A.M. Mandel – Ph.D. (Phys.-Math.), Associate Professor, 

Department of Physics, Moscow State University of Technology «STANKIN»

E-mail: arkadimandel@mail.ru

V.B. Oshurko – Dr.Sc. (Phys.-Math.), Professor, Head of Department of Physics, 

Moscow State University of Technology «STANKIN»

S.G. Veselko – Ph.D. (Phys.-Math.), Associate Professor, 

Department of Physics, Moscow State University of Technology «STANKIN»

K.G. Solomakho – Post-graduate Student, Assistant, 

Department of Physics, Moscow State University of Technology «STANKIN»

A.A. Sharts – Ph.D. (Phys.-Math.), Associate Professor, 

Department of Physics, Moscow State University of Technology «STANKIN»

In present work a self-consistent problem of calculating the effective mass, g-factor and electron spectrum in ideal quantum wires has been resolved. Here 1D semiconductor heterostructure is considered as an ideal quantum wire if electron motion in transverse  direction contains a single bound level. Thus, in these heterostructures, the motion of an electron along the wire can be considered as classical while in the transverse direction we have the «limiting case» of dimensional quantization. As it was shown in present work, it can clear up some new interesting manifestations of the fundamental principles of quantum mechanics. The information about electron’s «longitudinal» and «transverse» effective mass (both in the barrier material and in the wire material) is necessary to calculate the electron spectrum. At the same time, these masses are critically dependent on the radius of the filament and on the  energy of the ground state of the electron. This relationship produces the self-consistent problem of mass or energy calculations.  Proposed solution is based on the well-known Kane theory, which describes the formation of the effective mass and g-factor of an electron in bulk semiconductors of composition AIIIBIV. In present work this theory is generalized to case of «non-completed» zone structure of transverse levels. Here the main idea is that the energy gap between the top of the valence band and the ground state of the electron in the potential well can be considered as traditional bandgap in semiconductor. Heterostructures of the covariant type were considered. In this case we avoid the effects of holes binding, i.e. exciton, complex spectrum etc. The solution of the  corresponding Schrödinger equations with the continuity condition of the logarithmic derivative at the filament boundary gives the energy of the (unique) transverse level. As it was found, the value of this energy level defines four different effective masses of the electron. Two of them are the longitudinal and transverse masses in the wire material. They appear as result of dimensional quantization depending on the wire radius. The other two masses are the traditional (known) effective masses in the wire material and the matrix material. It emphasized that the energy level value begins to grow from a certain critical radius of the wire. Below this radius it is exponentially suppressed. Such suppression is a result of the circular symmetry of the wire cross-section, and disappears when it is broken. This gives a new possibility of control of quantum wire shape using spectroscopic methods. It is found that the g-factor of an electron as well as in quantum dots, is always a difference of two quantities. One of them relates to the material of the wire and  depends on its geometrical characteristics. The other one is determined by the material of matrix and is constant. In addition, the 

g-factor can also be controlled by external fields for various technical applications.

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4. Mandel' A.M., Oshurko V.B., Veselko S.G., Solomakho K.G., Pershin S.M., Sharts A.A. Raschet g-faktora v malykh kvantovykh tochkakh. Kratkie soobshcheniya po fizike FIAN. 2018. № 9. S. 39–45. [in Russian]
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10. Mandel' A.M., Oshurko V.B., Solomakho G.I. O lokalizatsii magnitnym polem odnoelektronnykh sostoyaniy v okrestnosti kvantovykh tochek drobnoy razmernosti. Elektromagnitnye volny i elektronnye sistemy. 2014. № 6. S. 67–74. [in Russian]
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15. Rodionov V.N., Kravtsova G.A., Mandel' A.M. O vliyanii sil'nykh elektricheskogo i magnitnogo poley na prostranstvennuyu dispersiyu i anizotropiyu opticheskikh svoystv poluprovodnikov. Pis'ma v ZhTF. 2003. T. 78. V. 4. S. 253–257. [in Russian]
16. Rodionov V.N., Kravtsova G.A., Mandel A.M. The lack of the stabilization of quasi-stationary electron states in a strong magnetic field. Doklady Physics. 2002. V. 47. № 10. P. 725–727.
17. Rodionov V.N., Kravtsova G.A., Mandel' A.M. Volnovaya funktsiya i raspredelenie tokov veroyatnosti elektrona, dvizhushchegosya v odnorodnom magnitnom pole. TMF. 2010. T. 164. № 1. S. 157–171. [in Russian]
18. Rodionov V.N., Kravtsova G.A., Mandel' A.M. Ionizatsiya iz korotkodeystvuyushchego potentsiala pod deystviem elektromagnitnykh poley slozhnoy konfiguratsii.Pis'ma v ZhTF. 2002. T. 75. V. 8. S. 435–439. [in Russian]
19. Rodionov V.N., Kravtsova G.A., Mandel' A.M. Ionizatsiya sil'nym lazernym izlucheniem pri uchete deystviya kvantuyushchego magnitnogo polya. Vestnik MGU. Ser. 3 «Fizika. Astronomiya». 2002. № 5. S. 6–12. [in Russian]