M. Kitazawa, T. Koide, T. Kunihiro, Y. Nemoto

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M. Kitazawa, T. Koide, T. Kunihiro, Y. Nemoto
in preparation
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1 Introduction
Color Superconductivity (CSC)
CSC in the intermediate density region
T
Strong coupling nature of QCD
Large fluctuation of the pair field
Chiral Symmetry Broken
CSC
SC CSC HTSC
D / EF 0.001 0.1 0.1
m
0
Similarity between CSC and high TC superconductor?
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Precursory Mode in CSC
M.K., T.K., T.K., Y.N., PRD 65, 091504 (2002)
(1) Spectral Func. of Pair Field


(2) Collective Mode
e?0 (T?TC)
As T is lowered toward TC,
The peak of r becomes sharp. The collective mode
moves toward the origin.
Soft mode
The peak survives up to e 0.2 electric SCe
0.005
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Pseudogap in High Temperature SC (HTSC)
Pseudogap
Anomalous depression of the density of state near
the Fermi surface in the normal phase.
BCS
Pseudogap
Renner et al.(96)
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Conceptual phase diagram of HTSC
There are still no common consensus for the
origin of the pseudogap in HTSC.
T-matrix approximation
Yanase,Yamada(01),
Analogy in BKT transition
Loktev et al.(01),

It is believed that large fluctuation of
pair-field causes the pseudogap.
x doping
Pseudogap in low density nuclear matter
A.Schnell G.Roepke, P.Schuck PRL83 1926(1999)
Pseudogap appears!
TC4.34MeV
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2 Formulation
Density of State N(w)
Model
Nambu-Jona-Lasinio model (2-flavor,chiral limit)
tSU(2)F Pauli matrices lSU(3)C Gell-Mann
matrices C charge conjugation operator
Parameters
M.K. et al., (2002)
so as to reproduce
Klevansky(1992), T.M.Schwarz et al.(1999)
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Green Function and Self Energy
T-approximation
where,
free progagator
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S has spinor indices
0 in chiral limit
Decomposition of G into positive and negative
energy part
projection op.
where,
self-energy for the positve and negative energy
particles.
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Remarks on S
two possibilities of collective excitation in
the color space
ImQ converges without cutoff
Notice
ReQ - from dispersion relation
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3 Numerical Results
Self Energy S-
Re S-
at Fermi momentum kF400MeV
Re S- affects the dispersion relation of the
positive energy particles w w(p).
Around the Fermi surface,
increases
decreases
enhances the formation of the pseudogap
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Im S-
momentum dependence
The peak of Im S- w m p
on-shell
the most preferable excitation
w mk
peak of ImS
They coincide at km
Dispersion of free quark
w km
Pseudogap appears around the Fermi surface!
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1-Particle Spectral Function r0(k,w)

• 400 MeV
• e0.01

quasi-particle peak, w k-m
quasi-particle peak of anti-particle, w -k-m
quasi-particle peak is depressed around the Fermi
energy.
growth of ImS around the Fermi energy.
Fermi Surface
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Density of State N(w)
m 400 MeV
There exists a pseudogap structure in N(w) above
TC.
N(w)/104
The pseudogap survives up to e 0.05 ( 5 above
TC ).
w
Fermi surface
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m Dependence of Pseudogap
As m is increased, pseudogap becomes wider and
(slightly) deeper.
reflection of the increasing phase space near the
Fermi surface
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Summary
We explored the pseudogap phenomena of CSC above
TC and found that there exists pseudogap
structure up to 5 larger than TC.
We have shown that the fluctuation of the pair
field affects. There might exists rich physics
not only inside the CSC but also above TC .
Future Work
Investigate the more quantitative understanding
of the pseudogap.
To explore the experimental observables which
reflects the pseudogap.