2015-10-281 BCS-BEC Crossover in Relativistic System and Its Possible Realization in QCD BCS-BEC Crossover in Relativistic System and Its Possible Realization

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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


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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


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Eagles (1969): Pairing without superconductivityEagles (1969): Pairing without superconductivity


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)


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


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


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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


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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-=


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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


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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


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K.Levin and Qijin Chen, et.al, Phys.Rept. 412, 1(2005)

Nonzero Temperature:


Pseudogap theory

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Tc Calculation

NBEC regime

RBEC regime

mm< Bound states above Tc


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BCS-BEC Crossover in QCD?

Two color QCD QCD at finite isospin density

Phys.Rev.D75:096004,2007


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


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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


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Quark pesudogap remarkable!

Diquark condensation and color superconductivity

NJL model, 2SC phase

400 , 5MeV m MeVm= =


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.


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!


Documents

2015-10-281 BCS-BEC Crossover in Relativistic System and Its Possible Realization in QCD BCS-BEC Crossover in Relativistic System and Its Possible Realization