Exciton Mott Transition and Pair Condensantion in … · Exciton Mott transition and quantum pair cont l i i dtd ensation in electron-hl thole systems: Dynamical mean-field theory

Exciton Mott transition and quantum pair d ti i l t h l tcondensation in electron-hole systems:

Dynamical mean-field theory

Tetsuo OgawaDepartment of Physics, Osaka University, Japan

Collaborators:Y. Tomio, K. Asano, T. Ohashi, P. Huai, H. Akiyama, and M. Kuwata-Gonokami

Contents:Electron-hole systems in quasi-thermal-equilibrium

Quantum cooperative phenomenaQ p pModern theoretical methods and e-h Hubbard model

Exciton Mott transition in high-d: DMFT and slave-boson MFTAbsorption spectra in the half-filled caseAbsorption spectra in the half filled caseRole of inter-site interaction : Extended DMFT

Quantum pair condensation and crossover in high-d: SCTMAToward the complete phase diagramToward the complete phase diagramAbsence of exciton Mott transition in 1-d: bosonization, RG, and CPT

PHOTOINDUCED PHASE TRANSITIONS (PIPT)

Creation and control of macroscopic states of matter by light:

Electronic phase transitionsStructural phase transitionsStructural phase transitions

Two types of PIPT process:“Ph ” t iti i h t it d“Phase” transitions in photoexcited

statesPhase transitions via photoexcited

states


Quantum cooperative phenomenaQuantum cooperative phenomenaModern theoretical tools and e-h Hubbard model

Exciton Mott transition in high-d: DMFT and slave-boson MFTAbsorption spectra in the half filled caseAbsorption spectra in the half-filled caseRole of inter-site interaction : Extended DMFT

Quantum pair condensation and crossover in high-d: SCTMAT d th l t h diToward the complete phase diagramAbsence of exciton Mott transition in 1-d: bosonization, RG, and CPT

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

Characteristics of Electron-Hole Systems

2-component quantum many-body systemOpposite charges, different effective masses, mass anisotropy. Fermion→ Pauli blocking

Coexistence of repulsive and attractive Coulomb interactionsThe same order of magnitude, Free-electron theory/Fermi liquid theory invalid

“Exciton” and “excitonic molecule” can be formedExciton and excitonic molecule can be formed.An exciton or a biexciton is (quasi)bosonic.

Tunable particle density by irradiation intensityN t l # f l t # f h l d l ti d d tNot always # of electrons = # of holes→modulation doped system

Variable strength and range of Coulomb interactionStatic and dynamical screenings, dielectric confinement in low dimensions

Excited states with energy higher than thermal energy at RTmeV (Teraheltz, IR), eV (visible), keV (UV, X-ray): Wide range of light energy

Open system with phonon bath: Intraband energy relaxationOpen system with phonon bath: Intraband energy relaxation1st step of energy decay, open boundary problem

Open system with photon bath: Interband radiative recombination2nd step of energy decay, cavity QED, cavity polaritons

e-hplasmal acit irC

erut are pm eT

Exciton Motttransition

-samohT

imreF

lekcuH-eybeD

BCS-like

e-hliquid

Schematic metastable phase diagram of a 3D e-h system

daB

Insulator

d > aB> d < aB<

Exciton gasBiexciton gas

e-h Droplet

Metal

Bose condensation

InsulatorCoherence（Condensation to

a single quantum state）

T

neh

Coexisting region

:

©K. Asano

PECULIARITY OF ELECTRON-HOLE SYSTEMS

DOUBLE-FACE ASPECTS OF BOSONIC AND FERMIONICDOUBLE-FACE ASPECTS OF METALLIC AND INSULATING

Insulating, bosonic exciton/biexciton gas ⇔ Metallic, fermionic e-h plasmaDOUBLE-FACE ASPECTS OF CLASSICAL AND QUANTUM

e-h plasma/liquid condensation ⇔ exciton BEC/e-h BCS condensatione h plasma/liquid condensation exciton BEC/e h BCS condensation

FINE TUNABILITY FROM WEAK TO STRONG COUPLINGFine tuning of particle density dynamical screeningFine tuning of particle density, dynamical screening

FINE-CONTROLLED PREPARATION OF INITIAL STATESPhoto-pumping vs carrier-injectionPhoto-pumping vs carrier-injectioncw pumping vs pulsed pumpingTuning of energy profile, particle density, carrier balance, coherence, polarization

FINE CONTROLLED COUPLING TO PHOTON FIELDSFINE-CONTROLLED COUPLING TO PHOTON FIELDSCoherence in material (e-h) systemCoherence in material (e-h) + photon systems, polariton-laser crossoverCavity QED, feedback due to photons, control of interband recombination rate

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＊

?

MANY-FACETED and UNIFIED APPROACHES

Particle densityLow density High density

nsiti

on

Particle density

n M

ott t

ran

InteractionStrong coupling Weak coupling

E i (X) h l

Exc

itonExciton (X) gas

Biexciton (XX) gasExciton BEC

e-h plasmae-h droplete-h BCS

Approach from low density/strong

coupling

Approach from high density/weak

couplinggTheory covering all regions

X-density expansionX-bosonization

Screened HFTL bosonization

DMFT・extended DMFTSCTMA

CPTX-X interaction RPASlave boson MFA

DMRG

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

MEAN-FIELD THEORIES for LATTICE FERMION MODELS

Static MFANo ω dependence

How can electronic correlation and quantum fluctuation be treated? © K. Asano

ω -dependence Dynamical MFAω d d

Hartree Approx.

No ω-dependence

GS at zero temperature Finite temperature, DOS

Coherent Potential Approx. (CPA)

k-dependenceω-dependence

Hartree Approx.

Correlationneglected

Coherent Potential Approx. (CPA)One-bodyApprox.

No fluctuation

No Mott transitionOnly energy shift→ Hartree-Fock approx.

Mott insulator OKOnly upper/lower Hubbard bands→ RPA, SCTMA

LocalExact correlationeffects in a site

Slave-Boson MFA Dynamical MF Theory (DMFT)Equivalent to Gutzwiller variationalMott transition with mass divergence:

Both coherent peak and U/L Hubbard bandsE t i di iLocal

correlationeffects in a siteNo k-dependence

Mott transition with mass divergence: Brinkmann-Rice picture OKOnly coherent peak

Exact in ∞ dimensionsMap to effective Anderson modelNumerical calculation → Finite size effects

Quantum Cluster Theory (QCT)

Nonlocal1 or 2 dimensions OKIntersite interaction OKCPT cell-DMFT DCA

Cluster Slave-Boson MFA (?)

Not yet

Exact correlationeffects

in many sites( l t ) correlation

CPT, cell DMFT, DCANumerical calculation → Finite size effects(a cluster)

k-dependence





creation operator of electron

creation operator of holee-e (h-h) on-site repulsion e-h on-site attraction

eh

te

th-U’

U

ε(k)

k

ε

ρ0(ε)

conduction band

valence band

electrons

holes

4te

4th

2-band Hubbard Model and bare DOS (Tomio)

- Elliptic DOS assumed- Undoped initially (#e=#h)

A lattice fermion model (site representation)

Georges, et al., Rev. Mod. Phys. 68 (1996) 13Dynamical MeanDynamical Mean--Field Theory (DMFT)Field Theory (DMFT)

lattice model ⇒ single-site impurity problem embedded in effective mediummapping

impurity modellattice model

map U

-U’

∞→dDMFT becomes exact in 3=dand good approximation in

DMFT requires only locality of self-energy

∞→dDMFT includes full local correlations

DMFT becomes exact in 3dand good approximation in

⇒

cf. 2-orbital Hubbard model:Koga, et al., PRB 66 (2002) 165107,

Phase diagram at 1/2 filling (n=1)

th/te =1 th/te =0.5

“orbital selective” Mott transition: Koga, et al., PRL 92 (2004) 216402

0 1 2 3 4 50

1

2

3

4

5

U′/(te+th)

U/(

t e+

t h)

(I) Metal

e

h

(II) MottHubbard insulator

th/te=1

(III) Biexcitonlike insulator

e

h

0 1 2 3 4 50

1

2

3

4

5

U′/(te+th)

U/(

t e+

t h)

(I) Metal


th/te=0.5


(IV) eMetal hInsulator

(I) Metal(I) Metal

(II) Mott-Hubbard insulator

(II) Mott-Hubbard insulator

(III) Biexciton-like insulator (III) Biexciton-like insulator

(I) (II): “band-selective” Mott-Hubbard transition except for th/te =1

(I) (III): no “band-selective” transition for any th/teposition of phase boundary is universal with regard to th/te

competition of interactions and e-h relative motion

(IV) e-Metalh-Insulator

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

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3

0.1

0.25

U‘

U

X2 Gas

X Gas

e-h Plasma

ts1

dn2 ?dn2

0.5

Filling factor

1/8 Filling

Phase diagrams for 2-band Hubbard model at T=0n=0.25 (1/8 filling) th/te=1

DMFT Slave-boson MFT

1st-order transition

2nd-order transition?

Metallic phase

Exciton phase

Biexciton phase

normal phases only

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





Absorption spectra in MH/BX insulatorAbsorption spectra in MH/BX insulator

4t

ε

μe2t

ε

μe Δ

electron bande2t U′=1 U′=4

U=5

0≈≈

Eg0

DOS0≈≈

2t

2t

ωωωω====ωωωω++++μμμμe++++μμμμh~

0

0.5

ε

μh

ε

μh

hole band

4t2t

Δh2t

0

0.5 χ(ω

) U′=2 U′=5

(a) U=U′=0 (b) Insulator at U, U′ ≠ 0

0

0.5

−Im

χ3

4

5

(t e+

t h)

e

h


e

0

0.5

U′=3 U′=5.5

0

1

2

3

U/(t

e+

(I) Metal

th/te=1


e

h

3 4 5 6 70

0.5

3 4 5 6 70 1 2 3 4 5

0

U′/(te+th)

3 4 5 6 70

3 4 5 6 7ω/(2t) ω/(2t)

ωb

t /t 1

Isolated absorption peak vs exciton-like insulator phase

6n=1.0 (half filling)

th/te =1

n=0.25 (1/8 filling)5

5

6e

h 4

5Exciton phase

3

4

U

h

(II) MH insulator

2

3

/(t e

+t h

)

Metallic phase

1

2 (I) Metal e

h

(III) BX insulator1

2

U/(

t

th/te=1

Biexciton phase

0 1 2 3 4 5 60

1

U′

(III) BX insulator

0 1 2 3 4 50

1

U′/(t +t )

th/te=1n=0.25

U′ U′/(te+th)

Region for an isolated absorption peak in half fillingRegion for an isolated absorption peak in half fillingcorresponds to the exciton-like insulator phase in not half filling.

Effects Effects of of interinter‐‐site interactions on EMTsite interactions on EMT

Extended spinless Hubbard model

∑∑∑∑=

++

=

++++

=

+ −+−−=heji

jjiiheji

jjiii

ihihieieheji

ii ccccvccccvccccUcctH ''α

ααααα

ααααα

αα

Extended spinless Hubbard model

=== hejihejiiheji ,,,,,,,,, ααα

Extended Dynamical mean-field theoryv/2t =0 25

( e-e & h-h repulsion v ) = ( e-h attraction v’ )

does not change the nature of MITv’/2t = 0.25v’/2t = 0.20

v/2t =0.25

tends to stabilize the metallic e-h plasma

( e e & h h repulsion v ) > ( e h attraction v’ )0.5

DOS v’/2t = 0.15

( e-e & h-h repulsion v ) > ( e-h attraction v )

stabilizes the insulating state 0.3

0.4

enhances mass density wave fluctuations0.1

0.2

-2 -1 0 1 20(ω-μe)/2t





Excitonic BECExcitonic BEC--BCS crossoverBCS crossover

Quantum mechanical coherence at low temperaturesQuantum mechanical coherence at low temperatures

ee--h pair condensationh pair condensationee--h pair condensationh pair condensationexciton BEC stateexciton BEC stateexciton BEC stateexciton BEC state ee--h BCS stateh BCS stateee--h BCS stateh BCS stateee h pair condensationh pair condensationee h pair condensationh pair condensation

ee heeh

eeinsulatorinsulatorinsulatorinsulator

exciton BEC stateexciton BEC stateexciton BEC stateexciton BEC state ee h BCS stateh BCS stateee h BCS stateh BCS state

t li k li

heehcrossovercrossovercrossovercrossover

d < aBd >> aB

strong coupling weak couplingbosonic feature fermionic featureCoulomb correlation Coulomb correlation

plays a key role in plays a key role in crossover problemcrossover problem

properties of pair condensed phase pair condensed phase ((BECBEC--BCS crossover & optical responseBCS crossover & optical response))

present study:present study:crossover problem.crossover problem.

p ope es o pa co de sed p asepa co de sed p ase (( p pp p ))simplest model : 2-band Hubbard modelmethod: self-consistent t-matrix approx. (SCTMA) + local approx. (LA)

systematic study on optical spectra and systematic study on optical spectra and excitonic BECexcitonic BEC--BCS crossover at finite temperaturesBCS crossover at finite temperatures

SCTMA for eSCTMA for e--h pair condensed phase h pair condensed phase SCTMA: self-consistent t-matrix approx.

e ee h

Dyson equationh e

h= ＋＋e e

e e eeΓ Γ ＋ e eΓ h

eh e h

ee eh p＋ e h e

= ＋＋h e

e hΓe h

h

＋e e

e

eΓ Γh

h

e hp ee eh

e

＋＋＋…= UΓ ee

local approx. (LA)

h

Γ eeΓ(q,iωn)

＋= -U ’Γh e

eh＋＋ …＋ Γ(iωn)

SCTMA+LA: lid f

＋＋=Γ -U ’p ＋…valid for

low-density & high-dimension

weakweak--coupling regioncoupling region strongstrong--coupling regioncoupling region

he

he

he mmmm

tt +∝

+1

BCSBCS--BEC BEC crossovercrossover

hehe

he mmtttt

+∝+

reduced mass→relative motion

motion of center of mass

e-h BCS (excitonic ins.) exciton BEC

⎥⎦

⎤⎢⎣

⎡′

+−=

Uttt

wwTF

hehec )(2

exp13.1 0 ααα ερ

0 1 2 3 40

0.02

0.04

6 8 10 20 4010−3

10−2

U′/(te+th)

γ=1

Tc/

(te+

t h)

n=0.25U=U′

γ=0.5

γ=0.2

Tc

U′′′′(te+th)/(teth) [ ])1/(ln122nn

nU

ttT he

c −−

′=

: cutoff energy ~αw ( )αε FO

γγ

+∝

1BCS

cT 2)1( γγ

+∝BEC

cT

effect of mass difference (γ=th /te )

Condensation temperature in BCS-BEC crossover (Tomio)

effect of U

0 1 2 3 40

0.02

0.04

U′/(te+th)

U=0

T c/(

t e+

t h)

U=1

U=2

n=0.25BCS

In BCS regime, In BCS regime,

TTc is strongly suppressed byc is strongly suppressed by UU..

suppression of

excitonic correlation

γ=th/te =1

0 1 2 3 40

0.2

0.4

U′

U=0

Deh

n=0.25

U=1

U=2

density of occupied sites

∑='

'σσ

σσhi

eieh nnD

TTcc is insensitive to is insensitive to

UU in BEC regime.in BEC regime.

eh

Condensation temperature in BCS-BEC crossover (Tomio)





TOPOLOGY OF COMPLETE PHASE DIAGRAM

EMT vs QC

Low density regime:Low-density regime:QC is harder to emerge.EMT can be observed. → (b) or (c)

High-density regime:QC is easier to emerge.EMT is buried in QC.→ (d)→ (d)

Role of repulsion: QC is suppressedQC is suppressed.→EMT is easier to be observed. f ) Att ti H bb d d lcf.) Attractive Hubbard model





Ivanov and Haug PRL71(1993) 3182.

Mott’s Criterion at T=0

Spinless electrons and holes⇒ Repulsive X-X interaction T

C]K[

EX=16.8meV60

40

20

0

e-h Plasma

X Gas

ExcitonCrystal

0 1 2 3 4 5rs=1/naB

Heitler-London Method

Spin ⇒ Biexciton Crystal ? ?

Exciton Crystal

Arkhipov et al. cond-mat 0505700.

Bosons with dipole-dipole interaction

BEC ?

r -3

e+ e-

e- e+

e+ e-

e+ e-

e± e±

e± e±

g1(ee)

g2 (q)(ee)

g4 (q)(ee)

g1(hh)

g2 (q)(hh)

g4 (q)(hh)

-g1(eh)

-g2 (q)(eh)

-g4 (q)(eh)

( ) + ( )g2, 4 q ~ ln /,g g qL2 4 1

h+ h-

h- h+

h+ h-

h+ h-

h± h±

h± h±

e+ h-

e- h+

e+ h-

e+ h-

h± h±

h± h±

Forward scatterings ⇒ Excactly solvableBackward scatterings

Long-rangeCoulomb

Short Range

(ij) (ij)

Linearband

Interband BSexists only in

nondoped case

k kFe

Fh( ) ( )=

Intraband BS

Scalingdimension

<kF2 kF2

g-ology in 1D e-h systems

↑

↑

-g1(eh)e+ h-

e- h+

Relevant ⇒

RG / SCHA ⇒ Relevancy

Insulator even at the high density limit⇔ No metal-insulator transition

©(c)½ = 0 ©(e)¾ = 0 ©(h)¾ = 0

H(eh)bs = ¡ 8g(eh)1

(2¼®)2

Zdx cos

p2©(c)½ cos

p2©(e)¾ cos

p2©(h)¾

H½ +H¾ +H(ee)bs +H(hh)bs +H(eh)bs(c)

MassiveMasslessMassiveMassive

↑

↑

“Commensurate Filling”

C

V

Backward Scattering

TL Hamiltonian Phase Lock

ChargeMasse-Spinh-Spin

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

for comparison Phases in a high-densiy 1D e-h system

biexciton crystallization(or biexciton BEC)

Always insulatingNO exciton Mott transition

T > ∆

h-CDW/SDW(or exciton BEC)Short-range

Interaction

Long-rangeCoulomb

"biexciton liquid"

e-h backward scattering: negligible

Biexcitonic correlation is suppressed.

T < ∆gap gap

Strong instability toward

(bad metallic)

∆gap : a charge gap induced by e-h backward scattering

SUMMARY

Objects:Balanced electron-hole systems in quasi-thermal-equilibriumIn high dimensions and in 1 dimensionIn high dimensions and in 1 dimension

Subjects:Exciton Mott transition (EMT): X gas / e-h plasma Q t d ti (QC) it BEC / h BCSQuantum condensation (QC): exciton BEC / e-h BCS

Theoretical tools and models:e-h Hubbard model, DMFT, slave-boson MFAextended e-h Hubbard model, extended DMFTSelf-consistent T-matrix approx. (SCTMA)e-h Tomonaga-Luttinger model, bosonization, RG, SCHAg g , , ,Cluster perturbation theory (CPT)

Important findings:Two insulating phases: exciton-like and biexciton-likeTwo insulating phases: exciton like and biexciton likeEMT: 1st-order transitionMC temperature vs QC temperatureXX crystal and absence of exciton Mott transition in 1dXX crystal and absence of exciton Mott transition in 1d…

PROBLEMS TO BE SOLVED

1) From lattice fermion model to continuum-space fermion modelDMFT for continuum models (Ohashi, Ueda, TO)Excitation modes: collective individualExcitation modes: collective – individualComparison with hydrogen metals, positronium condensates, superconductivity

2) Description of low-density regime (X gas, XX gas)S lf i t t it th (H i A TO Ph i E 40 1401 (2008))Self-consistent exciton-gas theory (Hanamiya, Asano, TO: Physica E 40, 1401 (2008)).Biexciton Auger scattering (Watanabe, Asano, TO)

3) Description of intermediate-density regime (e-h-X-XX mixture, crossover)D i l iDynamical screening

4) Dynamics for/against condensationPhoto excitation vs Current injection, e-h transport, Relaxation/condensation dynamics

5) Imbalanced e-h systemsFFLO order (Yamashita, Asano, TO)

6) DimensionalityCluster perturbation theory (Asano, Nishida, TO), Dynamical DMRG (Asano, TO)

7) Photon physicsTwo-particle Green function, diagrammatic extension of DMFT (Ohashi, TO)p g ( )Cavity effects, Temporal/spatial coherence of PL, Polariton condensation vs lasing, Nonlinear optical responses, Lasing process

SIMILAR SYSTEMS

T=10 K Hadron QCD systems:quark-gluon plasma (QGP) vs hadron gas/liquid vs color SC

12

quark gluon plasma (QGP) vs hadron gas/liquid vs color SCT=10 K Warm dense matter:

weakly-coupled plasma vs condensed matter

5

T=1 K e-h systems (condensed matter): e-h plasma/liquid vs exciton gas vs exciton BEC, e-h BCS

T=10 K Cooled atoms and optical lattices:-6T 10 K Cooled atoms and optical lattices: fermi gas vs molecular Bose gas vs superfluid, supersolid, spinor BEC

Common features:Common features:Competing several order parameters

Strong-coupling regime - weak-coupling regimeStrong coupling regime weak coupling regimePairing - antipairing, confinement - deconfinementQuantum coherence - classical coherenceFinite temperature effects

b K Aby K. Asano

Still just schematic !Three boundaries:

Exciton Mott transition (EMT)

Changing particle densityUnified treatment for EMT and QC

Exciton Mott transition (EMT)Quantum condensation (QC)Thermal ionization

Continuum-space modelOptical responses

Documents

Exciton Mott Transition and Pair Condensantion in … · Exciton Mott transition and quantum pair cont l i i dtd ensation in electron-hl thole systems: Dynamical mean-field theory