excitonic aharonov-bohm effect in type-ii quantum...

Excitonic Aharonov-Bohm Effect in Type-II Quantum Dots

Igor L Kuskovsky Department of Physics

Queens College of CUNY, Queens, NY 11367

Acknowledgements

B. Roy (QC) H. Ji (QC) S. Dhomkar (QC) M. C. Tamargo (CCNY) D. Smirnov (NHMFL) Y. Kim (NHMFL) J. Ludwig (NHMFL)

L. Mourokh (QC) A. O. Govorov (Ohio U.) F. Peeters (U. Antwerp) M. Tadic (U. Belgrade) I. C. Noyan (Columbia U) U. Manna (Columbia U)

Aharonov-Bohm Effect Classical electrodynamics: the vector potential, A, is

considered a mere mathematical auxiliary -- convenient for calculations, but having no direct physical meaning

Quantum mechanics: the potential(s) play a more significant role, for the Hamiltonian is expressed in terms of ϕ and A, not E and B: Nevertheless, it was taken for granted that there could be no

electromagnetic influences in regions where E and B are zero

In 1959 Aharonov and Bohm showed that the vector potential can affect the quantum behavior of a charged particle even in regions where electromagnetic field is zero (a magnetic flux exists, while no effects of the classical Lorentz force are present)

Aharonov-Bohm Effect

Consider an electron on a circular orbit with and without presence of a Solenoid (the bound Aharonov-Bohm Effect) Solenoid lifts two-fold (direction of rotation) degeneracy The energy of a [positive] particle moving along the current of the

solenoid (l > 0) is lowered The energy now depends on the magnetic filed inside the solenoid,

although the magnetic filed at the particle’s location is ZERO

2

2

2

2

22

2

2

0 0 ... ,2 ,1 ,0 ,

Φ−==

≠Φ=Φ±±==

hqll

ill

lmR

EmR

lE

le

φψ

Aharonov-Bohm Effect

Excitonic-AB Effect in Magneto-PL

As the flux increases, |L| changes from 0 to 1, 2, 3 …

Two important outcomes: Energy Oscillation(s) (“known”) PL Intensity Oscillation(s) - due

to selection rules Multiple Oscillation in strong

confinement or weak coupling A single ‘peak’ in strong coupling

regime

• The Excitonic [“Optical”] AB Effect refers to manifestation of the Aharonov-Bohm phase in the optical emission of polarized excitons [“dipoles“] – overall neutral quasi-particle

• Quantum Rings and Type-II Quantum Dots

e.g., Kalameitsev, et al., JETP Lett. 68, 669 (1998); Govorov, et al., PRB RC 66, 081309 (2002); Janssens, et al., PRB 67, 235325 (2003)

BRRR he 0)(2 −=∆Φ π

he llL +=

2

020

2

0 2

Φ

∆Φ++= L

MREE excexc

2/)(0 he RRR +=

20

22 )(R

RmRmM hhee +=

Excitonic-AB Effect in Magneto-PL The 1st transition of the electron orbital number to non-zero

value occurs at the magnetic field BAB for which,

0 1 2 3 4 5

Excit

on En

ergy (

arb. u

nits)

Φ/Φ0

le = 0 le = -1 le = -2

20

AB20

Φ=BRπ

meV 5.0~8

2

20

2

2

020

2

0

MRE

LMR

EE

exc

excexc

=∆

Φ

∆Φ++=

Excitonic-AB Effect in Magneto-PL

The ground sate for a QR,

No transition to dark states is expected without external fields, e.g., electric field*

Romer and Raikh, PRB 62 7045 (2000); *Fischer, et al., PRL 102, 096405 (2009)

ΦΦ

+−∝∆ −e πργπ 2

0

00 2cos1

Type-II Heterosturctures In Type-II heterostructures,

the charge carriers are spatially separated

• In QDs: one type of carriers is confined within the QD whereas the other is attracted via the Coulomb interaction, creating spatially indirect (type-II) exciton • Electrical dipole across interface is formed

In ideal type-II QDs the ‘barrier’ carrier would locate above-below the QD

Kuskovsky, et al., PRB 76, 035342 (2007)

Blue = Highest Electron Density

Type-II Quantum Dots: Examples

2.2 2.3 2.4 2.5 2.6 2.7 2.8

10-4 10-3 10-2 10-1 100

2.4

2.5

2.6

2.7

2.8

2.9

3.0

3.1

T = 10K

Blue band Green band 1 Green band 2 Linear fit I1/3

ex

PL P

eak

posi

tion

(eV)

Excitation Intensity (arb. units)

Iex = 0.0001Imax

Inte

nsity

(arb

. uni

ts)

Energy (eV)

Blue band Green band 1 Green band 2

Iex = 0.1Imax

• cw PL – Emission energy shifts

to higher values with increasing excitation

Roy et al., Eur. Phys. J. B, 86, 31 (2013)

Type-II Quantum Dots: Examples

0 50 100 150 200 250

0.01

0.1

1

10

0 100 200 300

0.01

0.1

1

PL In

tens

ity (a

rb.u

.)

Time (ns)

calculated Iexc

1

Iexc2

Iexc3

Iexc1 >Iexc

2 >Iexc3

PL In

tens

ity (a

rb.u

.)

Time (ns)

• Time-resolved PL – Long-lived due to weak

overlap of the carriers’ wave functions

– Dependent on Iex, for overlap of the wave functions depends on the concentration of photo-generated carriers

Gu et al., PRB 71, 045340 (2005); Shuvayev et al., PRB 79, 115307 (2009)

Type-II Exciton Lifetimes and Binding Energies from Temperature Dependent TRPL

0 0

1 1 1[1 exp( / )] exp( / )b B a Br nr

C k T k Tε ετ τ τ

= − − + −

0.0 0.2 0.4 0.6 0.8 1.0 1.2

0.010

0.015

0.020

0.025

0.030

1/

τ (ns

-1)

Sample C2.34 eV

1/kBT (meV-1)

~130 K

Yi, et al., PRB 71, 045340 (2005); Ji, et al., J. Electr. Mat. 42, 3297 (2013)

Ionization/Re-capture

Type-II Exciton Lifetimes and Binding Energies from Temperature Dependent TRPL

0 0

1 1 1[1 exp( / )] exp( / )b B a Br nr

C k T k Tε ετ τ τ

= − − + −

Sample Photon Energy

(eV)

Exciton Binding Energy (meV)

𝝉𝒓𝟎 (ns)

Activation Energy (meV)

𝝉𝒏𝒓𝟎 (ns)

A 2.48 6.20 64.7 90.7 0.10

B 2.48 7.34 91.9 103.0 0.15 2.36 7.44 93.1 111.1 0.18

C 2.34 11.30 99.9 83.1 1.37

Yi, et al., PRB 71, 045340 (2005); Ji, et al., J. Electr. Mat. 42, 3297 (2013)

Disk-like Type-II QDs in Magnetic Field

Blue = Highest Electron Density M

agne

tic F

ield

No AB Effect

Kuskovsky, et al., PRB 76, 035342 (2007)

Single Type-II QD: Strain The AB effect was observed is

InP/GaAs QDs (Ribeiro, et al., PRL, 92, 126402 (2004))

However, no oscillations were observed by de Godoy, et al., in the same system (PRB 73, 033309 (2006))

Madureira, et al., APL 90, 212105 (2007) showed that the ability to observe it depends on the growth conditions and specifics of the system

Stacked Type-II QDs

Blue = Highest Electron Density

No AB Effect Possible • Red = Highest Electron (Hole) Density at

0 T (upper) and 6 T (lower)

AB effect is Possible

Mag

netic

Fie

ld

Samples MEE-MBE Shutter Sequence

Schematic of the Samples

Kuskovsky, et al., PRB 63 155205 (2001);PRB 76, 035342 (2007)

n = 1 or 3

Example: ZnMgTe/ZnSe

Manna et al, JAP 111, 033516 (2012)

• XRD simulations showed • A minimal amount of Te (< 1%)

inside the spacer • ~ 32% of Mg inside the QDs

Quantum Dots Form Stacks, which results in “averaging” out QDs size variations

Strain cannot be completely ruled out

Qualitative Model

Kuskovsky, et al., PRB 76, 035342 (2007); Dhomkar, et al., APL 103, 181905 (2013); Manna, et al., JAP 111, 033516 (2012); Ji et al., (2014) - unpublished

-0.50 -0.45 -0.40 -0.35 -0.30 -0.25 -0.20

-0.03

0.00

0.03

q x(A-1)

SL(-1)SL(-2)

10-5 10-4 10-3 10-2 10-1 100103

104

105

106

107

108

109

Slope = 1.02

Int.

PL In

tens

ity (a

rb. u

nits

)

Excitation Intensity (arb. units)

D47T = 9.0 K

The AB Signature in PL Intensity

2.1 2.2 2.3 2.4 2.5

D47, 1.5 NDFT =5.4 K

6.00 T 4.00 T 2.00 T 1.39 T 0.65 T 0.00 T

Inte

nsity

(arb

. uni

ts)

Photon Energy (eV)-6 -4 -2 0 2 4 6

2450

2500

2550

2600

2650D47, 1.5 NDFT =5.4 K

Int.

Inte

nsity

(arb

. uni

ts)

Magnetic Field (T)

• The AB peak is only observed in Faraday Configuration, as expected • The AB signature is ‘masked’ at high excitation intensities


• The AB peak is only observed in Faraday Configuration, as expected • The AB signature is ‘masked’ at high excitation intensities

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

D47, 1.5 NDFT =5.4 K

Int.

Inte

nsity

(arb

. uni

ts)

Magnetic Field (T)

4.7%

BAB ~1.40 T

AB Signature in Intensity of Polarized PL

-20 -10 0 10

0.4 0.8 1.2 1.6 2.0 2.4

Inte

grat

ed In

tens

ity (a

rb. u

nits

)

Magentic Field (Tesla)

D47, T = 1.9 K

Inte

grat

ed In

tens

ity (a

rb. u

nits

)

Magentic Field (Tesla)

~1.37 T

~15.2%

The AB ‘peak’ appears only in one polarization Largest reported

magnitude Possibly was masked by

some background emission

AB Signature in Energy of Polarized PL

-15 -10 -5 0 5 10 152.28

2.29

2.30

2.31

2.32

2.33

2.34

2.35

2.36

Ener

gy (e

V)

Magnetic Field (T)

0.9000

0.9167

0.9333

0.9500

0.9667

0.9833

1.000D47T = 0.36K

The AB energy peak also become evident in polarized PL

meV 5.0~8

2

20

2

2

020

2

0

MRE

LMR

EE

exc

excexc

=∆

Φ

∆Φ++=


Magnetic field of the 1st angular momentum transition increases with decreasing Te concentration

Attribute to ‘size’ of QDs

Correlating with PL at zero magnetic field, allows to estimate QD density*, binding energy of excitons*, as well as the in-plane size of type-II exciton** 0 1 2 3 4

0.3

0.6

0.9

1.2

1.5

1.8

~ 1.85 T

~ 1.90 T

~ 2.08 T

~ 1.42 T

~ 1.88 T~ 1.88 T

Norm

. Int

. Int

ensi

ty (a

rb. u

nits

)

Magnetic Field (T)

~ 2.06 T

Kuskovsky, et al., PRB 76, 035342 (2007); *Ji et al., – unpublished; **Roy et al., APL 100, 213114 (2012)

‘Spectral Analysis’

• ‘Double peak’ in the AB oscillation points to at least two different QD stacks, with corresponding type-II exciton sizes of 18.2 & 17.9 nm

• TRPL at B = 0 also confirms two distinct decays in these spectral regions.

• There is a non-monotonic change in the AB oscillation magnitude

0.00.20.40.60.81.0

2.0

2.1

2.2

2.3 2.4 2.5 2.6 2.7 2.8

2.0

2.5

3.0

3.5

Nor

m. P

L (a

rb. u

nits)

a)

B AB (T

)

b)

Peak

Cou

nts (

%)

Energy (eV)

c)

Roy, et al., APL, 100, 213114 (2012); PRB, 86, 165310 (2012); *ErJPB 86:31, 1 (2014)

‘Spectral Analysis’

• ‘Double peak’ in the AB oscillation points to at least two different QD stacks, with corresponding type-II exciton sizes of 18.2 & 17.9 nm

• TRPL at B = 0 also confirms two distinct decays in these spectral regions.

• There is a non-monotonic change in the AB oscillation magnitude

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

~2.15 T~1.98 T

D50 2.465 eV 2.520 eV 2.641 eV

PL

Inte

nsity

(arb

. uni

ts)

Magentic Field (T)

~2.15 T

~1.98 T

Roy, et al., APL, 100, 213114 (2012); PRB, 86, 165310 (2012); *ErJPB 86:31, 1 (2014)

0 50 100 150

0.01

0.1

1

Nor

mal

ized

Inte

nsity

(arb

. uni

ts)

Time(ns)

2.43 eV 2.48 eV 2.53 eV 2.58 eV 2.63 eV 2.69 eV 2.75 eV

Sample B T= 9K

Type-II QDs in Single-Cycle Samples

0 5 10 15 20

T = 4.2K

Inte

grat

ed P

L In

tens

ity (a

rb. u

nits

)B (T)

~2.1T

• Samples that did not exhibit “type-II behavior” at low temperatures at zero magnetic field

Kuskovsky, et al., Supperlattices & Microstruct., 47, 87-92 (2010)

Type-II QDs in Single-Cycle Samples The QD related PL appears at elevated

temperatures, and behaves the same as that observed for samples grown with three Zn-Se-Te cycles

Kuskovsky, et al., Supperlattices & Microstruct., 47, 87-92 (2010)

Built-in Electric Field?

Was proposed by Fischer et al., [PRL 102, 096405 (2009)] as caused by an in-plane electric field

Samples with low amount of Te exhibit relatively narrow AB ‘peak’, which indicates a presence of built-in electric fields

Roy, et al., PRB, 86, 165310 (2012)

Decoherence of the AB Excitons

Attempt to use excitonic AB effect to study quantum decoherence

It is inherently a contactless approach Decoherence of the AB excitons

should be of the same nature as that of AB oscillations observed in transport

0 1 2 3 4

Int.

Inte

nsity

(arb

. uni

ts)

Magnetic Field (T)

Tem

pera

ture

0.3

1 -

27.1

K

0 1 2 3 4

Int.

Inte

nsity

(arb

. uni

ts)

Magnetic Field (T)

T = 27.1 K


∆𝐼𝐴𝐴 ∝ 𝑒𝑒𝑒 − 𝐿𝐿𝐷(𝑇)

Assuming Ballistic regime, 𝐿𝐷(𝑇) ∝ 𝜏𝐷(𝑇)

∆𝐼𝐴𝐴 ∝ 𝑒𝑒𝑒 − 𝜏𝜏𝐷(𝑇)

At high temperatures, phonon mediated decoherence dominates, and

𝜏𝐷−1(𝑇) ∝ 𝑇3

0 7000 14000 21000 28000

2

3

4

5 10 15 20 25 300

15

30

45

60

T3 (K3)

Ln(Integarted Peak PL) Linear Fit C

Ln(In

tega

rted

Pea

k P

L)

Peak AB counts Fit to v*exp[-BT3]

Inte

grat

ed P

eak

T (K)


1 10

1

10

1 2 3

7.5

7.8

8.1

AB

Mag

nitu

de R

(%)

Temperature (K)

AB M

agni

tude

R (%

)

Temperature (K)

1 100

2

4

6

8

τ-1D~T3

AB M

agni

tude

R (%

)

Temperature (K)

y = Cexp[-αT-β T3]

C = 8.1; α = 0.04 K-1; β = 9.2×10-5 K-3

τ-1D~T

∆𝐼𝐴𝐴 ∝ 𝑒𝑒𝑒 − 𝜏

𝜏𝐷(𝑇)

Phonon mediated decoherence

𝜏𝐷−1(𝑇) ∝ 𝑇3 Below 1÷3 K, carrier-

carrier scattering or thermal averaging dominate, so that we assume

𝜏𝐷−1(𝑇) ∝ 𝑇

Summary Polarized 2D excitons are perfect

objects to study Aharonov-Bohm effect of neutral quasi-particles

Stacked type-II QDs are among the best systems for such experiments as QD size variations are averaged out

We did observed strong AB signal in PL intensity of in stacked sub-monolayer ZnTe/ZnSe type-II QDs

Multiple sets of QDs can be detected and size of exciton is measured with sub-nanometer precision

In some samples, the observed ‘peaks’ are narrow, suggesting presence of in-plane electric fields

We have attempted to measure decoherence using contactless techniques

More detailed studies required to verify a non-monotonic behavior at

very low temperatures understand polarized magneto-PL

excitonic aharonov-bohm effect in type-ii quantum...

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