1. Transport and spin transport of excitons Leonid V. Butov, UCSD
• 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)

2. What temperature is “cold” for exciton gas?
transition from classical to quantum gas takes place when thermal
de Broglie wavelength is comparable to interparticle separation
3D:
2D:
mexciton ~ matom
Kelvin for excitons
is like
microKelvin for atoms
3D gas of Rb atoms:
n = 1015 cm-3, matom = 105 me → TdB ~ 5×10-6 K
2D gas of excitons in GaAs QW
n = 1010 cm-2, mexciton= 0.2 me → TdB ~ 3 K
n < nMott ~ 1/aB2 ~ 2×1011 cm-2

3. 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
Indirect excitons in coupled quantum wells
Electron-electron bilayers
in magnetic fields at n =1
Electron-hole bilayers
with gate-induced carriers
Electron-hole bilayers
with photoexcited carriers e e
solving these challenges has led to studies of
various experimental systems
and various types of exciton condensate

4. Why indirect excitons in CQW ?
times longer exciton lifetime due to
separation between electron and hole layers
103 times shorter exciton cooling time
than that in bulk semiconductors
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)
TX ~ 100 mK
has been realized experimentally
30 times below TdB TX
~ 10 ns to cool to 300 mK
~ 100 ns to cool to 100 mK
A.L. Ivanov et al
in PRL 86, 5608 (2001)
Time (ns)
high quality CQW samples with small in-plane disorder are required to overcome exciton localization

5. Repulsive interaction between indirect excitons
Repulsive dipole-dipole interaction
● stabilizes exciton state against formation of metallic EHL
● results in effective screening of in-plane disorder
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
A.L. Ivanov, EPL 59, 586 (2002)
R. Zimmermann d
indirect excitons
are oriented dipoles
also high quality CQW samples with small initial disorder are required to overcome exciton localization
Repulsive interaction in experiment
exciton energy increases with density
L.V. Butov, A. Zrenner, G. Bohm, G. Weimann, J. de Physique 3, 167 (1993)
energy shift: dE ~ n/C  estimate for exciton density
approximation for short-range 1/r3 interaction C = e/4pe2d
C. Schindler, R. Zimmermann, PRB 78, (2008)
 C and n in experiments are higher

6. potential energy of indirect excitons can be controlled by voltage
the ability to control electron fluxes by an applied gate voltage
electronic circuit devices
mesoscopics
the field which concerns electron transport in a potential landscapes
potential energy of indirect excitons can be controlled by voltage e h
in-plane potential landscapes
can be created for excitons by voltage pattern
e.g. traps, lattices, circuit devices
the ability to control exciton fluxes by an applied gate voltage
excitonic circuit devices
mesoscopics of bosons
in semiconductors

7. have built-in dipole moment ed
indirect excitons d
have long lifetimes
have built-in dipole moment ed
can cool down to 0.1 K well below TdB ~ 3K
can travel over
large distances
energy can be controlled by gate voltage
condensation
pattern formation
transport
spin transport
potential profiles
can be created and in situ controlled
cold Bose gases in solid-state materials
excitonic devices
optical methods → local probe of excitons

8. Exciton pattern formation and exciton transport

9. Pattern Formation: Exciton Rings and Macroscopically Ordered Exciton State
inner ring
external ring
same
PL intensity
position on the ring (mm)
spatial order on
macroscopic lengths
ring
fragmentation
localized bright spots
410 mm
T=1.8 K
T=4.7 K
appears abruptly at low T
L.V. Butov, A.C. Gossard, D.S. Chemla,
Nature 418, 751 (2002)
2D-fire

10. Inner ring exciton transport over tens of microns
PL pattern spatial distribution of
optically active low energy excitons
flow of excitons out of excitation spot due
to exciton drift, diffusion, phonon wind, etc.
exciton
transport
over tens
of microns
PL Intensity E E
repulsive
interaction
→ drift
Energy (eV)
r (mm) k k
excitons can travel in a dark state after
having been excited until slowed down
to a velocity below photon emission
threshold, where they can decay radiatively
excitation spot
high TX
exciton drift
lower occupation
of radiative zone
inner ring
lower TX
excitons relax
to radiative zone
higher occupation
of radiative zone
inner ring forms due to
exciton transport and cooling
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)
Discussion

11. Localization-delocalization transition for exciton transport in random potential
exp.
theory
exp.
theory
low densities:
emission profile follows excitation spot
excitons are localized in random potential
high densities:
emission extends well beyond excitation spot
excitons screen random potential, travel away from excitation spot and form inner ring

12. Kinetics of inner ring formation time of inner ring ~ 30 ns
exp theory
formation time of inner ring ~ 30 ns
kinetics of inner ring
estimate of exciton transport characteristics
DX reaches ~ 20 cm2/s
PL jump vs r → excitons outside laser spot
including inner ring region
are cooled to Tlattice even during laser excitation
A.T. Hammack, L.V. Butov, J. Wilkes, L. Mouchliadis, E.A. Muljarov, A.L. Ivanov, A.C. Gossard,
PRB 80, (2009)

13. External ring external ring forms at interface between
above barrier laser excitation creates
additional number of holes in CQW
electrons
excitons
holes
heavier holes have higher
collection efficiency to CQW E
excess holes are photogenerated in the laser
excitation spot
electron source is spread out over the entire
plane due to current through the CQW
from n-doped GaAs layers z
external ring forms at interface between
electron-rich and hole-rich regions y
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 x
same for
e ↔ h
L.V. Butov, L.S. Levitov, B.D. Simons, A.V. Mintsev, A.C. Gossard, D.S. Chemla, PRL 92, (2004)
R. Rapaport, G. Chen, D. Snoke, S.H. Simon, L. Pfeiffer, K.West, Y.Liu, S.Denev, PRL 92, (2004)
external ring

14. 1.5 ms 2.5 ms 3 ms 4 ms Kinetics of external ring and LBS rings
time
100mm
- 9.5 ms
- 8.8 ms
- 6.5 ms
0.2 ms
1.5 ms
2.5 ms
3 ms
4 ms
-10ms
5ms
laser pulse e h
external ring
LBS ring
expansion of external ring collapse of external ring a b c d f g i j
collapse of external ring
expansion of LBS rings
250 50
kinetics of external and LBS rings
estimation of e and h transport characteristics
De ~ 80 cm2/s, Dh ~ 20 cm2/s
De = 200 cm2/s
Dh = 16 cm2/s
80 cm2/s
Radius (mm)
Radius (mm)
30 cm2/s
40 cm2/s c
26 cm2/s
Sen Yang, L.V. Butov, L.S. Levitov, B.D. Simons, A.C. Gossard, PRB 81, (2010)

15. macroscopically ordered exciton state (MOES)
indirect exciton PL
direct exciton PL – pattern of hot
spots
localized bright spots
have hot cores
no hot spots
in external ring
and LBS rings
rings are far from hot spots
due 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)

16. Spontaneous coherence
the increase of the coherence length x is correlated with the macroscopic spatial ordering of excitons
x ~ 2 mm >> the classical value ~ ldB ~ 0.1 mm
PL Contrast along the Ring
spontaneous coherence =
= condensation in k-space
Coherence Length (mm)
MOES is a state with:
● macroscopic spatial ordering and
● large coherence length → a condensate in k-space
Temperature (K)
model: L.S. Levitov, B.D. Simons, L.V. Butov, PRL 94, (2005)
experimental method:
Mach-Zehnder interferometry
with spatial and spectral resolution
probing coherence far from laser both in space and energy: coherence is spontaneous
Sen Yang, A. Hammack, M.M. Fogler, L.V. Butov,
A.C. Gossard, PRL 97, (2006)
left arm
right arm

17. Exciton transport in potential landscapes • Lattices • Traps
Exciton transport in potential landscapes • Lattices • Traps • Circuit devices • Random potentials

18. potential energy of indirect excitons can be controlled by voltage
Exciton transport in potential landscapes • Lattices • Traps • Circuit devices • Random potentials
potential energy of indirect excitons can be controlled by voltage e h
in-plane potential landscapes for excitons
can be created by voltage pattern
can be controlled in-situ by voltages
on timescale much shorter than exciton lifetime
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
A.T. Hammack, N.A. Gippius, Sen Yang, G.O. Andreev, L.V. Butov, M. Hanson, A.C. Gossard, JAP 99, (2006)

19. Exciton Optoelectronic Transistor (EXOT)
source
drain
gate
Exciton Optoelectronic Transistor (EXOT) x
exciton flow is on
exciton flow is off
Gate
QWs n i
photonic
source
drain
optical
input
gate
output
Exciton energy
energy bump
controlled by
the Gate 1
5 mm ON
OFF ON
photon input
photon output
electronic control
Intensity
OFF
Distance (mm)
Time (ns)
prototype EXOT performs switching at speeds > 1 GHz
prototype excitonic IC performs directional switching and merging
similar in geometry and operation
to electronic FET
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

20. 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, (2009)

21. Collection of exciton cloud to trap center with increasing density
Width
5 mm
5 mm
5 meV
width of exciton
cloud in trap
▲ exp
▬ theory
5 mm
density →
repulsive interaction
screening of disorder
collection to trap bottom
cold exciton gas in trap
excitation power (mW)
can be controlled in situ like traps for cold atoms

22. Atoms in lattices Excitons in lattices
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)
atoms in lattices – system with controllable parameters
use atoms in lattices to emulate solid state materials
Excitons in lattices
Elattice =
3.7 meV
Elattice = 0
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, (2009)

23. Localization - delocalization transition (LDT)
loc: emission profile follows excitation spot
deloc: emission extends well beyond excitation spot
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
Elattice >> Erand
interaction energy at LDT ≈
amplitude of unscreened
lattice
estimate for the strength of disorder: Erand ~ 0.8 meV

24. Conveyers

25. Electrostatic conveyers for excitons
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, (2007)
this conference
Electrostatic conveyers for excitons
conveyers are created by applying AC voltages to lattice electrodes → traveling lattice
wavelength  electrodes
amplitude  voltage
speed  frequency
conveyer off conveyer on
study dynamic LDT
with varying
conveyer amplitude
conveyer speed
exciton density
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
phonon wind in the conveyer frame
crossing phonon velocity

26. Spin transport of excitons

27. Spin transport of excitons
exciton spin transport over substantial distances requires
• exciton transport over substantial distances
• long spin relaxation time
long tr
high D

28. Spin-Flip Pathways polarization relaxation time
tex th te tr
polarization relaxation time
optically active
states
Polarization of emission decays
when both e and h flip their spins. This can occur in two-step process due to separate e and h spin flips
and single step process due to exciton spin flip.
tex is determined by exchange interaction between e and h
control tp by changing e-h overlap
dark
states
GaAs SQW
direct exciton
GaAs CQW
indirect exciton
with small e-h overlap
M.Z. Maialle, E.A. de Andrada e Silva,
L.J. Sham, PRB 47, (1993).
fast depolarization
within tens of ps
orders of magnitude enhancement of exciton spin relaxation time
exciton spin transport
over substantial
distances is problematic
makes possible
exciton spin transport
over substantial distances
J.R. Leonard, Y.Y. Kuznetsova, Sen Yang, L.V. Butov, T. Ostatnick´y, A. Kavokin, A.C. Gossard, Nano Lett. 9, 4204 (2009)

29. Density dependence
deloc
loc
tP of indirect excitons reaches several ns >> tP of direct excitons
P and tP drop with increasing density
decrease of tP is correlated with the increase D → tP drops when excitons become delocalized mo
complies with DP spin relaxation mechanism

30. Spin transport of excitons
experiment theory experiment and theory
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

31. Decrease of P and tP with increasing density
complies with D’yakonov-Perel’ spin relaxation mechanism
spin splitting constant
experiment:
theoretical estimate:

32. Vortices

33. Vortices quantized vortex is characterized by point (or line)
around which phase of wave function varies by 2pn
fork-like dislocation in phase pattern is signature of quantized vortex
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, (2001)
F. Chevy, K.W. Madison, V. Bretin, J. Dalibard, PRA 64, (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)
polariton half-vortices

34. indicating the presence of quantized vortices
Fork-like topological defects in interference pattern of indirect excitons
indicating the presence of quantized vortices
Pex
for different polarizations
hor
vert s1 s2
topological defects in multicomponent spin systems
Y.G. Rubo, PRL 99, (2007)
A.A. High, A.T. Hammack, J.R. Leonard, L.V. Butov, T. Ostatnicky´, A. Kavokin, Y.G. Rubo, A.C. Gossard, unpublished

35. Number of forks in various regions of exciton pattern formation
number of forks in LBS ring region
LBS ring region
external
ring
region
excitation
and
inner
ring
region
number of forks in external ring region
no forks in excitation and inner ring region

36. Acknowledgements UCSD: Aaron Hammack Alex High Alex Winbow
Anton Mintsev
Averi Thomas
James Lohner
Jason Leonard
Joe Graves
Gabriele Grosso
Katya Novitskaya
Martin Griswold
Mikas Remeika
Sen Yang
Yuliya Kuznetsova
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)
Collaborators in studies of indirect excitons:
Gerhard Abstreiter, WSI
Daniel Chemla, UCB&LBNL
Valerii Dolgopolov, ISSP RAS
Alexander Dzyubenko, CSB
Michael Fogler, UCSD
Nikolai Gippius, Blaise Pascal
Arthur Gossard, UCSB
Atac Imamoglu, UCSB
Alexei Ivanov, Cardiff
Alexey Kavokin, Southampton
Leonid Levitov, MIT
Peter Littlewood, Cambridge
Yuri Lozovik, IS RAS
Yuri Rubo, Cuernavaca
Ben Simons, Cambridge
Arthur Zrenner, WSI
supported by ARO, NSF, DOE