Figure 41. Simulation of zero-dimensional state of an exciton in a high magnetic field by using the ‘technological’ quantum well.

Figure 42. Simulation of one-dimensional state of an exciton in a high magnetic field by using the ‘technological’ quantum well.

the prospective quantum-dimensional phenomena under conditions equal to the ideal quality of a real structure.

In quasi-1D systems, an increase in the oscillator strength is governed by the system proximity to the ideal onedimensional case. Since the application of ultrahigh magnetic fields simulates an ideal 1D situation (see figure 42), such magnetic-field experiments become very attractive and promising. It is all the more so since, here, the influence of geometrical and other structural imperfections is excluded.

14. Magneto-quantum exciton polymer

Another unique aspect of the DE studies is associated with the simulation of behaviour of the matter in ultrahigh magnetic fields of the order of 105–107 T, which presumably exist in the vicinity of neutron stars 56, 57, 58. In such intense fields, the interaction of the electron shells with the external magnetic field becomes stronger than the Coulomb interaction between the electrons and nucleus. In other words, the Larmour radius becomes less than the Bohr radius for the hydrogen atom.

Figure 43. The binding energy of the ‘one-dimensional’ hydrogen atom (exciton) depending on the magnetic field.

Under these circumstances, the behaviour of the atom is quite analogous to that of the DE. There is the only difference. Because of lesser exciton mass (μ m0, where m0 is the free electron mass) in the substance with the permittivity ε0 1, the effective magnitude of the magnetic field turns out to be ε02/μ times larger than that for the atom. Thereby, the effective magnetic field affecting an exciton is 104–107 times higher than ‘the same’ external field affecting an atom. In PbTe taken as an example, where the significant role of excitons in the magnet-optical absorption was disclosed in paper [32], the magnitude of the laboratory 10 T magnetic field corresponds to the 108 T field applied to a hydrogen atom.

The ultrahigh magnetic fields cause remarkable modification of electronic states in an atom. Precessing around the nucleus, all the electrons begin to move in comparatively thin cylindrical regions with the cylinder axis directed along the field. The spectrum of the atomic excited states is also modified by the high magnetic field, so that it consists of the equidistant Landau levels and spin-rotation levels. Besides, there is a broad band due to longitudinal movement near each level. Furthermore, the atom binding energy increases with the field. In fields of an order of 108 T, this energy for the hydrogen atom reaches several hundreds eV (see figure 43).

Such atoms have got large electric quadruple momentum and have to form stable molecules. Thus, the formation of unusual molecules becomes possible, when collectivization of the electronic cloud takes place and the electrons constitute a negatively charged needle, the atoms locating along its direction. Remarkably, the binding energy for the diatomic molecule of this substance is much higher than the energy of an isolated atom. As a result, the atoms inevitably form diatomic molecules.

The energy of inter-atomic interaction in ultrahigh magnetic fields may be so high that the substance in the vicinity of a neutron star can solidify in condensed matter even at temperatures 106 ◦C [56, 57]. In this case, the solid phase will have rather the structure of a polymeric wire than

Figure 44. Exciton ‘polymer’ in the ultrahigh magnetic field (a model).

the crystal structure (see figure 44). Magnetic fields of the order of 103 T can now be created under laboratory conditions, namely in ‘explosion-generators’ [59]. Thus, there is a unique opportunity to observe the behaviour of such a DE substance under terrestrial conditions making use of extremely high laboratory magnetic fields as well as of semiconductor crystals with narrow forbidden gaps.

15. Conclusion

I have attempted to force into a short paper all the interband magneto-optics of semiconductors after 65 years of its progress, beginning with a brief chronicle of the discovery of a key interband magneto-optical phenomenon, that is diamagnetic exciton (DE), and finishing with relatively new ideas that emerged in recent years.

Upon a short discussion of the DE concept as the very core of any interband optical phenomenon in semiconductor crystals in a high magnetic field, I have reviewed special features of the DE effect in the majority of research objects of the practical interest as well as methods of the extraction of exact parameters of crystal band structures from the magnetooptical spectra. Among the materials, wideand narrow-gap semiconductor crystals, their solid solutions, diamond-like semiconductors, and hexagonal crystals have been considered. There is an example of special interest, PbTe, where, due to possibly negligible binding energy, the idea itself of the exciton origin of spectra might seem dubious. The Rydberg exciton states and their magneto-optics is another important topic. It covers a wide range of crystals with relatively wide forbidden gaps. The calculation methods developed for them are however quite effective and even preferable in cases of relatively narrow-gap crystals. The DE-science application to lowdimensional semiconductor systems such as multiple quantum wells (MQW) and superlattices (SL) is also very efficient. The correct determination of the DE binding energies is the key to analysing magneto-optics here too. These energies depend on any quantum number of the state as well as on the magnetic

field strength and help to ‘restore’ the virtual spectrum of transitions between the Landau subbands. The magnetooptical analysis of more complex low-dimensional systems is an interesting elaboration of the subject. Among them, I would mention MQW with the mixed-type heterojunctions (‘type I–type II’), where the ‘Coulomb wells’ are formed, or the ‘MQW–SL’ systems with Bragg mirrors for the electrons that form the ‘above-barrier’ exciton. I deliberately discuss only the main phenomenon of the absorption oscillations, not mentioning its many derivatives such as the interband Faraday and Voigt effects, or a lot of modulation effects, etc. since they are limited and controlled by the same physical principles. In all these cases, DE appears to be both a physical phenomenon the same by nature and a source of valuable information on the energy spectrum of states.

The question arises whether the interband magnetospectroscopy (DE spectroscopy) is exhausted or some new discoveries are possible. At last, do we need new research? Zakharchenya, one of the discoverers of the DE effect, once answered in the following way (see the Preface to [9]): ‘ . . . it is clear that such an effective method as the magnetooptics of semiconductors will be never deposited in the depot of former methods of studying the electronic processes in crystals. It is safe to say that this method will many times manifest itself in all its glory in fundamental and applied physics of semiconductors, just as seemingly archaic Hall effect revived and shone with new facets in recent years after the discovery of quantum oscillations in this effect . . . ‘. It is worth recalling that the boom in research of magneto-optics of semiconductors soon after the discovery of the effect in 1957 was replaced by a noticeable decline after a while. There had been at least three reasons for that. First, the DE spectra could be easily observed in crystals of high perfection level only, whereas the crystal-growth technologies did not provide a sufficient amount of new such crystals. Second, to observe the most informative transmission spectra, ultrathin samples are necessary, and this is not easy. Third, to obtain the necessary information about the energy spectrum of a crystal, one must be able to calculate the DE binding energies correctly. Only the use of accurate DE energies to adjust positions of the experimental extrema of obtained spectra allows one to restore the positions of relevant transitions between the Landau subbands. Thus, only in this way can an accurate and selfconsistent computation be assured for all parameters of the crystal energy spectrum by one of the methods mentioned above. The accurate information on the band parameters is needed to develop new semiconductor devices that make use of a variety of semiconductors: monocrystalline diamond; silicon carbide; aluminium, gallium, and indium nitrides; zinc sulphide and oxides. This is anything but a complete list of crystals in the ‘queue’ for studying DE. For example, the DE spectra of GaN crystals have been obtained in magnetoreflection experiments only. They remain untreated because the well-known computational methods do not work in this case, either those for the binding energies or ones for the band parameters, which use, e.g., quasi-cubic approximation as in the case of hexagonal CdSe. The spectra of InCuSe2, which is crystallizing in the chalcopyrite lattice, will be possibly soon

treated in this approximation. Simulation of low-dimensional state is another direction of the DE spectroscopy development. Here, the narrow gap crystals can play a key role, opening even the possibility of penetration into the physics of neutron stars.

References

[1]Gross E F and Zakharchenya B P 1956 Dokl. AN USSR 111 564

[2]Gross E F, Zakharchenya B P and Pavinsky P P 1957 Zh. Tech. Phys. 27 2179

[3]Burstein and Picus G S 1957 Phys. Rev. 105 1157

[4]Zwerdling S and Lax B 1957 Phys. Rev. 106 51

[5]Macferlane G G et al 1959 J. Phys. Chem. Solids 8 388

[6]Kanskaya L M, Kokhanovskii S I and Seisyan R P 1979 Fiz. Tekh. Polupr. 13 2424

Kanskaya L M, Kokhanovskii S I and Seisyan R P 1979 Sov. Phys.-Semicond. 12 1420

[7]Varfolomeev A B, Zakharchenya B P and Seisyan R P 1968

Pis’ma Zh. Eksp. Teor. Fiz. 8 123

[8]Seisyan R P, Varfolomeev A B and Zakharchenya B P 1968

Fiz. Tekh. Polupr. 2 1276

[9]Zakharchenya B P and Seisyan R P 1969 Usp. Fiz. Nauk 97 194

[10]Elliott R J and Loudon R 1959 J. Phys. Chem. Sol. 8 382–8

[11]Seisyan R 1984 Diamagnetic Exciton Spectroscopy (Moscow: Nauka) 284

[12]Agekyan V T, Zhilich A G, Zakharchenya B P

and Seisyan R P 1976 Fiz. Tekh. Polupr. 5 193 Agekyan V T, Zhilich A G, Zakharchenya B P

and Seisyan R P 1972 Fiz. Tekh. Polupr. 6 1924

[13] Seisyan R, Abdullaev M A and Zakharchenya B P 1972 Fiz. Tekh. Polupr. 6 408

Seisyan R, Abdullaev M A and Zakharchenya B P Sov. Phys.-Semicond. 6 351

[14] Seisyan R, Abdullaev M A and Zakharchenya B P 1973 Fiz. Tekh. Polupr. 7 958

Seisyan R, Abdullaev M A and Zakharchenya B P Sov. Phys.-Semicond. 7 649

[15]Glutsch S, Siegner U, Mycek M A and Chemla D S 1994

Phys. Rev. 50 170

[16]Vasilenko D V, Luk’yanova N V and Seisyan R P 1999 Fiz. Tekh. Polupr. 33 19

Vasilenko D V, Luk’yanova N V and Seisyan R P 1999

Semiconductors 33 15

[17]Abdullaev M A, Kokhanovskii S I, Makushenko Yu M and Seisyan R P 1989 Fiz. Tekh. Polupr. 23 1156

[18]Abdullaev M A, Coschug O S, Kokhanovskii S I

and Seisyan R P 1990 J. Cryst. Growth. 101 802–7

[19]Aliev G N, Koshchug O S, Nesvizhskii A I, Seisyan R P and Yazeva T V 1992 Fiz. Tverd. Tela 34 2393

[20]Aliev G N, Koshchug O S, Nesvizhskii A I, Seisyan R P and Yazeva T V 1993 Fiz. Tverd. Tela 35 1514

[21]Aliev G N, Datsiev R M, Ivanov S I, Kop’ev P S

and Sorokin S V 1996 J. Cryst. Growth 159 523–7

[22]Kokhanovskii S I, Makushenko Y M, Seisyan R P, Efros Al L, Yazeva T V and Abdullaev M A 1991 Fiz. Tverd. Tela

23 1719

[23]Delgarno A, Damburg R J and Kolosov V V et al 1985

Rydberg States of Atoms and Molecules (Moscow: Mir)

[24]Pidgeon C R and Brown R N 1966 Phys. Rev. 146 575

[25]Gel’mont B L, Mikhailov G V, Panfilov A G, Razbirin B S, Seisyan R P and Efros A L 1987 Fiz. Tverd. Tela 29 1730

[26]Seisyan R P, Rodina A V, Kapustina A V and Petrov B V 2000 Fiz. Tverd. Tela 42 1207

[27]Varfolomeev A B, Seisyan R P, Efros Al L and Yakimova R N 1977 Fiz. Tekh. Polupr. 11 1067

Varfolomeev A B, Seisyan R P, Efros Al L and Yakimova R N

Sov. Phys.-Semicond. 11 631

[28]Ivanov-Omskii V I et al 1983 Solid State Commun. 46 25

[29]Kanskaya L M, Kokhanovskii S I, Seisyan R P and Efros Al L 1981 Fiz. Tekh. Polupr. 15 1854

Kanskaya L M, Kokhanovskii S I, Seisyan R P and Efros Al L

Sov. Phys.-Semicond. 15 1079

[30] Kanskaya L M, Kokhanovskii S I, Seisyan R P and Efros Al L 1982 Fiz. Tekh. Polupr. 16 2037

Kanskaya L M, Kokhanovskii S I, Seisyan R P and Efros Al L

Sov. Phys.-Semicond. 16 1315

[31]Kanskaya L M, Kokhanovskii S I, Seisyan R P and Efros Al L 1982 Solid State Commun. 43 613

[32]Geiman K I, Kokhanovskii S I, Seisyan R P, Yukish V A

and Efros Al L 1986 Fiz. Tverd. Tela 28 855 Kokhanovskii S I, Seisyan R P, Yukish VA and Efros Al L

1986 Pis’ma Zh. Eksp. Teor. Fiz. 43 332

[33]Kokhanovskii S I, Makushenko Y M, Seisyan R P, Efros Al L, Yazeva T V and Abdullaev M A 1991 Fiz. Tekh. Polupr.

25 493

[34]Ivanov-Omskii V I, Kokhanovskii S I, Seisyan R P,

Smirnov V I, Yukish V A, Yuldashev S U and Efros Al L 1983 Fiz. Tverd. Tela 25 1214

Ivanov-Omskii V I, Kokhanovskii S I, Seisyan R P, Smirnov V I, Yukish V A, Yuldashev S U and Efros Al L

Solid State Commun. 46 26

[35]Markosov M S 2008 Width of the excitonic absorption line in AlGaAs alloys (Abstract.) SPb. Ioffe Institute

[36]Seisyan R P and Zakharchenya B P 1991 Landau Level Spectroscopy ed E I Rashba and G Landwehr (North Holland: Elsevier Amsterdam) 343–443

[37]Kavokin A V, Nesvizhskii A I and Seisyan R P 1993 Fiz. Tekh. Polupr. 27 977–89

[38]Kavokin A V, Nesvizhskii A I and Seisyan R P 1995 Proc. SPIE 2362 460–8

[39]Kokhanovskii S I, Kavokin AV, Nesvizhskii A I, Sasin M E, Seisyan R P, Sinitsyn M A and Yavich B S 1995 Semicond. Sci. Technol. 10 611–5

[40]Kavokin A V, Kokhanovskii S I, Sasin M E, Goupalov S V and Ustinov V M 1997 Fiz. Tekh. Polupr. 31 1109–20

[41]Moumanis K, Seisyan R P and Sasin M E 1998 etc Fiz. Tverd. Tela 40 797

[42]Sasin M E, Moumanis K, Kokhanovskii S I, Seisyan R P, Gibbs H M and Khitrova G 1997 Phys. Status Solidi 164 67–72

Sasin M E, Moumanis K, Kokhanovskii S I, Seisyan R P, Gibbs H M and Khitrova G 1998 Fiz. Tverd. Tela 40 797–9

[43]Seisyan R P, Mounanis Kh, Kokhanovskii S I, Sasin M E, Kavokin A V, Gibbs H M and Khitrova G 2001 Recent Res. Devel. Physics 2, Transworld Research Network

pp 289–314 Kerala, Trivandrum, India

[44]Vladimirova M R, Kavokin A V, Kaliteevski M A, Kokhanovski S I, Sasin M E and Seisyan R P 1999 Pis’ma Zh. Eksp. Teor. Fiz. 69 727–32

[45]Akhmediev N N 1980 Zh. Eksp. Teor. Fiz. 79 1534–43

[46]Aliev G N, Lukyanova NV and Seisyan R P et al 1997 Phys. Status Solidi. A 164 193

[47]Kosobukin V A, Seisyan R P and Vaganov S A 1993

Semicond. Sci. Technol. 8 1235–8

[48]Aliev G N, Koschug O S and Seisyan R P 1994 Fiz. Tverd. Tela 36 373–88

Aliev G N, Datsiev R M, Ivanov S I, Kop’ev P S, Seisyan R P and Sorokin S V 1996 J. Cryst. Growth 159 523–7

Aliev G N, Coschug-Toates O and Seisyan R P 1996 J. Cryst. Growth 159 843–7

[49] Seisyan R P, Kosobukin V A and Vaganov S A et al 2005

Phys. Status Solidi C 2 900–5

Seisyan R P, Kosobukin V A and Markosov S 2006 Fiz. Tekh. Polupr. 40 1321