Section: Introductionmentioning

confidence: 99%

Spectral and Transport Properties of One-Dimensional Nanoring Superlattice

Pyataev

Kokoreva

2013

Int. J. Mod. Phys. B

View full text Add to dashboard Cite

Spectral properties of periodic one-dimensional array of nanorings in a magnetic field are investigated. Two types of the superlattice are considered. In the first one, rings are connected by short one-dimensional wires while in the second one rings have immediate contacts between each other. The dependence of the electron energy on the quasimomentum is obtained from the Schrödinger equation for the Bloch wave function. We have found an interesting feature of the system, namely, presence of discrete energy levels in the spectrum. The levels can be located in the gaps or in the bands depending on parameters of the system. The levels correspond to bound states and electrons occupying these levels are located on individual rings or couples of neighboring rings and do not contribute to the charge transport. The wave function for the bound states corresponding to the discrete levels is obtained. Modification of electron energy spectrum with variation of system parameters is discussed.

show abstract

Electron transport in a two-terminal Aharonov–Bohm ring with impurities

Cited by 9 publications

References 47 publications

Finite-element methods for spatially resolved mesoscopic electron transport

Finite-element methods for spatially resolved mesoscopic electron transport

Periodic chain of disks in a magnetic field: bulk states and edge states

Spectral and Transport Properties of One-Dimensional Nanoring Superlattice

Contact Info

Product

Resources

About