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23/4/2023/4/20 11
BCS-BEC Crossover BCS-BEC Crossover in Relativistic System and Its in Relativistic System and Its Possible Realization in QCD Possible Realization in QCD
Lianyi He and Pengfei Zhuang
Physics Department, Tsinghua U.
References: Phys.Rev.D75:096003,2007 Phys.Rev.D75:096004,2007Phys.Rev.D76:056003,2007 E-print Arxiv: 0709.2246
ATHIC2008, TSUKUBA, JAPANATHIC2008, TSUKUBA, JAPAN
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Impact of SuperconductivityImpact of Superconductivity
Phenomena Order parameter Pair Breaking effect
Metallic superconductivity
Zeeman Splitting
Superfluidity in Ultracold Fermi atoms
Population imbalance
Chiral symmetry
breaking in QCD
Baryon chemical potential
Color superconductivity
in dense quark matter
Isospin chemical potential
Strange quark mass
flavor superfluidity
in isospin matter
Baryon chemical potential
21†L Rq q
Tq q
5ui d
0ZE H
21
21
NN
NNP
Bm
Im
sm
Bm
ATHIC2008, TSUKUBA, JAPANATHIC2008, TSUKUBA, JAPAN
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Theoretical History of Crossover:Theoretical History of Crossover:
• Leggett (1980)Leggett (1980) noted that BCS T=0 wavefunction noted that BCS T=0 wavefunction could becould be generalized to arbitrary attraction: a generalized to arbitrary attraction: a smoothsmooth BCS- BCS-BEC crossover !BEC crossover !
2/12
2/1
1 kB
kBk
N
Nv
BCSBCS
0exp 2/10
kkk k ccNB
BECBEC
Introduction to BCS-BEC CrossoverIntroduction to BCS-BEC Crossover
weak couplingstrong coupling
ATHIC2008, TSUKUBA, JAPANATHIC2008, TSUKUBA, JAPAN
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Eagles (1969): Pairing without superconductivityEagles (1969): Pairing without superconductivity
ATHIC2008, TSUKUBA, JAPANATHIC2008, TSUKUBA, JAPAN
In HTSC, the root of PG is not quite clear. The pre-formed boson mechanism is only one explanation.
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Experimental evidence for pseudogap in ultracold fermions
Science 307, 1296 (2005)Science 307, 1296 (2005)
0,0
0,4
0,0
0,4
-20 0 20 40
0,0
0,4
0,0
0,4
(d)
(c)
(a)
frac
tiona
l los
s in
|2>
RF frequency offset (kHz)
(b)
Science 305, 1128 (2004)
ATHIC2008, TSUKUBA, JAPANATHIC2008, TSUKUBA, JAPAN
T *
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T
BEC?
SQGP?
Relativistic BCS-BEC Crossover
Motivation:1) QCD phase diagram at moderate temperature and density, strong coupling nature! 2) BCS-BEC crossover in CSC? Pseudogap of CSC3) NJL model: BCS theory of chiral symmetry breaking. Chiral pesudogap above Tc?
pseudogap?
CSC SBc
ATHIC2008, TSUKUBA, JAPANATHIC2008, TSUKUBA, JAPAN
Quark Spectrum and pseudogap, M. Kitazawa, et.al. 2005
Structure change of Cooper pairs,H.Abuki, et.al.2002
Progress in this field of research
H.Abuki and Y.Nishida: NSR approach, new crossover: BCS-BEC-RBECL.He and P.Zhuang: BCS-Leggett theory at zero T and pesudogap theory at finite T BCS-BEC vs. Chiral RestorationJ.Deng and Q.Wang: Boson-fermion model in mean field and beyond mean fieldM.Kitazawa, D.Rischke and I.Shovkovy: Possible Diquark BEC in NJLT.Brauner: Collective Excitation 1/N expansion including quantum fluctuation (with H.Abuki)
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Zero Temperature: BCS-Leggett mean Field Theory
Model Lagrangian
Mean Field Equations
k <L
ATHIC2008, TSUKUBA, JAPANATHIC2008, TSUKUBA, JAPAN
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Fermionic Excitation Spectrum
( )2
2 2 20kE k m m- = + - +D ( )
22 2 2
0kE k m m+ = + + +D
fermion anti-fermion
1. Non-relativistic limit
2. Criterion for BCS and BEC: Minimum of the dispersion BCS: at , existence of Fermi surface BEC: at , molecule condensation 3. The role of fermion mass (new aspect in QCD) BCS-BEC Chiral symmetry breaking& restoration
22202k NR
kE
mm-
æ ö÷ç ÷= - +Dç ÷ç ÷çè ø
k m= m mm- = NR mm m= -
( )2 20k kE m Em+ -= + +D ?
0k ¹0k =
Û mm>Û mm<
Û
ATHIC2008, TSUKUBA, JAPANATHIC2008, TSUKUBA, JAPAN
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The Non-Relativistic Limit
fk
mz=
For small value of the parameter , the NR version of BCS-Leggett result is recovered
z
1
f sk ah=
2
2f
f
k
me =
The condition or is neededm mm- =1h z-=
ATHIC2008, TSUKUBA, JAPANATHIC2008, TSUKUBA, JAPAN
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Relativistic Effect I: BCS-NBEC-RBEC Crossover
2 2f fE k m= +
Physical picture: 2
12b
s
E mma
= : Þ 1s ca
ml =: 1h z-:
RBEC: , anti-particles available!0m®ATHIC2008, TSUKUBA, JAPANATHIC2008, TSUKUBA, JAPAN
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Relativistic Effect II: Density Induced Crossover
ATHIC2008, TSUKUBA, JAPANATHIC2008, TSUKUBA, JAPAN
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Collective Mode Evolution
Effective action
Dispersion of the collective mode
Goldstone mode1
3fkcm
=BCS
NBEC ( )2 2 8
2 2B BB
B B B
n ak kq
m m m
pw
æ ö÷ç ÷= +ç ÷ç ÷çè ø
( )q cqw =
Bogoliubov theory
RBEC ( )q qw ; Ultra-relativistic BEC
A-B mode
ATHIC2008, TSUKUBA, JAPANATHIC2008, TSUKUBA, JAPAN
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K.Levin and Qijin Chen, et.al, Phys.Rept. 412, 1(2005)
Nonzero Temperature:
ATHIC2008, TSUKUBA, JAPANATHIC2008, TSUKUBA, JAPAN
Pseudogap theory
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Tc Calculation
NBEC regime
RBEC regime
mm< Bound states above Tc
ATHIC2008, TSUKUBA, JAPANATHIC2008, TSUKUBA, JAPAN
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BCS-BEC Crossover in QCD?
Two color QCD QCD at finite isospin density
Phys.Rev.D75:096004,2007
ATHIC2008, TSUKUBA, JAPANATHIC2008, TSUKUBA, JAPAN
In the BEC region, quark energy gap is different from the order parameter! Can be confirmed in Lattice!
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Chiral restoration vs. BCS-BEC crossover
2B m
mm= =
BEC
BCS
ATHIC2008, TSUKUBA, JAPANATHIC2008, TSUKUBA, JAPAN
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1c
g
g
2
2
4c
c
gN
Quark mass is still large above chiral phase transition!
Nc dependence
qq Condensation and Chiral Phase Transition
Pseudogap in QCD?
NJL Model
ATHIC2008, TSUKUBA, JAPANATHIC2008, TSUKUBA, JAPAN
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Quark pesudogap remarkable!
Diquark condensation and color superconductivity
NJL model, 2SC phase
400 , 5MeV m MeVm= =
ATHIC2008, TSUKUBA, JAPANATHIC2008, TSUKUBA, JAPAN
0
0.57cT <D
A high Tc superconductor!
( )0
0.5pg cTD
D:
2/3TC pg 0T ®
Non-Fermi liquid behavior at low T!
(High T, see M.Kitazawa, 2005)
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Summary1. BCS-BEC crossover theory has been generalized to relativistic system, both at zero and at finite temperature.2. Proper NR limit is recovered and new relativistic effects are found.3. Possible BCS-BEC crossover in diquark and isospin matter is discussed.4. The size of quark pseudogap in chiral and CSC phase transition is calculated.
ATHIC2008, TSUKUBA, JAPANATHIC2008, TSUKUBA, JAPAN
Outlook
1. Determine the pseudogap phase in QCD phase diagram2. Signals of diquark fluctuation and pesudogap in HIC3. Effect of the pseudogap on compact star cooling4. More precise theory, including quantum fluctuation
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Thank You!
ATHIC2008, TSUKUBA, JAPANATHIC2008, TSUKUBA, JAPAN