Linearly Polarized Emission of Quantum Wells

Subject to an In-plane Magnetic Field

N. S. Averkiev, A. V. Koudinov and Yu. G. KusrayevA.F. Ioffe Physico-Technical Institute, St.-Petersburg, Russia

D. Wolverson University of Bath, Bath, United Kingdom

G. Karczewski and T. Wojtowicz Institute of Physics, Warsaw, Poland

Supported by INTAS 03-51-5266

Geometry of the PL polarization measurements

x y

x y

I I

I I

zx

y

We measure the degree of polarization as we rotate the sample by angle about its normal z

0

B

PL

QW

Examples of the in-plane rotation angular scansof linear polarization in QWs

cos(0)

cos(2)

cos(4)

B≠0

…if the true symmetry of the QW states is:

In-plane rotation of the sample: what one may expect...

dD2 vC2

cos(0),cos(4)

cos(0),cos(2),cos(4)

can contain terms in x y

x y

I I

I I

0

B

PL

QW

Spin-flip Raman scattering: out-of-plane rotation dependence of the spectra

2.0

sincos

||

2222||

gg

ggBBh

02

3

2

30

2

3

2

32

3

2

3

02

3

2

30

1

11

11

1

Bg

BgBg

BgBg

Bg

hH

B = Bx iBy,

– the value of the in-plane deformation multiplied by the respective constant of the deformation potential,

– the energy separation between the heavy and the light holes,

g1 – the hole g-factor for the bulk

material; the principal axis of the deformation is taken for the x axis.

Theory I: the valence band Hamiltonian

4cos2cos2cos 24

22

20 BABABA

...

8

3

...2

3

...

2

*1

2

2

4

21

2

2

*11

0

kT

ggA

kT

ggA

ggA

e

e

Calculation results in the followingpolarization as a function of angle ():

– 0th harmonic

– “built-in” polarization

– 2nd harmonic

– 4th harmonic

Theory II: random directions of the in-plane distortions

There are two serious contradictions between the above theory (with a uniform in-plane distortion) and the experimental observations:

1. The theory predicts the relationship which is however not obeyed ( );

2. The theory predicts while the experiment shows that sometimes .

||g

g02.02.0

42 AA 42 AA

One has to introduce the directional scatter of the in-plane distortions:

24cos2cos1

)( 42 CCf

...

8

3...;

2

3...;; 42

*1

2

2

4221

22

*11

02

CkT

ggAC

kT

ggA

ggAC ee

Then, the re-calculated values of the harmonics will include the parametersof the distribution function f():

Comparison with experiment I:Zero magnetic field, “built-in” polarization

Symmetry: 180-deg periodicity (2nd angular harmonic)

Origin: mixing hh + lh by the in-plane distortion

Term responsible for: 2cos2

C

Comparison with experiment II:Magnetic field applied, polarization A2B2

Symmetry: 180-deg periodicity (2nd angular harmonic)

Origin: splitting of hh and e by the magnetic field

Term responsible for: 2cos

)(4

32

21

2 Tk

BggC

B

e

Comparison with experiment III:Magnetic field applied, polarization A0B2

Symmetry: rotation invariant

Origin: mixing hh + lh by the magnetic field

Term responsible for: 2

2*11

Bgg

Comparison with experiment IV:Amplitudes of harmonics vs magnetic field

2

2*112

0

BggBA

2

21

22

2 )(4

3

Tk

BggCBA

B

e

– quadratic in B as long as Bg1

– quadratic in B as long as TkBg Be

Conclusions

1. The magnetic field, angular and spectral dependences of the PL polarization along with the data on the spin-flip Raman scattering were used for construction and verification of a theoretical model.

2. We have carefully analyzed the contributions of different symmetry to the linear polarization of the PL of QWs, as well as the physical mechanisms underlying them.

3. We find that the valence band states in the QWs have a reduced symmetry in the QW plane, and the principal axes of the in-plane distortions show a scatter in direction.

4. We suggest an interpretation of the 4th angular harmonic of the linear polarization.