Indirect excitons in coupled quantum wells Exciton pattern formation and exciton transport Exciton...
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Transcript of Indirect excitons in coupled quantum wells Exciton pattern formation and exciton transport Exciton...
• Indirect excitons in coupled quantum wells
• Exciton pattern formation and exciton transport
• Exciton transport in potential landscapes • Lattices • Traps • Circuit devices • Random potentials
• Spin transport of excitons
• Conveyers
• Vortices
In collaboration with:
Michael Fogler, Joe Graves, Martin Griswold, Aaron Hammack, Alex High, Jason Leonard, Andrew Meyertholen, Katya Novitskaya, Mikas Remeika, Averi Thomas, Alex Winbow, Sen Yang, Yuliya Kuznetsova (UCSD)
Tomas Ostatnick´y, Alexey Kavokin (Southampton), Yura Rubo (Cuernavaca)
Leonid Levitov (MIT), Ben Simons (Cambridge)
Lois Smallwood, Leonidas Mouchliadis, Joe Wilkes, Egor Muljarov, Alexei Ivanov (Cardiff)
Micah Hanson, Arthur Gossard (UCSB)
Transport and spin transport of excitonsLeonid V. Butov, UCSD
1 2
22~ 3 K
dB
dBB
n
T nmk
What temperature is “cold” for exciton gas?1/ 222dB
Bmk T
3D: 1 3
22 32
0.527
dB
dBB
BEC dB
n
T nmk
T T
2D:mexciton ~ 10 -6 matom Kelvin for excitons
is likemicroKelvin for atoms
transition from classical to quantum gas takes place when thermal de Broglie wavelength is comparable to interparticle separation
3D gas of Rb atoms: n = 1015 cm-3, matom = 105 me → TdB ~ 5×10-6 K
2D gas of excitons in GaAs QWn = 1010 cm-2, mexciton= 0.2 me → TdB ~ 3 K
n < nMott ~ 1/aB2 ~ 2×1011 cm-2
How to realize cold exciton gases ?
Tlattice << 1 K in He refrigerators
finite lifetime of excitons could result to high exciton temperature: Texciton > Tlattice
find excitons with lifetime >> cooling time Texciton ~ Tlattice
Challenges for realization of exciton condensates
To solve: Find or design semiconductor structures where
short lifetime excitons have long lifetimes >> cooling times
competing ground states, e.g. EHL excitons form the lowest energy state
exciton destruction, e.g. due to Mott transition
excitons have large binding energy
disorder disorder is weak
solving these challenges has led to studies ofvarious experimental systems
and various types of exciton condensate
Indirect excitons in coupled quantum wells
Electron-electron bilayers in magnetic fields at =1
Electron-hole bilayers with gate-induced carriers
Electron-hole bilayers with photoexcited carriers
_
_
+
+
h
e
e e
GaAs
AlxGa
1-xAs
z
E
K
E
excitondispersion
2D: coupling of E=0 state to continuum of energy states E > E
0
effective cooling of 2D excitons by bulk phonons
3D: coupling of E=0 state to single state E=E0exciton energy relaxation
by LA-phonon emission
E0=2M
xv
s
2
~ 0.05 meV
AlAs/GaAsCQW
GaAs/AlGaAsCQW
h
e
h
e
X
TX ~ 100 mKhas been realized experimentally
30 times below TdB
Why indirect excitons in CQW ?103-106 times longer exciton lifetime due to separation between electron and hole layers
103 times shorter exciton cooling time than that in bulk semiconductors
0 50 1000.1
1
TX
Time (ns)
A.L. Ivanov et al in PRL 86, 5608 (2001)
~ 10 ns to cool to 300 mK~ 100 ns to cool to 100 mK
realization of cold exciton gas in separated layers was proposed by Yu.E. Lozovik & V.I. Yudson (1975); S. I. Shevchenko (1976);T. Fukuzawa, S.S. Kano, T.K. Gustafson, T. Ogawa (1990)
Repulsive interaction between indirect excitons
_
_
+
+
h
e
indirect excitons are oriented dipoles
Repulsive dipole-dipole interaction● stabilizes exciton state against formation of metallic EHL
● results in effective screening of in-plane disorderA.L. Ivanov, EPL 59, 586 (2002)R. Zimmermann
D. Yoshioka, A.H. MacDonald, J. Phys. Soc. Jpn. 59, 4211 (1990)X. Zhu, P.B. Littlewood, M. Hybertsen, T. Rice, PRL 74, 1633 (1995)
the ground state is excitonic
1.54 1.55 1.56 1.57
PL
Int
ensi
ty
Wex
=4 W/cm2
Wex
=0.5 W/cm2
Energy (eV)
energy shift: E ~ n/C estimate for exciton density approximation for short-range 1/r3 interaction C = /4e2d
Repulsive interaction in experimentexciton energy increases with density L.V. Butov, A. Zrenner, G. Bohm, G. Weimann, J. de Physique 3, 167 (1993)
C. Schindler, R. Zimmermann, PRB 78, 045313 (2008) C and n in experiments are higher
also high quality CQW samples with small initial disorder are required to overcome exciton localization
d
potential energy of indirect excitons can be controlled by voltage
the ability to control electron fluxes by an applied gate voltage
electronic circuit devices mesoscopicsthe field which concerns electron transport in a potential landscapes
in-plane potential landscapes can be created for excitons by voltage pattern e.g. traps, lattices, circuit devices
zE edF
the ability to control exciton fluxes by an applied gate voltage
excitonic circuit devices mesoscopics of bosons in semiconductors
e
h
condensation pattern formation
potential profilescan be created and in situ controlled
indirect excitons
energy can be controlled by gate voltage
can cool down to 0.1 K well below TdB ~ 3K
can travel over large distances
have built-in dipole moment ed
cold Bose gases in solid-state materials excitonic devices
transportspin transport
edFE
have long lifetimes
optical methods → local probe of excitons
d
Exciton pattern formation and exciton transport
external ring
ring fragmentation localized bright spots
Pattern Formation: Exciton Rings and Macroscopically Ordered Exciton State
same
spatial order on macroscopic lengths
0 20 400
400
800
Po
siti
on
on
th
e ri
ng
(m
)
Peak number
inner ring
410 m
T=1.8 K T=4.7 K
0 2 4 60
Am
plit
ud
e o
f th
eF
ou
rier
Tra
nsf
orm
T (K)
appears abruptly at low T
L.V. Butov, A.C. Gossard, D.S. Chemla, Nature 418, 751 (2002)
n
~ 0.1 meV
Kdrift
K0
E
K
K
0 40 80 120
1.546
1.547
1.548
1.549
0 40 80 120
flow of excitons out of excitation spot due to exciton drift, diffusion, phonon wind, etc.
r (m)
En
ergy
(eV
)
PL pattern spatial distribution of optically active low energy excitons
excitons can travel in a dark state after having been excited until slowed down to a velocity below photon emissionthreshold, where they can decay radiatively
PL
In
ten
sity
repulsive interaction → drift
excitation spothigh TX exciton drift
lower occupation of radiative zone
inner ringlower TX excitons relax to radiative zone
higher occupation of radiative zone
exciton transport over tensof microns
k k
E E
Inner ring
L.V. Butov, A.C. Gossard, D.S. Chemla, Nature 418, 751 (2002)
A.L. Ivanov, L. Smallwood, A. Hammack, Sen Yang, L.V. Butov, A.C. Gossard, EPL 73, 920 (2006)
inner ring forms due to exciton transport and cooling
Localization-delocalization transition for exciton transport in random potential
exp.
theory
exp.
theory
low densities:emission profile follows excitation spotexcitons are localized in random potential
high densities:emission extends well beyond excitation spotexcitons screen random potential, travel away from excitation spot and form inner ring
Kinetics of inner ring
formation time of inner ring ~ 30 ns
kinetics of inner ring
estimate of exciton transport characteristicsDX reaches ~ 20 cm2/s
PL jump vs r → excitons outside laser spotincluding inner ring region are cooled to Tlattice even during laser excitation
exp. theory
A.T. Hammack, L.V. Butov, J. Wilkes, L. Mouchliadis, E.A. Muljarov, A.L. Ivanov, A.C. Gossard, PRB 80, 155331 (2009)
External ring
above barrier laser excitation creates additional number of holes in CQW
heavier holes have higher collection efficiency to CQW
holes created at the excitation spot diffuse out this depletes electrons in the vicinity of the laser spot creating electron-free and hole rich region
electrons
excitons
holes
excess holes are photogenerated in the laser excitation spotelectron source is spread out over the entire plane due to current through the CQW from n-doped GaAs layers
same for e ↔ h
x
y
z
E
L.V. Butov, L.S. Levitov, B.D. Simons, A.V. Mintsev, A.C. Gossard, D.S. Chemla, PRL 92, 117404 (2004)
R. Rapaport, G. Chen, D. Snoke, S.H. Simon, L. Pfeiffer, K.West, Y.Liu, S.Denev, PRL 92, 117405 (2004)
external ring forms at interface between electron-rich and hole-rich regions
0 1 2 3 4 5
Delay (s)
Rad
ius
(m
)
Rad
ius
(m
)
0
250
00 1 2 3 4 5
Delay time ( s)
c
40 cm2/s
Dh = 16 cm2/s
26 cm2/s
100m
- 9.5 s - 8.8 s - 6.5 s 0.2 s 1.5 s 2.5 s 3 s 4 s
-10s 0 5slaser pulse
e
h
external ring
LBS ringh
e
expansion of external ring collapse of external ring
a b c d e f g h
ij
50
80 cm2/sDe = 200 cm2/s
30 cm2/s
0
collapse of external ring expansion of LBS rings
kinetics of external and LBS rings
estimation of e and h transport characteristics
De ~ 80 cm2/s, Dh ~ 20 cm2/s
Kinetics of external ring and LBS ringstime
Sen Yang, L.V. Butov, L.S. Levitov, B.D. Simons, A.C. Gossard, PRB 81, 115320 (2010)
rings are far from hot spotsdue to long lifetimes of indirect excitons TX ≈ Tlattice
rings form is region where cold and dense exciton gas is created
macroscopically ordered exciton state (MOES)
localized bright spots have hot cores
no hot spots in external ring and LBS rings
indirect exciton PL direct exciton PL – pattern of hot spots
Spontaneous coherence
experimental method:Mach-Zehnder interferometry with spatial and spectral resolution
probing coherence far from laser both in space and energy: coherence is spontaneous
2 4 6 8 100
1
2
3
0
Co
her
enc
e L
eng
th (m
)
Temperature (K)
PL
Co
ntr
ast
alo
ng
th
e R
ing
left arm right arm
the increase of the coherence length is correlated with the macroscopic spatial ordering of excitons
~ 2 m >> the classical value ~ dB ~ 0.1 m
2 (1) ( )
~ 1
ikn d re g r
k
kr spontaneous coherence =
= condensation in k-space
Sen Yang, A. Hammack, M.M. Fogler, L.V. Butov, A.C. Gossard, PRL 97, 187402 (2006)
MOES is a state with:● macroscopic spatial ordering and● large coherence length → a condensate in k-spacemodel: L.S. Levitov, B.D. Simons, L.V. Butov, PRL 94, 176404 (2005)
Exciton transport in potential landscapes • Lattices • Traps • Circuit devices • Random potentials
Exciton transport in potential landscapes • Lattices • Traps • Circuit devices • Random potentials
potential energy of indirect excitons can be controlled by voltage
in-plane potential landscapes for excitons can be created by voltage pattern
zE edF e
h
A.T. Hammack, N.A. Gippius, Sen Yang, G.O. Andreev, L.V. Butov, M. Hanson, A.C. Gossard, JAP 99, 066104 (2006)
obstacle: in-plane electric field can lead to exciton dissociation
proposed design in which in-plane electric field is suppressed
allows creating virtually arbitrary in-plane potential landscape for excitons by voltage pattern
can be controlled in-situ by voltageson timescale much shorter than exciton lifetime
source
drain
gate
ONOFF5 m
Exciton Optoelectronic Transistor (EXOT)
photon input photon outputelectronic control
prototype EXOT performs switching at speeds > 1 GHz
prototype excitonic IC performs directional switching and merging
Time (ns)
xexciton flow is on
exciton flow is off
Gate
QWs
n
i
photonicsource
photonicdrain
opticalinputgate
opticaloutputgate
Ex
cit
on
en
erg
y
energy bump controlled by the Gate
similar in geometry and operation to electronic FET
0
1
0 20Distance (m)
Inte
nsi
ty
ON
OFF
A.A. High, A.T. Hammack, L.V. Butov, M. Hanson, A.C. Gossard, Opt. Lett. 32, 2466 (2007)
A.A. High, E.E. Novitskaya, L.V. Butov, M. Hanson, A.C. Gossard, Science 321, 229 (2008)
demonstrated operation up to ~ 100 K G. Grosso, J. Graves, A.T. Hammack, A.A. High, L.V. Butov, M. Hanson, A.C. Gossard, Nat. Photonics 3, 577 (2009)
delay between signal processing and optical communication is effectively eliminated in excitonic devices → advantage in applications where interconnection speed is important
A.A. High, A.K. Thomas, G. Grosso, M. Remeika, A.T. Hammack, A.D. Meyertholen, M.M. Fogler, L.V. Butov, M. Hanson, A.C. Gossard, PRL 103, 087403 (2009)
5 m
eV
5 m
5 m 5 m
Width
Collection of exciton cloud to trap center with increasing density
density →
▲ exp▬ theory
excitation power (W)
repulsive interaction
screening of disorder
collection to trap bottom
cold exciton gas in trap
can be controlled in situ like traps for cold atoms
width of exciton cloud in trap
Elattice = 0
Elattice =
3.7 meV
M. Greiner, O. Mandel, T. Esslinger, T.W. Hansch, I. Bloch, Nature 415, 39, (2002)J.K. Chin, D.E. Miller, Y. Liu, C. Stan, W. Setiawan, C. Sanner, K. Xu, W. Ketterle, Nature 443, 961 (2006)
Excitons in lattices
Atoms in lattices
atoms in lattices – system with controllable parameters
use atoms in lattices to emulate solid state materials
controllable: exciton density, interaction, mass lattice amplitude, structure, constant
a tool with a number of control knobs for studying the physics of excitons
M. Remeika, J. Graves, A.T. Hammack, A.D. Meyertholen, M.M. Fogler, L.V. Butov, M. Hanson, A.C. Gossard, PRL 102, 186803 (2009)
Localization - delocalization transition (LDT)
estimate for the strength of disorder: Erand ~ 0.8 meV
Elattice >> Erand
interaction energy at LDT ≈ amplitude of unscreened lattice
model attributes LDT to interaction-induced percolation of exciton gas through external potential
Etotal = Elattice + Erand
Elattice << Erand
interaction energy at LDT ≈ amplitude of unscreened random potential
loc: emission profile follows excitation spotdeloc: emission extends well beyond excitation spot
Conveyers
A.G. Winbow, J.R. Leonard, M. Remeika, A.A. High, E. Green, A.T. Hammack L.V. Butov, M. Hanson, A.C. Gossard, unpublished
conveyer off conveyer on
Electrostatic conveyers for excitons
study dynamic LDT with varying conveyer amplitude conveyer speedexciton density
conveyers are created by applying AC voltages to lattice electrodes → traveling lattice
wavelength electrodesamplitude voltagespeed frequency
Transport of electrons, holes, excitons, and polaritons via SAW
C. Rocke, S. Zimmermann, A. Wixforth, J.P. Kotthaus, G. Böhm, G. Weimann, PRL 78, 4099 (1997)P.V. Santos, M. Ramsteiner, R. Hey, PSS B 215, 253 (1999)J. Rudolph, R. Hey, P.V. Santos, PRL 99, 047602 (2007)this conference
phonon wind in the conveyer framecrossing phonon velocity
Spin transport of excitons
Spin transport of excitons
exciton spin transport over substantial distances requires
• exciton transport over substantial distances
• long spin relaxation time
long r
high D
Spin-Flip Pathways
Tnnnnn
nwt
n
2112
,
he
S z
2
3,
2
11
he
S z
2
3,
2
11
he
S z
2
3,
2
12
he
S z
2
3,
2
12
ex
h
ee
r r 111 2 exheP
2/~ eP exP ~
2rex
optically activestates
dark states
hwewew
hw
ewh
wewexwrexw
hw
hwexw
hwewexwrew
hwew
hwew
w
0
1
1
0
polarization relaxation time
GaAs SQWdirect exciton
GaAs CQWindirect excitonwith small e-h overlap
fast depolarization within tens of ps
makes possibleexciton spin transport over substantial distances
ex is determined by exchange interaction between e and h
control p by changing e-h overlap
J.R. Leonard, Y.Y. Kuznetsova, Sen Yang, L.V. Butov, T. Ostatnick´y, A. Kavokin, A.C. Gossard, Nano Lett. 9, 4204 (2009)
M.Z. Maialle, E.A. de Andrada e Silva, L.J. Sham, PRB 47, 15776 (1993).
orders of magnitude enhancement of exciton spin relaxation time
II
IIP
exciton spin transport over substantial distances is problematic
100
101
102
103
0
30
100
101
102
103
0
5
10
0 5 10 150
10
20
30
108
109
1010
1011
10-3
10-1
101
100
101
102
103
0
30
108
109
1010
1011
0
5
10
10-3 10-1 101
0.1
1
10
<P
> (
%)
Pex
(W)
r clou
d (m
)
Pex
(W)
f
e
PH
WH
M (
%)
rcloud
(m)
D (
cm2/s
)N
b (cm-2)
ca
b
ExtractedResults
Fit ParametersFitted Data
Pr=
0 (%
)
Pex
(W)
d
p
(ns
)
Nb (cm-2)
P (
ns)
D (cm2/s)
mo
Density dependence
P of indirect excitons reaches several ns >> P of direct excitons
P and P drop with increasing density
decrease of P is correlated with the increase D → P drops when excitons become delocalized
loc
deloc21)(~ rcloud Dr
rP
pP
complies with DP spin relaxation mechanism
-20 0 20 -10 0 10
0
30
0
7
0
5
-20 0 20
Inte
nsity
(a.
u.)
Radius (m)
2.3
230 W
x100
x5.8
x1
Radius (m) Radius (m)
45
P (
%)
TheoryExperimentexperiment theory experiment and theory
Spin transport of excitons
extension of polarization profiles beyond excitation spot shows exciton spin transport
spin transport of indirect excitons originates from long spin relaxation time and long lifetime
Decrease of P and P with increasing density
AmeV 25
AmeV 20
complies with D’yakonov-Perel’ spin relaxation mechanism
exeBexT
Bex
e
ee
mmTkmk
TkDm
kΩ
Ωτ
212
21
2
timescattering momentum
precessionspin offrequency 2
timerelaxationspin
42211 162 DmeeP
experiment:
theoretical estimate:
spin splitting constant
Vortices
quantized atom vortices S. Inouye, S. Gupta, T. Rosenband, A.P. Chikkatur, A. Görlitz, T.L. Gustavson, A.E. Leanhardt, D.E. Pritchard, W. Ketterle, PRL 87, 080402 (2001)F. Chevy, K.W. Madison, V. Bretin, J. Dalibard, PRA 64, 031601(R) (2001)Z. Hadzibabic, P. Krüger, M. Cheneau, B. Battelier, J. Dalibard, Nature 441, 1118 (2006)
quantized optical vortices J. Scheuer, M. Orenstein, Science 285, 230 (1999)and references therein
quantized polariton vortices K.G. Lagoudakis, M. Wouters, M. Richard, A. Baas, I. Carusotto, R. André, Le Si Dang, B. Deveaud-Plédran, Nature Physics 4, 706 (2008)K.G. Lagoudakis, T. Ostatnický, A.V. Kavokin, Y.G. Rubo, R. André, B. Deveaud-Plédran, Science 326, 974 (2009)
quantized vortex is characterized by point (or line) around which phase of wave function varies by 2n
fork-like dislocation in phase pattern is signature of quantized vortex
Vortices
polariton half-vortices
Pex
Fork-like topological defects in interference pattern of indirect excitonsindicating the presence of quantized vortices
hor vert 1 2
topological defects in multicomponent spin systemsY.G. Rubo, PRL 99, 106401 (2007)
for different polarizations
A.A. High, A.T. Hammack, J.R. Leonard, L.V. Butov, T. Ostatnicky´, A. Kavokin, Y.G. Rubo, A.C. Gossard, unpublished
LBS ring region
external ring
region excitation and
inner ring
region
80 100 120 140 160 1800
5
10
15
20
25
hori vert sigma1 sigma2
num
ber
of f
orks
Excitation Power
80 100 120 140 160 180
0
2
4
6
8
10
12 hori vert sigma1 sigma2
num
ber
of f
orks
excitation power
number of forks in LBS ring region
number of forks in external ring region
no forks in excitation and inner ring region
Number of forks in various regions of exciton pattern formation
Acknowledgements
supported by ARO, NSF, DOE
UCSD:Aaron Hammack Alex HighAlex WinbowAnton MintsevAveri ThomasJames LohnerJason Leonard Joe GravesGabriele GrossoKatya NovitskayaMartin GriswoldMikas RemeikaSen YangYuliya Kuznetsova
Collaborators in studies of indirect excitons:Gerhard Abstreiter, WSIDaniel Chemla, UCB&LBNLValerii Dolgopolov, ISSP RASAlexander Dzyubenko, CSBMichael Fogler, UCSDNikolai Gippius, Blaise PascalArthur Gossard, UCSBAtac Imamoglu, UCSBAlexei Ivanov, CardiffAlexey Kavokin, SouthamptonLeonid Levitov, MITPeter Littlewood, CambridgeYuri Lozovik, IS RASYuri Rubo, CuernavacaBen Simons, CambridgeArthur Zrenner, WSI
In collaboration with: Tomas Ostatnick´y, Alexey Kavokin (Southampton)
Yuri Rubo (Cuernavaca)
Andrew Meyertholen, Michael Fogler (UCSD)
Leonid Levitov (MIT)
Ben Simons (Cambridge)
Lois Smallwood, Leonidas Mouchliadis, Joe Wilkes, Egor Muljarov, Alexei Ivanov (Cardiff)
Micah Hanson, Arthur Gossard (UCSB)