Impurity center in a semiconductor quantum ring in the presence of a radial electric field

Abstract

The problem of an impurity electron in a quantum ring (QR) in the presence of a radially directed strong external electric field is investigated in detail. Both an analytical and a numerical approach to the problem are developed. The analytical investigation focuses on the regime of a strong wireelectric field compared to the electric field due to the impurity. An adiabatic and quasiclassical approximation is employed. The explicit dependencies of the binding energy of the impurity electron on the electric field strength, parameters of the QR and position of the impurity within the QR are obtained. Numerical calculations of the binding energy based on a finite-difference method in two and three dimensions are performed for arbitrary strengths of the electric field. It is shown that the binding energy of the impurity electron exhibits a maximum as a function of the radial position of the impurity that can be shifted arbitrarily by applying a corresponding wire-electric field. The maximal binding energy monotonically increases with increasing electric field strength. The inversion effect of the electric field is found to occur. An increase of the longitudinal displacement of the impurity typically leads to a decrease of the binding energy. Results for both low-and high-quantum rings are derived and discussed. Suggestions for an experimentally accessible set-up associated with the GaAs/GaAlAs QR are provided.

Solutions of the Schrödinger equation for Dirac delta decorated linear potential

“…The change in the ground state energy is the largest. As we have discussed above, this is due to the value of |Ψ n | 2 at the position of the Dirac function x 1 = l. Finally we investigated the change in ground state energy for 8 Dirac delta functions at random locations between 0 and 10 l. By using the given electric field E s = 7.5 10 4 V /cm and the effective mass of an electron m * = 0.067 m 0 for GaAs/GaAlAs heterostructure [14,15], we estimate the parameter l given in Equation (4) Table 2 The energies E n (in units of 2 2ml 2 ) for the low-lying bound states (n=1-10) with linear potential (LP) and delta decorated linear potential (DDLP) which contains one Dirac delta functions at x 1 = l. σl = +2 and σl = −2 represent attractive and repulsive Dirac delta potentials respectively.…”

Influence of lateral electric field on intraband optical absorption in concentric double quantum rings

“…In the past decade, a number of works were devoted to the theoretical investigation of the influence of electric fields on the electronic and optical properties of QR structures [16][17][18][19][20][21][22][23][24][25][26][27][28]. For instance, in Ref.…”

“…[17] a magnetic field perpendicular to the ring plane was used and has been shown that the electric field may suppress the Aharonov-Bohm oscillations of the lower energy levels.The problem of the impurity electron in QRs in the presence of a radially directed strong external electric field has been done in details in Ref. [18], where both the analytic and numerical approaches to the problem are developed.…”

Donor impurity states in elliptical quantum rings subjected to a magnetic field

“…These QRs are promising structures because of the Aharonov-Bohm (AB) effect which can be modulated by tailoring the shape and the size of the QRs [1][2][3]. In particular, semiconductor QRs have been the subject of extensive theoretical and experimental studies [4][5][6][7][8][9][10][11], due to the novel physical phenomena they exhibit and because of their potential applications in optoelectronic and tunneling devices.…”