Electron position: jumping in double concentric quantum rings
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Electron position: jumping in double concentric quantum rings I. Filikhin, S. Matinyan, J. Nimmo and B.Vlahovic North Carolina Central University, Durham, NC, 27707, U.S.A. ABSTRACT Semiconductor heterostructures as quantum dots or quantum rings (QR) demonstrate discrete atom-like energy level structure. In an atom the position of an electron can be changed by electromagnetic field influence with accompaniment of quantum number change. In present work we show that in the weak coupled Double Concentric Quantum Ring (DCQR), the electron jumping is possible due to tunneling accompanied with level anti-crossing which has a place in a magnetic field. We study DCQR composed of GaAs in an Al0.70Ga0.30As substrate under influence of a magnetic field. In our model the DCQR is considered within three dimensional single sub-band effective mass approach. When a magnetic field is applied in the z direction, perpendicular to the DCQR plane. The results of the numerical calculations for DCQR are presented for DCQRs of different geometry. INTRODUCTION Quantum rings (QR) manifest specific electron proprieties in a magnetic field [1]. Double concentric rings [2,3] are relatively new quantum objects which have potential to have applications to nano science and nano-technology. In the present paper, we visualize interesting features occurring in DCQRs composed of GaAs in an Al0.70Ga0.30As substrate and particularly the single electron transfer from one ring to another under influence of a transverse magnetic field B . Therefore, we concentrate here, in contrast with the previous related papers, to the electron transition between the electron levels with different radial quantum number n . We will see that in the DCQR that have been place in a magnetic field, the electron spatial transition between the rings can occur due to electron energy levels anti-crossing. Also we study the geometry dependence of energy gap between the anti-crossed levels. The present work is close to Ref. [4] where the effect of a magnetic field on the energy levels of electrons and holes for cylindrical shaped DCQR was determined for fixed size and for radial quantum number n =1,2, with orbital quantum number | l | changing from 1 to 4. THEORY Thus, we come to the single electron scheme, and using the single sub-band approach that is justified due to the relatively large band gap of GaAs, the problem can be expressed by the following Schrodinger equation:
(Hˆ
kp
)
+ Vc (r ) Ψ (r ) = EΨ (r ) .
(1) 2
= ∇ , m* (r ) is the electron Here Hˆ kp is the single band kp-Hamiltonian operator Hˆ kp = −∇ 2m * effective mass, and Vc (r ) is the band gap potential, Vc (r ) = 0 inside the QR and is equal to E c
137
outside the QR, where E c is defined by the conduction band offset for the bulk. Ben-DanielDuke boundary conditions are used on interface of the material of QR and substrate. Introducing a magnetic field in the z direction ( B = Bˆz ) acting on a particle with a charge q , the Schrödinger equation (1) in cylindrical coordinates becomes: § 1 ∂ § ρ ∂Ψ · 1 ∂ 2
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