(a )

(b)

Figure 25. (a) Dependence of m/m c in InSb on Eg/(2Ec + Eg) obtained from a direct analysis of the OMA spectra with isolation of double cyclotron energies for the electron. The straight line is a least-squares fit. (b) Dependence of dimensionless differences E and half-sums on Eg/(2Ec+ Eg) for light hole transitions from

lv+ = −1,0 states. The straight lines are least-squares fits.

Figure 26. Sums of squared deviations between experimental OMA spectrum (after Coulomb-interaction corrections for interband transitions) and theory for the diamagnetic excitons in InSb under

variation of the energy band parameters Ep, F, γ 1,2,3, k, q, N1 and dielectric constant ε0 obtained by computer fitting.

of superlattices and the artificially created ‘above-barrier’ exciton.

10.1. First magneto-optical observation of the ‘Coulomb-well’ effects and oscillatory states in the InGaAs/GaAs quantum wells (1993–94)

The ‘Coulomb well’ effect [39] appears as one of the most specific manifestations of the magneto-optics of 2D state. It exists due to an additional localization of the hole and owing to its Coulomb attraction to the electron confined by the quantumwell potential. In principle, such an effect exists in any type of quantum wells, in quantum wires, and in quantum dots.

However, most distinctly, it manifests itself in the case of the mixed-type heterojunction, e.g. in the (In,Ga)As/GaAs heterojunction. In such a system, there concurrently exists a ‘mixture’ of heterojunctions of types I and II. As a result, an attractive potential for both electron and heavy hole as well as a repulsive potential for both electron and light hole are simultaneously present in a layer of InGaAs ternary solution. In such objects, magneto-optics of exciton with a heavy hole is described within the conventional theory [40–42], whereas the ‘light-hole’ exciton gets a number of specific features. The ‘light-hole’ exciton does not create the usual ‘fan’ diagram (see figure 28) until the magnetic field becomes high enough. The ‘Coulomb well’ reveals itself by the formation of a series of discrete oscillatory states (see figures 29 and 30). We observed such a magneto-optical phenomenon for the first time. In the most complete form, the work by R P Seisyan with coauthors on the ‘Coulomb well’ formed in the (In, Ga)As/GaAs heterostructure was described in the book [43], published in Kerala, India. The relevant chapter is called ‘Fine structure of excitons in high quality InGaAs/GaAs quantum wells’.

10.2. Observation of above-barrier exciton and its magneto-optics (1996–2000) [44]

The behaviour of artificially produced ‘above-barrier’ exciton in the magnetic field is another peculiar magneto-optical phenomenon of the 2D system of quantum wells and superlattices. The above-barrier exciton occurs in a system of superlattices separated by enlarged barriers. Whereas the band structure of a superlattice is an alternation of allowed and forbidden 1D minibands, the enlarged layer (barrier) is analogous to an impurity centre in a primary crystal lattice. As a result, discrete ‘impurity’ levels form in the forbidden minibands. Among the levels are the ones situated at the abovebarrier energies.

Bragg ordered superlattices are optimal from the standpoint of spatial localization of an above-barrier electron. In them, the thicknesses of the layers are one quarter of the de Broglie wavelength of electrons with energy corresponding to the above-barrier state. At the same time, the enlarged barrier is to be formed by the layer with a thickness equal to half de Broglie wavelength. Under such conditions, as calculations show, the depth of penetration of electrons into the region of superlattice mirrors is quite limited. The DE magneto-optics was observed just in such a heterostructure. Figure 31 shows the design of the developed heterosystem, and figure 32 presents the corresponding fan chart and their analytical treatment taking into account the DE binding energies for the minibands and localized state. As follows from the experimental data, the oscillator strength of the artificial above-barrier exciton exceeds that of the exciton ground state in a superlattice. This fact confirms the exceptional efficiency of interferencial above-barrier localization in the Wigner–von Neumann scenario.