Y.A.Pusep Institute of Physics of São Carlos, University of São Paulo Collaborators: Experiment – A.D.Rodrigues, UFSCar. Theory - S.S.Sokolov, B.Verkin.

Delocalization-localization Transition of Plasmons in Random GaAs/AlGaAs

Superlattices

Y.A.Pusep

Institute of Physics of São Carlos, University of São Paulo

Collaborators:

Experiment – A.D.Rodrigues, UFSCar.Theory - S.S.Sokolov, B.Verkin Institute for Low-Temperature Physics and Engineering, National Academy of Sciences of Ukraine.Samples – H.Arakaki, C.A. de Souza, IFSC/USP.

MotivationWhy plasmons ?

Advantages of optical and electrical circuits:Fast data transfer by transmitting optical signals through minuscule nanoscale structures .

Optical fibers versus electrical circuits. Diffraction limit.

Manipulation of plasmons (localization and propagation).

Electrons and Plasmons1. Electrons: single-particle excitations

2. Plasmons: collective excitations

Outline

1. Random superlattices

2. Raman scattering by collective excitations

3. Plasmon localization: theory and experiment

4. Conclusions

Artificially disordered superlattices

DSL

Nwell

E

0

= /W

(GaAs)n(Al

0.3Ga

0.7As)

m

W

Z E(kz)

kz /D

SL

Criterion of Localization

Electrons

( = 0, w T = 0) 0, /T < 0

( = 0, w T = 0) = 0, /T > 0

metal (kFl>1):

insulator (kFl<1):

Obs: l is the electron free path length, kF = 2π/λe, λe is the electron wavelength.

Criterion of Plasmonlocalization - ?

Theory of plasmon localization

Plasmon wave function:

with0.2 0.4 0.6 0.8 1.0 1.2

0

10

20

30

Lc R

0

p,

cm-1

2R0/L

c

Lc R

0

R0= 7 nm

U0= 12 cm-1

Results of calculations

Neutral impurity scattering potential:

Localized plasmon: Lc < R0

Delocalized plasmon: Lc > R0

2. Relation between Lc and R0 determine propagation of

plasmons:

1. Plasmon damping (Гp) independent ofdisorder parameter (Lc, δ) indicates localization.

Criteria of Plasmon localization

Raman scattering of plasmons in presence of disorder

2 20

2 2

( ) ( / 2)( ) exp

2 ( ) ( / 2)

c

p p

q q L dqI

q

Non-conservation of quase-momentum [Yu.A.Pusep, et al., Phys.Rev.B 58, 10683 (1998)]:

360 380 400 420 440 460 480 500

TO

Raman shift (cm-1)

Ra

ma

n in

ten

sity

Al0.2

Ga0.8

As:Si

N=2x1018cm-3L+

2

Lc= 8.6nm

p= 6 meV

0.5 1.0 1.5 2.0 2.50

5

10

0

10

20

30

0

1

2

3

p (

cm-1)

Lc (

nm

) p

(m

eV)

Electron concentration (x1018cm-1)

(a)

R0= 0.25 nm

U0 = 0.6 eV

(b)

Doped superlattices(weak plasmon localization)

Disordered superlattices(strong plasmon localization)

0

50

100

150

200

0.0 0.2 0.4 0.6 0.8 1.0 1.2

4

6

8

10

0

10

20

30

p(m

eV) (a)

R0=20nm

U0=15meV

T = 10K

Lc(n

m)

Disorder Strength,

p(c

m-1)

(b)

Lc > R0 Lc < R0

T = 250K

0 50 100 150 200 2502

3

4

5

0 50 100 1504

6

8

10

Lc (

nm

)L

c (n

m)

Lc>R

0

(a)

Lc<R

0

Temperature (K)

Temperature (K)

(b)

Lc > R0

Lc < R0

Weak plasmon localization:(plasmonic “metal”)

Strong plasmon localization:(plasmonic “insulator”)

Temperature Effect

Conclusions

Delocalized plasmon: Lc > Ro – the increasing disorder results in increasing plasmon linewidth;

Localized Plasmon: Lc < Ro – no influence of the disorder on plasmon linewidth;

The independence of the plasmon linewidth on disorder is the manifestation of plasmon localization.

The increasing temperature enhances the localization of the weakly localized plasmons, while it causes the delocalization of the strongly localized plasmons.

Yu.A.Pusep, A.D.Rodrigues, S.S.Sokolov, Phys.Rev.B 80, 205307 (2009).

Thank you!

Raman line shapes (q=0)

Damped plasmon: Overdamped plasmon:

250 300 350 400 450 500

TO

GaAs

p=450 cm-1

p=5 cm-1

L+

R

am

an

inte

nsi

ty

Frequency

LO

200 300 400 500 600 700 800

LO

Ram

an in

tens

ity

Frequency

TO GaAs

p=450 cm-1

p=500 cm-1

L+

Raman line shapes (q≠0)

360 380 400 420 440 460 480 500

TO

Raman shift (cm-1)

Ram

an in

tens

ity Al0.2

Ga0.8

As:Si

N=2x1018cm-3L+

2

L= 8.6nm

Non-conservation of the quase-momentum:

Raman scattering in disordered GaAs/AlGaAs superlattices

350 400 450

200 300 400 500

LO2

LO1 1.2x1018 cm-3

(b)

TO2

+

2+

1

1.13

0.59

= 0.18

Raman shift (cm-1)

(GaAs)m(Al

0.3Ga

0.7As)

6:Si

Ram

an in

tens

ity (

arb.

units

)

-

TO1

+

2

TO2+IF 1.1x1018 cm-3

7.0x1017 cm-3

5.0x1017 cm-3

(a)

0.2 0.4 0.6 0.8 1.0 1.20

5

10

15

Disorder Strength,

I(- )/

I( )

0.0 0.1 0.2 0.3 0.4 0.5200

250

300

350

400

450

500

550

600

650

700

TO(AlAs)

LO(AlAs)

TO(GaAs)

LO(GaAs)

-

Fre

quen

cy

(cm

-1)

Wave number q (Units of /a)

(GaAs)17

(Al0.3

Ga0.7

As)6

n = 1.2x1018cm-3

60 70 80 90 100 110

0.4

0.6

0.8

1.0

(a)

SL = 1.13

Distance Z, nm

Ele

ctro

n c

on

cen

tra

tion

, x1

018

cm

-3

40 50 60 70 80 90

0.4

0.6

0.8

1.0

(b)

SL = 0.47

50 60 70 80 90 100

0.4

0.6

0.8

1.0

(c)

SL = 0.18

Criterion of Localization

Electrons

T.F.Rosenbaum et al., Phys.Rev.Lett. 45, 1723 (1980)

Y.Liu, et al., Phys.Rev.Lett. 67, 2068 (1991)

( = 0, w T = 0) 0, /T < 0

( = 0, w T = 0) = 0, /T > 0

metal (kFl>1):

insulator (kFl<1):