Upload
others
View
18
Download
2
Embed Size (px)
Citation preview
Photoinduced Phase Transitions“DYCE” O ti l Ph i“DYCE” Optical Physics
Tetsuo Ogawa Ph DTetsuo Ogawa, Ph.D.Vice-Dean, Professor, Department of Physics, Osaka University, Japan
Vice-Director, Photon Pioneers Center (PhoPs), Osaka University, Japan
Collaborators:K. Asano, T. Ohashi, K. Kamide, T. Yoshioka, K. Koshino, Y. Tomio, P. Huai
Contents:
M. Kuwata-Gonokami, H. Akiyama, S. Koshihara, V. I. Sugakov
Contents:Optical science using dynamically correlated electrons and holes (DYCE)Photoinduced structural phase transitions
Domino processDomino processPhotoinduced electronic phase transitions
Exciton Mott transitionQ t i d ti it BEC d h BCS d tiQuantum pair condensation: exciton BEC and e-h BCS condensation
Cavity-polariton condensation and photon condensation (lasing)
Ogawa Group in Dept. of Physics
17 July 2009@Building H, GSS, OU
From Matter to Light / From Light to Matter
T f tiElectron-hole
Electron latticeClassical photonsQuantum photons
TransformationCouplingHybridizationElectron-lattice Quantum photonsHybridizationTransfer
Cooperative phenomena in matter systems“Photoinduced phase transitions (PIPT)”
Cooperative phenomenain photon systems
Cooperative phenomenain photon-matter coupled systems
Exciton Mott transitione-h BCS
Exciton BEC Cavity polariton BEC Laser oscillation
PHOTOINDUCED PHASE TRANSITIONS (PIPT)
Light is not necessarily a probe inLight is not necessarily a probe in condensed-matter physics.
Creation and control of new states of matter by light irradiation:
Electronic phase transitionsElectronic phase transitionsStructural phase transitions
Two types of PIPT process:“Phase” transitions in photoexcited
statesPhase transitions via photoexcited
states
QUANTUM COOPERATIVE PHENOMENA
By changing temperature, pressure, particle density, interaction strength, …Phase transitionPhase transition
ex): gas-liquid-solid, metal-insulator, localization-delocalization, …In e-h systems: Exciton Mott transition (e-h plasma – exciton gas)
Q t d ti (Quantum condensation (“Macroscopic (long-range) quantum order”)ex): Bose-Einstein condensation (BEC), superconductivity, superfluidity, …In e-h systems: Exciton BEC, e-h BCS-like state, BEC-BCS crossovery , ,
One body⇔Many bodyI t f i t ti l i t ti d i l i X X i t tiImportance of interparticle interaction: dynamical screening, X-X interactionN-particle system ≠ 1-particle system × N → “nonlinearity”, “cooperation”
Cl i l⇔Q tClassical⇔QuantumQuantum statistics: Pauli exclusion, BEC (“interactionless phase transition”)Quantum fluctuation (particle-wave duality): material coherence vs optical Q (p y) pcoherence, …
Contents:
Optical science using dynamically correlated electrons and holesg y y
Photoinduced structural phase transitionsDomino mechanismDomino mechanism
Photoinduced electronic phase transitionsExciton Mott transitionExciton Mott transitionQuantum pair condensation
Cavity polariton condensationCavity-polariton condensation
UttLINE OF OUR SttUD
KEYWORDS:
Global(cooperative,nonlocal)phaSe changes
Photoinduced phenomena
intersite(intermolecule)cOup‖ngs
EXPERIMENTSi
Photoinduced st■lctural transitions in PDA c]wstalS
Photoinduced HS/]LS transitions in spin‐ cFOSSOVeF COmpOunds
Photoinduced feromagnetism in(In,Mn)As/GaSb
MODEL SYSTEM&PHENOMENA:
A mol∝ ule(site)haS tWO local:y‐stable structures:A and B
Onendimensional stacking
lntersite(intermolecule)e:astic interaction
One‐site excitation by irradiation(photOinduced nucleation)
Before ll14diation
A A A A A A A
Just after illadiation
A A A A A
A A A A A A A A
⑪AA A B A A A A A A
⑪What happens under which conditions?
OUR GOALi
To clarify spatiotemporal dynamics of photoinduced nucleationTo clarify the role of intersite interactionsTo distinguish between adiabatic and diabatic regimesTo compare nucleation picture with mean-field description
ゝ0」OC〇
一〇〇OJ
Deterministic Domino mechanismstarting at the spontaneous emissionThe strong friction case
1st lattice relaxation
Spontaneous emission2nd lattice relaxation
B
local
adiabatic
potentialCO事0〓OX00ち
二L
▲ハ
ち U,
Local order parameter櫨ノ
3
5
2
A0 0′一 ・
U
ミ一ヽ
ツヽ仁∽ A. 。
υ
”E一争S留一r,二
Phase D塾24菫里堕」勉狙旦LЛ些璽生
Ad"abat;c limit,Single-site excitati onTte strary friction case
k o . 1 5
0 . 1
0 . 0 5
}nly ininduu,d
ε=―aζr.1t〒1。1
P intursite uuphry mnf
Phasefr?アルbal fれ中欣rt″絆J″″虐by single- site stirnulation,
一 ̈ ei嚇鴫糀7ハDeterninistic @ri odid Donifio necirnu smonly nne spontanea$ e,tr,issi'Ir
;' TTTorestomtion
プ々タリ
・a鳳締|
Contents:
Optical science using dynamically correlated electrons and holesg y y
Photoinduced structural phase transitionsDomino mechanismDomino mechanism
Photoinduced electronic phase transitionsExciton Mott transitionExciton Mott transitionQuantum pair condensation
Cavity polariton condensationCavity-polariton condensation
Quasi-Equilibrium
e #density = h #density
carrier-carrier scattering
carrier-phonon scattering
ValenceBand
ConductionBand
Photo-Excitation True Equilibrium
photon
Intra-BandRelaxation
~ ps
Inter-BandRelaxation
~ ns
Recombination
1. e-h Density
2. Effective Temperature
Electron-hole system as an excited electronic state
photon
Electron-hole systems
Exciton Mott transitionThermal separation ?
Exciton Mott transitionC/Q boundary
E it G h Plre Exciton Gas(insulating)
e-h Plasma(metallic)ra
tur
CoexistencePseudo gap?
(Bosonic) (Fermionic)
mp
er
Q C d ti
Pseudo gap?
Tem
e-h LiquidQ. Condensation
E h D it
BEC e-h BCSStrong coupl Weak couplE-h DensityStrong coupl. Weak coupl.
Relation between exciton Mott transition & optical gain/absorption
daB
Insulator Metal
Exciton gas e-h plasma/liquid
Eg μ*
Negative absorption = Gain
Low density High density
1. neh=02. neh=5×1015cm-3
3. neh=3×1016cm-3
4. neh=8×1016cm-3
X
Excitonpeak
μEg*
?
The e-h (two-band) Hubbard Model
H = ¡X
®=e;h ¾="#
X
hiji
t® cyi®¾ci®¾ +U
X
®=e;h
X
i
ni®"ni®# ¡UX
¾¾0="#
X
i
nie¾nih¾0
Kinetic Term
Previous studies cover only local parts of the whole phase diagram.
⇒ We need to obtain globally the phase diagram.
Minimal model of the e-h system
Repulsive Interaction(Intraband)
Attractive Interaction(Interband)
the lattice fermion model (in the tight-binding picture) - different masses of electron and hole - screened on-site interactions as parameters independent of density - Frenkel-type excitons without co-transfer - modern theoretical tools applicable
0
cf.) the continuum-space model (in the nearly-free electron picture) - effective-mass and envelope fn. approximations - (long-range) Coulomb interactions dependent on density - Wannier-type excitons with finite bandwidth
n=0.25
0 1 2 3 4 50
1
2
3
4
5
U′/(te+th)
U/(
t e+
t h)
th/te=1n=0.25
Metallic phase
Biexciton phase
Exciton phase
Exciton/Biexciton phase :Metal
exciton Mott transition
1st-order transition
0 1 2 30
0.5
1
U′
Z α
U=3
n=0.25, Ns=3, β=30
Metallic phase
Exciton phase
Quasiparticle weights
Biexciton phase
Interacting DOS
−2 0 2
0
0
U′=1.5
ρα (ω)
ω
U=3
U′=2.5
U′=3.5
Metallic phase
Exciton phase
Biexciton phase
th/te =1
Phase diagram for 2-band Hubbard model at T=0
U=U’ n=0.25quasiparticle weights
U’-n phase diagram at T=0
0 1 2 3 4 50
0.5
1
−4 −2 0 2 4
−4 −2 0 2 4
U′/(te+th)
n
Metallic phase
Exciton phase
Mott−Hubbard insulator
ω
ω
ρα(ω)
ρα(ω)
U=U′
th/te =1
coexistent region
crossover region
1 2 30
0.5
1
U′
Zα
T=0.02
T=0.1
cf. binding energy of a free exciton→
phase diagram in low-density limit
0 1 2 30
0.5
U′
EB
∝ U′
Phase diagram for 2-band Hubbard model at T>0 (Tomio)
TMC
BIEXCITON CRYSTAL in 1D
High-density electron-hole system in 1DBosonizationForward and backward scatteringsForward and backward scatteringsLong-range Coulomb interaction
Mass Density ⇔
1 ¥
2kF Mass Density Wave(Biexciton Crystal)
⇒ Short-range part
biexciton BEC/BCS
Phase Seperation?
H(m)½ =v(m)
2¼
Zdx
·K(m)
³@x£
(m)½
2́+
1
K(m)
³@x©
(m)½
2́¸
©(m)½ / m(e)©(e)½ +m(h)©(h)½
K(m) =
s¹v
v(e)F + v
(h)F ¡ g½=¼
v(m) =
r¹vhv(e)F + v
(h)F ¡ g½=¼
i¹v =
v(e)F v
(h)F
v(e)F + v
(h)F
g½ = g(e)½ + g(h)½
K(m)free =
qv(e)F v
(h)F
v(e)F + v(h)F
K(m)
~ 0.3 (Bulk GaAs)
Character of the Ground State
“Acoustic Mode” ⇔ Mass“Optical Mode” ⇔ Charge
Asymmtery of e and h mass ⇒ Stabilize the biexciton crystal order
Double layer e-h systems
Charge balancedCharge balanced
Parallel dipolesRepulsive?
Charge imbalanced
Exciton BEC?
g
TrionsFFLO?
Exciton luminescence from quantum wells:central spot and fragmented ringcentral spot and fragmented ring
fragments of lluminescence
View from above
L. Butov et al.m260Nature 418 (2002),
PRL 92 (2004)T=1.8 K
Pex=390 W
Exciton luminescence Exciton luminescence Butov et al., Butov et al.,
Nature 418 751 (2002)Nature 418 751 (2002)
Chernyuk A.A., Sugakov V.I.:Chernyuk A.A., Sugakov V.I.:
PRB 74, 085303 (2006),PRB 74, 085303 (2006),Nature 418, 751 (2002)Nature 418, 751 (2002)
Exciton front propagation in photoexcited GaAs quantum wells
Sen Yang,1 L. V. Butov,1 L. S. Levitov,2 B. D. Simons,3 and A. C. Gossard4
1Department of Physics, University of California at San Diego, La Jolla, California 92093-0319, USA2Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
3Cavendish Laboratory, Madingley Road, Cambridge CB3 OHE, United Kingdom4Materials Department, University of California at Santa Barbara, Santa Barbara, California 93106-5050, USA
�Received 20 August 2009; revised manuscript received 10 February 2010; published 16 March 2010�
We report on the study of spatiotemporal self-organization of carriers in photoexcited GaAs quantum wells.Propagating interfaces between electron-rich and hole-rich regions are seen as expanding and collapsingexciton rings in exciton emission patterns. The interfaces preserve their integrity during expansion, remainingas sharp as in the steady state, which indicates that the dynamics is controlled by carrier transport. The frontpropagation velocity is measured and compared to theoretical model. The measurements of expanding andcollapsing exciton rings afford a contactless method for probing the electron and hole transport.
DOI: 10.1103/PhysRevB.81.115320 PACS number�s�: 78.67.De, 71.35.�y, 72.20.�i, 78.55.Cr
I. INTRODUCTION
Front propagation in conducting media driven by injec-tion or photoexcitation of carriers with opposite polarities isfundamental and ubiquitous in nature and technology. Di-verse examples of moving interfaces resulting from self-organization of charge carriers range from traveling fronts ofimpact ionization in semiconducting structures1–4 to transientdynamics in fuel cells.5,6 The ability to control front propa-gation and spatial width is important in applications, includ-ing subnanosecond high-voltage pulse power ramps1–4 andignition of fuel cells.5,6
In this paper, we report on the study of expanding andcollapsing exciton rings, formed at the boundaries betweenelectron-rich and hole-rich regions in GaAs quantum wells.Such self-organization of excitons in steady-state ringlikepatterns has been observed a few years ago7 and thoroughlystudied recently.8–11 Here, we use spatiotemporal imaging ofring dynamics to measure its formation and propagation.
The real time imaging of expanding and collapsing exci-ton rings opens up several avenues of investigation. In thiswork, we demonstrate that the dynamics of exciton rings canbe used for probing the electron and hole transport. Similarto other optical methods, this technique is contactless andtherefore can be applied even when good contacts are diffi-cult to make �see Ref. 12 and references therein�. In particu-lar, in this paper we study coupled electron-hole �e−h� layersseparated by 4 nm barrier �12 nm between the centers of eand h layers�. The task of making separate contacts tocoupled e−e or e−h layers for transport measurements be-comes challenging for systems with sub-10 nm barrier width.Yet, this is the most interesting regime, in which strong in-terlayer correlations can give rise to a variety of electronicstates.13–21
As we shall see, the use of ring dynamics as a vehicle forstudying carrier transport is made possible because ring ex-pansion and collapse occur on time scales which are muchlonger than the ring formation time. The observation thatexciton rings preserve their integrity during expansion andcollapse shows that the characteristic times for the latter aremuch slower than those for self-organization of electrons,holes, and excitons into ringlike patterns.
In Sec. II, we present the experimental data on excitonfront propagation in photoexcited GaAs quantum wells seenas expanding and collapsing rings in exciton emission pat-terns. In Sec. III, we summarize the transport model of ex-citon rings, developed in Ref. 8, which interprets the rings interms of the boundaries between electron-rich and hole-richregions. In Sec. IV, we compare experimental data with nu-merical simulations of the ring dynamics and use the mea-surements of the front propagation velocity for estimatingthe electron and hole diffusion coefficients. A short summaryof the work is given in Sec. V. The unit calibration and fittingprocedure are described in the Appendix.
II. EXPERIMENTAL RESULTS
The coupled quantum well structure �CQW� used in theseexperiments was grown by molecular beam epitaxy. It iscomprised of two 8 nm GaAs QWs separated by a 4 nmAl0.33Ga0.67As barrier and surrounded by 200 nmAl0.33Ga0.67As layers �for details on the CQW see Ref. 7�.The recombination lifetime of the indirect excitons in theCQW is about 50 ns.23 The measurements were performedusing time-resolved imaging with 200 ns integration windowand 2 �m spatial resolution at T=1.4 K. The electrons andholes were photogenerated using rectangular excitationpulses of a semiconductor laser at 1.95 eV, above theAl0.33Ga0.67As gap ��1.93 eV�, with a 8 �m spot. The pulsewidth was 10 �s, with the edge sharpness better than 1 ns,and the repetition frequency of 67 kHz �Fig. 1�i��. The periodand duty cycle were chosen to provide time for the pattern toapproach equilibrium during the laser pulse and to allowcomplete decay of the emission between the pulses. Differentpulse widths and repetition frequencies were found to yieldsimilar results. Time-dependent emission images were ac-quired by a nitrogen-cooled CCD camera after passingthrough a time-gated PicoStar HR TauTec intensifier with atime-integration window of 200 ns. An 800�5 nm interfer-ence filter, chosen to match the indirect exciton energy, wasused to remove the low-energy bulk emission and high-energy direct exciton emission. The spectral filtering andtime-gated imaging provided the direct visualization of the
PHYSICAL REVIEW B 81, 115320 �2010�
1098-0121/2010/81�11�/115320�6� ©2010 The American Physical Society115320-1
Quantum Condensations in Imbalanced e-h Systems
Fulde-Ferrell Phase
e-h pair with CM momentum Q
Fulde and Ferrell: PR135, 705(1964).
Sarma Phaseh Fermi circle
k
e Fermi circle
-k+Q
-k’+Q
k ’
(Breached pair phase)
Sarma: J. Phys. Chem. Sol. 24, 1029 (1963).W. V. Liu and F. Wilczek: PRL90, 047002 (2003).
Condensation of e-h pair with Q=0 + Normal hole liquid
c-band
v-band
Mixing FermiLevel
c.f. Inhomogeneous solution: A. I. Larkin and Y. N. Ovchinnikov, Sov. Phys. JETP 20, 762 (1965).
ke kh
1
0
n(k)
kke kh ke kh
e h
SF: superfluid phase (excitonic insulator) FF: Fulde-Ferrell phasePP: partially polarized normal phaseUnstable: no uniform solution
-1
-0.5
0
0.5
1
1 2
FF
FF
PP
PP
SFUnstable
Unstable
Polariz
ation
InteractionStrength
e ric
hh ric
h-1
-0.5
0
0.5
1
0.5 1 2 4 8 16
α
rs
PP
PP FF
SFSarma
c.f. Previous calculationInstability of Sarma phase
toward FF phase
Phase Diagram at Zero Temperature
Interlayer distanceMass ratioParameters
Pieri et al. PRB75,113301 (2007).
Contents:
Optical science using dynamically correlated electrons and holesg y y
Photoinduced structural phase transitionsDomino mechanismDomino mechanism
Photoinduced electronic phase transitionsExciton Mott transitionExciton Mott transitionQuantum pair condensation: exciton BEC and e-h BCS
Cavity polariton condensationCavity-polariton condensation
Polariton BEC in a microcavityy
N‐layers of semiconductor quantum wells in distributed Bragg reflectors
• single photon mode
N layers of semiconductor quantum wells in distributed Bragg reflectors
single photon mode
• strong coupling with excitons
Bragg Mirror
photon
Pumping Laser
Excitons
output radiation → detection
Observation of the BECJ. Kasprzak et al, Nature 443, 409 (2006).
Condition: non‐resonant pumping + 16 CdTe Q‐wellsDetection: angle resolved emission spectrum (far‐field)
0 55P1.14Pth
1.67Pth
Bose narrowing in the momentum and energy space
0.55Pthth
Angular distribution
Emission P=Pth
energy
Spectrum
energy
th
momentum
pump powerPolariton BEC is similar to Bose‐Einstein Condensation of atomic gases in a thermal equilibrium!
Phase diagram
Different ground states are expected to occur depending on theDifferent ground states are expected to occur depending on the detuning and the pump power (total excitation density ntot).
Composite many-body systems
exciton eh Cooper pair ee meson qq diquark qqcharged exciton eeh baryon qqq anti-baryon qqq
----
---biexciton eehh positronium ee tetraquark qqqqpolariton eh+b metal hydrogen HH pentaquark qqqqq
Bose atom mol. gas AA hexaquark qqqqqq-
---
Even-odd mixture in imbalanced systemsExciton-trion mixtureMeson-baryon mixtureAtom-molecule mixture
Even-even mixture in balanced systems“Unitary limit” of BEC-BCS crossoverExciton biexciton mixture
Ch b l d/i b l d l t h l t
Exciton-biexciton mixtureMeson-tetraquark mixture
Charge-balanced/imbalanced electron-hole systemsare good stages for exploiting the roots of matter.
Comparison of electron-hole systems with
Toward COE of DYCE Optical Physics
Photon MatterMany electrons and holes<Excited states>
Dynamically correlated electron systems (DYCE)
Beyond the one-body band theory
New Optical Science, Materials Science, and Electronics
Ogawa group in OU is the unique and best placefor theoretical study of DYCE optical physicsto combine quantum many-body physics and
quantum nonlinear optics. q pJoin and contact: [email protected]