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

Grigory Minkov1,2

Andrew Sherstobitov 1,2

Alexander Germanenko 2

Оlga Rut 2 Sergey Dvoretskii 3

Nikolai Mikhailov 3

(decoration of Eugenius Rumyantsev)2

1Institute of Metal Physics, RAS, 2Ural Federal University3ИInstitute of Semiconductor Physics, RAS,

What I meant under "Myth and Realities"?

Do not believe a word of it .... not any!

Do not believe a word of it .... not any!,

unless stated what is neglected..

experimenter's commandments

Additional commandments Do not trust yourself too…

Myths..Mythlets

…

Reality.. Cooking..

Art!! theoristexperimenter

technologist

What I meant under "Myth and Realities"?

experimenter shows only those results that, as it seems, he understands…

Myths..

Mythlets…

Reality..

Experiment shows that…

experiment never shows nothing ..Only the interpretation of experiment shows…sometime..

“normal” and gapless semiconductors A2B6

Hg1-xCdxTe

“normal”gapless

5 10 15 20 25-100

0

100

200

k

c1

e2

e3

e1

h2

QW width (nm)

h1

E

k

E

dc

5 10 15 20 25-100

0

100

200

e2

e3

e1

h3h2

ener

gy (

meV

)

QW width (nm)

h1

gap

5

Gap versus width of CdTe/HgTe/CdTe quantum well

Independent quantization of conduction and valence bands

Quantization in framework of the Kane Hamiltonian

-15 -10 -5 0 5 10 15-50

0

50

100

150

200

250

k

E

Г8

Some history….

1. 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)

2. Y.R. Lin-Liu and L.J. Sham, Interface states and subbands in HgTe-CdTe heterostructures. Phys. Rev. B 32, 5561–5563 (1985).

3. 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)].

Не вырожденное состояние

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)

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

Very elegant waySingle valley Dirac fermions in zero-gap HgTe quantum wellsNature Phys.7:418-422,2011

IV. QUANTUM HALL EFFECT AND THE IDENTIFICATION OF ZERO-GAP SAMPLES

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

V а не Е!!

gap

IV. QUANTUM HALL EFFECT AND THE IDENTIFICATION OF ZERO-GAP SAMPLES2. H =n*(h/e) , n=CV/e C=const H =CVh/e2

Does not depend on gap Δ !!

Vg

EF

(E)

n

0

Vg, but not Е!! 1. why does one extrapolate this point-xy=0 ?.. … zero-mode Landau levels!

3. In principle C=(1/Cg+1/Cq(B,Vg))-1 .. but with real (Cq) it does not change the answer!! (печалька…..)

Let us inspect the result in more detail..

Сильно быстро спешили 1. greatly hastened quickly??

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?

4*1012

What is known about valence band spectrum?

Experimentally:

What does mean such a coincidence?

Сильно быстро спешили 2.

Theoretically

Is it OK?

4*1012

Experimentally: Сильно быстро спешили 2.Theoretically:

What does mean such a coincidence?

10 20 30 40

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

Vg= -9.5V

Vg= -0.5V

H, kOe

d/dH(

xx/

xx(0)

Что следует из совпадения?

Our data

To study spectrum we have found the hole effective mass from temperature dependence of the amplitude of SdH oscillations

p=1.05*1011см-2

Electron-like states

The energy spectrum is close to parabolic one at k>8*105 .Electron-like states, if there is, occures for small k.

Calculated mass is negative!!

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..

Проводимость двумя типами носителей

This is qualitatively similar but quantitatively ……What are the possible reasons?......

kP?single-particle approximation?

The dispersion E(k) reconstructed from the data analysis and calculated one within framework of isotropic six-band kP-model.

What about valence band spectrum at d<dc ? (“normal” spectrum)

happy coincidence

Unfortunately there was ungated structure….

Сильно быстро спешили 3.

!!

Our data for analogous structure:

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 thequantum well.

Effective mass, spectrum

At first sight the large spin-orbit splitting of the energyspectrum in the nominally almost symmetrical structure

seems very surprising….

Peculiarity of QHE

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, технологовмогут как-то прояснить картину….Only joint efforts of theorists, experimentalists, technologistscan somehow clarify the picture ....

Do not shoot the pianist - he plays as he can…

Myths..Mythlets

…

Reality.. Cooking..

Art!!

Post Scriptum:(Conclusion)

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. №