Pseudogap Phenomena in Color Superconductivity

1. カラー超伝導に付随した擬ギャップ現象 M. Kitazawa, T. Koide, T. Kunihiro, Y. Nemoto in preparation

2. １Introduction 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 m 0 Similarity between CSC and high TC superconductor?

3. 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 ε→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 toe ~ 0.2electric SC：e ~ 0.005

4. :density of state TC 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)

5. There are still no common consensus for the origin of the pseudogap in HTSC. Conceptual phase diagram of 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! TC=4.34MeV

6. 2Formulation Density of State N(w) Model Nambu-Jona-Lasinio model (2-flavor,chiral limit)： t：SU(2)F Pauli matrices l：SU(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)

7. Green Function and Self Energy :T-approximation where, :free progagator

8. 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.

9. Remarks on S :two possibilities of collective excitation in the color space ImQ converges without cutoff: Notice: ReQ - from dispersion relation:

10. 3Numerical Results Self EnergyS- Re S- at Fermi momentum kF=400MeV 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

11. Im S- momentum dependence The peak of Im S- w =m –p : on-shell : the most preferable excitation w =m–k peak of ImS They coincide at k=m Dispersion of free quark w =k–m Pseudogap appears around the Fermi surface!

12. 1-Particle Spectral Functionr0(k,w) • = 400 MeV e=0.01 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

13. 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

14. m Dependence of Pseudogap As m is increased, pseudogap becomes wider and (slightly) deeper. reflection of the increasing phase space near the Fermi surface

15. 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.