Behavior of excitonic levels in symmetric and asymmetric double quantum wells in a magnetic field

Abstract

We studied theoretically the excitonic energy levels and the optical absorption spectra for double quantum wells,both symmetric and asymmetric, in the presence of an homogeneous magnetic field. Within the effective mass approach, we expanded the excitonic wave-function, in an orthogonal basis formed by products of electron and hole wave-functions in the growth direction z, and one particle solutions of the magnetic Hamiltonian in the x − y plane. We applied our method to the case of AlxGa1−xAs, for which we showed how the exciton wave-function vary, and how the basis functions are mixed in a non trivial way by the effect of the Coulomb potential. By taking into account all the mixing between the elements in our base, we get anti-crossings between excited excitonic states not reported previously. 73.20.Dx,71.35.Ji

Magnetoexciton dispersion in GaAs-(Ga,Al)As single and coupled quantum

“…This assumption greatly simplifies our numerical calculations of the magnetoexciton energy and the Coulomb mass, but by neglecting the existence of the finite confinement potentials, we cannot provide a more realistic value for this part of the exciton energy related to the exciton confinement along zdirection, than the sum of the well-known terms h2 π 2 /2m c,v L 2 c,v . Obviously, the more realistic model of a symmetric (or asymmetric) DQW with finite quantum-well widths [29,30] will cause minor corrections to our main conclusions, which are: (1) the B-S formalism provides a term, which does not exists in the Schrodinger equation, and (2) the term plays an important role in determining the magnetoexciton dispersion. The basic features of the CQW's magnetoexcitons are the same as that of the SQW magnetoexcitons.…”

Theoretical and experimental study of the excitonic binding energy in GaAs/AlGaAs single and coupled double quantum wells

“…6, presents an interesting characteristic: for each Al% value, despite the relatively large error associated to the experimental data, E b tends to reduce when passing from the SQW to CDQW5 and then increases when going to the CDQW15 and CDQW30. Although this effect is not described by the theoretical approach used, it has been already predicted by other authors using more elaborated methods [20,21]. According to Bayer et al [22] who investigated the effect of inserting AlAs inter-well barriers in Al 0.30 Ga 0.70 As/ GaAs quantum wells, this reduction in E b can be explained by the fact that between the limiting cases of (i) having an inter-well barrier very thick (corresponding to two independent mini-wells of width L w ) and (ii) having no inter-well barrier (corresponding to a single well of width 2L w ), where the maximum of the electrons and holes wave functions are located at the center of the single well, narrow inter-well barriers cause smaller overlap of the carriers wave functions due to the difference between the masses of these particles (the electron wave functions are less disturbed by the inter-well barrier) and thus the Coulomb interaction between electrons and holes is lower and, consequently, E b decreases.…”

Optical response of magnetoexcitons in near-surface double quantum wells

“…The behavior of magnetoexcitons in semiconductor quantum-well heterostructures is of great interest at present (see, for example, the works [1][2][3][4][5][6][7][8] and references therein). In such a kind of nanostructures the discrete energy spectrum of excitons is due to the size quantization of the electron and hole in the growth direction of the quantum-well heterostructure and to the Landau quantization, resulting from the action of the transverse magnetic field.…”

“…Because of the chosen basis, the Coulomb potential c V (6) and the image one im V (7) give rise to off-diagonal terms. This procedure is commonly used [1][2][3][4][5], but in our case it leads to an algebraic system of equations for the coefficients of the expansion for Y , which are coupled to the amplitudes of the electric field E inside and outside the heterostructure. The numerical solution of such a system allows to obtain reflectivity and absorption spectra for the considered near-surface double quantum well.…”

“…In such a kind of nanostructures the discrete energy spectrum of excitons is due to the size quantization of the electron and hole in the growth direction of the quantum-well heterostructure and to the Landau quantization, resulting from the action of the transverse magnetic field. The Coulomb attraction between the electron and hole turns out to be considerably suppressed by the effect of both the confining potential and the strong (quantizing) transverse magnetic field.Magnetoexcitons in quantum-wells couple to light and give rise to resonances in optical spectra (photoluminescence [3,4,5], absorption [1,2,6], reflectivity [7,8], etc.). Commonly, quantum-well heterostructures are grown on substrates and may have a cap layer, overlying them.…”