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: ogawa@mailaps.org