Semiconductor Physics, Quantum Electronics & Optoelectronics, 25 (3), P. 240-253 (2022).
DOI: https://doi.org/10.15407/spqeo25.03.240

References

1. Castro Neto A.H., Guinea F., Peres N.M.R., Novo-selov K.S., and Geim A.K. The electronic properties of graphene. Rev. Mod. Phys. 2009. 81. P. 109. https://doi.org/10.1103/RevModPhys.81.109

2. Orlita M. and Potemski M. Dirac electronic states in graphene systems: optical spectroscopy studies. Semicond. Sci. Technol. 2010. 25. P. 063001. https://doi.org/10.1088/0268-1242/25/6/063001

3. Zolyomi V., Drummond N.D., Falko V.I. Band structure and optical transitions in atomic layers of hexagonal gallium chalcogenides. Phys. Rev. B. 2013. 87. P. 195403. https://doi.org/10.1103/PhysRevB.87.195403

4. Rybkovskiy D.V., Osadchy A.V., Obraztsova E.D. Transition from parabolic to ring-shaped valence band maximum in few-layer GaS, GaSe, and InSe. Phys. Rev. B. 2014. 90. P. 235302. https://doi.org/10.1103/PhysRevB.90.235302

5. Wickramaratne D., Zahid F., Lake R.K. Electronic and thermoelectric properties of van der Waals materials with ring-shaped valence bands. J. Appl. Phys. 2015. 118. P. 075101. https://doi.org/10.1063/1.4928559

6. Kibirev I.A., Matetskiy A.V., Zotov A.V., and Saranin A.A. Thickness-dependent transition of the valence band shape from parabolic to Mexican-hat-like in the MBE grown InSe ultrathin ?lms. Appl. Phys. Lett. 2018. 112. P. 191602. https://doi.org/10.1063/1.5027023

7. Ortner K., Zhang X.C., Pfeuffer-Jeschke A., Becker C.R., Landwehr G. and Molenkamp L.W. Valence band structure of HgTe/Hg1?xCdxTe single quantum wells. Phys. Rev. B. 2002. 66. P. 075322. 8. Minkov G.M., Germanenko A.V., Rut O.E., Sherstobitov A.A., Dvoretski S.A., and Mikhailov N.N. Weak antilocalization in HgTe quantum wells with inverted energy spectra. Phys. Rev. B. 2012. 85. P. 235312. https://doi.org/10.1103/PhysRevB.85.235312

9. Jiang Y., Thapa S., Sanders G.D. et al. Probing the semiconductor to semimetal transition in InAs/ GaSb double quantum wells by magneto-infrared spectroscopy. Phys. Rev. B. 2017. 95. P. 045116. https://doi.org/10.1103/PhysRevB.95.045116

10. Gross E.F., Perel V.I., Shekhmametev R.I. Inverse hydrogenlike series in optical excitation of light charged particles in a bismuth iodide (BiI3) crystal. JETP Lett. 1971. 13. P. 229.

11. Rashba E.I., Edelstein V.M. Magnetic Coulomb levels near the saddle points. JETP Lett. 1969. 9. P. 287-290.

12. Mahmoodian M.M., Chaplik A.V. Bielectron formed in a 2D system by the spin orbit interaction and image forces. JETP Lett. 2018. 107. P. 564-568. https://doi.org/10.1134/S0021364018090084

13. Sabio J., Sols F., and Guinea F. Two-body problem in graphene. Phys. Rev. B. 2010. 81. P. 045428. https://doi.org/10.1103/PhysRevB.81.045428

14. Lee R.N., Milstein A.I., and Terekhov I.S. Quasi-localized states in a model of electron-electron interaction in graphene. Phys. Rev. B. 2012. 86. P. 035425. https://doi.org/10.1103/PhysRevB.86.035425

15. Marnham L.L. and Shytov A.V. Metastable electron-electron states in double-layer graphene structures. Phys. Rev. B. 2015. 92. P. 085409. https://doi.org/10.1103/PhysRevB.92.085409

16. Sablikov V.A. Two-body problem for two-dimensional electrons in the Bernervig-Hughes-Zhang model. Phys. Rev B. 2017. 95. P. 085417. https://doi.org/10.1103/PhysRevB.95.085417

17. Downing C.A., Portnoi M.E. Bielectron vortices in two-dimensional Dirac semimetals. Nature Commun. 2017. 8. Art. No 897. https://doi.org/10.1038/s41467-017-00949-y

18. Kevorkian J. and Cole J.D. Perturbation Methods in Applied Mathematics. Springer-Verlag, New York, 1998.

19. By simple substitutions r > rp?, t > tp? one can show that for a given energy dispersion ?(p), the only actual parameter in Eqs (4), (5) and (9) that has an effect on trajectories in the phase-plane, as well as in real space,

20. Landau L.D. and Lifschitz E.M. Mechanics. Pergamon Press, Oxford, 3rd edition, 1976. https://doi.org/10.1515/9783112569122

21. The single energy band equation can be used for the analysis of electron states with energies nearby this band, when contributions of other remote energy bands are negligible.

22. Gradshteyn I.S. and Ryzhik I.M. Table of Integrals, Series, and Products. 6th edition. Academic Press, San Diego, 2000.

23. Bronshtein I.N., Semendyayev K.A., Musio G. and Muehlig H. Handbook of Mathematics. Springer-Verlag, New York, 4th edition, 2004. https://doi.org/10.1007/978-3-662-05382-9

24. Shibuya T. and Wulfman C.E. The Kepler problem in two-dimensional momentum space. Am. J. Phys. 1965. 33. P. 570. https://doi.org/10.1119/1.1971931. Par?tt D.G.W. and Portnoi M.E. The two-dimensional hydrogen atom revisited. J. Math. Phys. 2002. 43. P. 4681. https://doi.org/10.1063/1.1503868

25. Vasko F.T., Raichev O.E. Quantum Kinetic Theory and Applications. Electrons, Photons, Phonons. Kluwer Academic Publisher, Boston, 2005.

26. L.D. Landau and E.M. Lifshitz, Quantum Mechanics (Non-relativistic Theory). Pergamon Press, Oxford, 3rd edition, 1977. 27. Lampert M.A. Mobile and immobile effective-mass-particle complexes in nonmetallic solids. Phys. Rev. Lett. 1958. 1. P. 450. https://doi.org/10.1103/PhysRevLett.1.450

28. Kheng K., Cox R.T., d'Aubigne M.Y., Bassani F., Saminadayar K., and Tatarenko S. Observation of negatively charged excitons X? in semiconductor quantum wells. Phys. Rev. Lett. 1993. 71. P. 1752. https://doi.org/10.1103/PhysRevLett.71.1752

29. Shields A.J., Osborne J.L., Simmons M.Y., Pepper M., and Ritchie D.A. Magneto-optical spectroscopy of positively charged excitons in GaAs quantum wells. Phys. Rev. B. 1965. 52. P. R5523. https://doi.org/10.1103/PhysRevB.52.R5523

30. Prange R.E. and Girvin S.M. The Quantum Hall Effect. Springer-Verlag, New York, 1987; Chakraborty T. and Pietilainen P. The Quantum Hall Effects: Integer and Fractional. Springer, Berlin, 2nd edition, 1995.