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The energy spectrum of the carriers in HgTe quantum wells: "Myth and Realities"

The energy spectrum of the carriers in HgTe quantum wells: "Myth and Realities". Grigory Minkov 1,2. Andrew Sherstobitov 1,2 Alexander Germanenko 2 О lga Rut 2 Sergey Dvoretskii 3 Nikolai Mikhailov 3 ( decoration of Eugenius Rumyantsev) 2 1 Institute of Metal Physics, RAS ,

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The energy spectrum of the carriers in HgTe quantum wells: "Myth and Realities"

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  1. The energy spectrum of the carriers in HgTe quantum wells: "Myth and Realities" Grigory Minkov1,2 • Andrew Sherstobitov 1,2 • Alexander Germanenko2 • Оlga Rut 2 • Sergey Dvoretskii 3 • Nikolai Mikhailov3 • (decoration of Eugenius Rumyantsev)2 • 1Institute of Metal Physics, RAS, • 2Ural Federal University • 3ИInstitute of Semiconductor Physics, RAS,

  2. What I meant under "Myth and Realities"? Myths.. Reality.. Mythlets… Cooking.. Art!! theorist experimenter technologist experimenter's commandments Do not believe a word of it .... not any!, unless stated what is neglected.. Do not believe a word of it .... not any! Additional commandments Do not trust yourself too…

  3. What I meant under "Myth and Realities"? Myths.. Reality.. Experiment shows that… Mythlets… experiment never shows nothing .. Only the interpretation of experiment shows…sometime.. experimenter shows only those results that, as it seems, he understands…

  4. “normal” and gapless semiconductors A2B6 Hg1-xCdxTe gapless “normal”

  5. Gap versus width of CdTe/HgTe/CdTe quantum well Г8 Independent quantization of conduction and valence bands Quantization in framework of the Kane Hamiltonian 5

  6. Size quantization and the surface states in semiconductors V. A. Volkov and T. N. Pinsker Institute of Radio Engineering and Electronics, USSR Academy of Sciences (Submitted December 25, 1975) Zh. Eksp. Teor. Fiz. 70, 2268-2278 (June 1976) Some history…. Не вырожденное состояние M.I. Dyakonov, A.V. Khaetskii,  Size quantization of holes in semiconductors with complex valence band and a carriers in gapless semiconductor . Zh. Eksp. Teor. Fiz. 82, 1584 (1982); Sov. Phys. JETP 55,. 917 (1982) Y.R. Lin-Liu and L.J. Sham, Interface states and subbands in HgTe-CdTe heterostructures. Phys. Rev. B 32, 5561–5563 (1985). M.V. Kisin and V.I. Petrosyan, Size quantization in narrow gap and gapless semiconductors, Fiz.Tekn.Poluprovodn. 22, 829 (1988) [Sov.Phys.Semicond 22, 523 (1988)].

  7. Value of QW width is very important!! How do you know?: d<dc; d=dc; d>dc?

  8. Value of QW width is very important!! How do you know?: d<dc; d=dc; d>dc? Very elegant way Single valley Dirac fermions in zero-gap HgTe quantum wells Nature Phys.7:418-422,2011 IV. QUANTUM HALL EFFECT AND THE IDENTIFICATION OF ZERO-GAP SAMPLES gap V а не Е!!

  9. Let us inspect the result in more detail.. Vg, but not Е!! • why does one extrapolate this point-xy=0 ?.. • … zero-mode Landau levels! IV. QUANTUM HALL EFFECT AND THE IDENTIFICATION OF ZERO-GAP SAMPLES 2. H =n*(h/e) , n=CV/e C=const H =CVh/e2 Does not depend on gapΔ!! (E) n EF 0 Vg 3. In principle C=(1/Cg+1/Cq(B,Vg))-1 .. but with real (Cq) it does not change the answer!! (печалька…..) Сильно быстро спешили 1. greatly hastened quickly??

  10. Peculiarities of the energy spectrum results in unique transport, optics and other properties…… The energy E(k) for the conduction band is simple enough both for the wide (d > dc) quantum wells with the inverse subband ordering and for the narrow (d < dc) wells with the normal spectrum. what about valence band spectrum?

  11. What is known about valence band spectrum? Сильно быстро спешили 2. Experimentally: Theoretically Is it OK? 4*1012 What does mean such a coincidence?

  12. Experimentally: Theoretically: Сильно быстро спешили 2. 4*1012 What does mean such a coincidence?

  13. Our data Что следует из совпадения?

  14. To study spectrum we have found the hole effective mass from temperature dependence of the amplitude of SdH oscillations p=1.05*1011см-2 Calculated mass is negative!! The energy spectrum is close to parabolic one at k>8*105 . Electron-like states, if there is, occures for small k. Electron-like states

  15. А как при малых k? ОБЛАСТЬ ПЕРЕКРЫТИЯ. ПРОВОДИМОСТЬ ДВУМЯ ТИПАМИ НОСИТЕЛЕЙ. Описывается неплохо; с ростом поля n+p=const, но n, p могут зависеть от поля..

  16. Проводимость двумя типами носителей

  17. The dispersion E(k) reconstructed from the data analysis and calculated one within framework of isotropic six-band kP-model. This is qualitatively similar but quantitatively …… What are the possible reasons?...... kP? single-particle approximation?

  18. What about valence band spectrum at d<dc ? (“normal” spectrum) Сильно быстро спешили 3. !! happy coincidence Unfortunately there was ungated structure….

  19. Our data for analogous structure:

  20. The only model that describes our results is as follows: the subband of spatial quantization H1 is strongly split by spin-orbit interaction into two subbands, H1+ and H1−, due to asymmetry of the quantum well.

  21. Effective mass, spectrum

  22. At first sight the large spin-orbit splitting of the energy spectrum in the nominally almost symmetrical structure seems very surprising….

  23. Peculiarity of QHE

  24. И что мы знаем (понимаем) про HgTe quantum well? What does we know (understand) about HgTe quantum wells? Почти ничего…. Спектр валентной зоны…. Транспорт при пересечении zero-mod LL.. Роль краевых состояний…почему они столь слабо protected… Роль интерференции…. Роль взаимодействия…. we know almost nothing : Valence band energy spectrum… Conductivity, Hall effect at zero-mod LL crossing.. Role of edge states…. Why they are so poorly protected… Role of the interference (weak localization)…. Role of e-e, h-h, e-h interaction…. И только совместные усилия теоретиков, экспериментаторов, технологов могут как-то прояснить картину…. Only joint efforts of theorists, experimentalists, technologists can somehow clarify the picture ....

  25. Post Scriptum: (Conclusion) Myths.. Reality.. Mythlets… Cooking.. Art!! Do not shoot the pianist - he plays as he can…

  26. Thanks… «Черт прячется в деталях»….. Готов обсудить их с любой (доступной) степенью подробностей.. "The devil is in the details" ..... Ready to discuss them with any (available) level of details .. к. №

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