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

1
BCS-BEC Crossover in Relativistic
System and Its Possible Realization in QCD
Lianyi He and Pengfei Zhuang Physics Department,
Tsinghua U.
References Phys.Rev.D75096003,2007
Phys.Rev.D75096004,2007 Phys.Rev.D76056003,2007
E-print Arxiv 0709.2246
2
Impact 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
ATHIC2008, TSUKUBA, JAPAN
3
Theoretical History of Crossover
Introduction to BCS-BEC Crossover

• Leggett (1980) noted that BCS T0
  wavefunction could be
• generalized to arbitrary attraction a smooth
  BCS-BEC crossover !

weak coupling
strong coupling
ATHIC2008, TSUKUBA, JAPAN
4
Eagles (1969) Pairing without superconductivity
In HTSC, the root of PG is not quite clear. The
pre-formed boson mechanism is only one
explanation.
ATHIC2008, TSUKUBA, JAPAN
5
Experimental evidence for pseudogap
in ultracold fermions
Science 307, 1296 (2005)
Science 305, 1128 (2004)
ATHIC2008, TSUKUBA, JAPAN
6
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 CSC 3) NJL model BCS theory of chiral
symmetry breaking. Chiral pesudogap above Tc?
Quark Spectrum and pseudogap, M. Kitazawa, et.al.
2005
SQGP?
Structure change of Cooper pairs, H.Abuki,
et.al.2002
pseudogap?
SB
CSC
BEC?
ATHIC2008, TSUKUBA, JAPAN
7
Progress in this field of research
H.Abuki and Y.Nishida NSR approach,
new crossover
BCS-BEC-RBEC L.He and P.Zhuang BCS-Leggett
theory at zero T
and pesudogap theory at finite T
BCS-BEC vs. Chiral
Restoration J.Deng and Q.Wang Boson-fermion
model in mean field
and beyond mean field M.Kitazawa, D.Rischke and
I.Shovkovy
Possible Diquark BEC in NJL T.Brauner Collective
Excitation 1/N expansion
including quantum fluctuation
(with H.Abuki)
8
Zero Temperature BCS-Leggett mean Field Theory
Model Lagrangian
Mean Field Equations
ATHIC2008, TSUKUBA, JAPAN
9
Fermionic Excitation Spectrum
fermion
anti-fermion

• Non-relativistic limit
• Criterion for BCS and BEC Minimum of the
  dispersion
• BCS at , existence of Fermi
  surface
• BEC at , molecule condensation
• The role of fermion mass (new aspect in QCD)
• BCS-BEC Chiral symmetry breaking
  restoration

ATHIC2008, TSUKUBA, JAPAN
10
The Non-Relativistic Limit
For small value of the parameter , the NR
version of BCS-Leggett result is recovered
The condition or is
needed
ATHIC2008, TSUKUBA, JAPAN
11
Relativistic Effect I BCS-NBEC-RBEC Crossover
Physical picture
RBEC , anti-particles available!
ATHIC2008, TSUKUBA, JAPAN
12
Relativistic Effect II Density Induced Crossover
ATHIC2008, TSUKUBA, JAPAN
13
Collective Mode Evolution
Effective action
Dispersion of the collective mode
Goldstone mode
A-B mode
BCS
NBEC
Bogoliubov theory
RBEC
Ultra-relativistic BEC
ATHIC2008, TSUKUBA, JAPAN
14
Nonzero Temperature
Pseudogap theory
K.Levin and Qijin Chen, et.al, Phys.Rept. 412,
1(2005)
ATHIC2008, TSUKUBA, JAPAN
15
Tc Calculation
NBEC regime
RBEC regime
Bound states above Tc
ATHIC2008, TSUKUBA, JAPAN
16
BCS-BEC Crossover in QCD?
Two color QCD
QCD at finite isospin density
In the BEC region, quark energy gap is different
from the order parameter! Can be confirmed in
Lattice!
Phys.Rev.D75096004,2007
ATHIC2008, TSUKUBA, JAPAN
17
Chiral restoration vs. BCS-BEC crossover
BEC
BCS
ATHIC2008, TSUKUBA, JAPAN
18
Pseudogap in QCD?
Condensation and Chiral Phase Transition
NJL Model
Nc dependence
Quark mass is still large above chiral phase
transition!
ATHIC2008, TSUKUBA, JAPAN
19
Diquark condensation and color superconductivity
NJL model, 2SC phase
Quark pesudogap remarkable!
A high Tc superconductor!
ATHIC2008, TSUKUBA, JAPAN
20
Non-Fermi liquid behavior at low T!
(High T, see M.Kitazawa, 2005)
21
Summary 1. 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
   diagram
2. Signals of diquark fluctuation and pesudogap in
   HIC
3. Effect of the pseudogap on compact star cooling
4. More precise theory, including quantum fluctuation

ATHIC2008, TSUKUBA, JAPAN
22
Thank You!
ATHIC2008, TSUKUBA, JAPAN