Normal and superconducting states of -(ET) 2 X organic superconductors S. Charfi-Kaddour Collaborators : D. Meddeb, S. Haddad, I. Sfar and R. Bennaceur LPMC, Faculté des Sciences de Tunis, Tunis, Tunisia M. Héritier, LPS (Université Paris-Sud, Orsay)
Outline Normal state properties of -(ET) 2 X Spin fluctuations Self-energy correction Spectral function Density of states Comparison with experiments Superconducting pairing Phase segregation
Phase diagram 13 K 22 K 100 K 30 K AF SC I Metallic state SC D 8 -Br H 8 -Br Cu(NCS) 2 I3I3 H 8 -Cl T* Pressure Fermi liquid Strange Metal T -(BEDT-TTF) 2 Cu[N(CN) 2 ]Br Tc= 11.5 K -(BEDT-TTF) 2 Cu(NCS) 2 Tc= 9.5 K Normal state anomalies : Pseudogap ? What are the spin fluctuations effects on quasi-particles (q-p)?
Spin-lattice relaxation rate Metal : 1/ T 1 T = constant This abnormal behaviour desappears with pressure [A.Kawamoto 95], [K.Miyagawa 95], [Y.Nakazawa 95] [K.Kanoda 95] Anomalous behaviour around 60 K
Magnetic susceptibility Metal : T) = constant Pauli susceptibility Unusual behaviour at low temperature Of Pseudogap effect [A.Kawamoto 95], [K.Miyagawa 95], [Y.Nakazawa 95] [K.Kanoda 95]
Photo-emission : Fermi liquid ? Pt Fermi liquid : Inflexion point Absence of Fermi edge [R.Liu, 1995].
Fermi surface Magnetotransport measurements, J. Caulfield et al. (1994) Best nesting vector Band 1Band 2
Hubbard Hamiltonian weak coupling U : intra-band on-site coulomb repulsion U’ : inter-band on-site coulomb repulsion U = U’ B1B1 B2B2
Korringa law not satisfied : a spin fluctuation effect quand t 1 /t 2 =0.4 t 1 /t 2 =0.5 t 1 /t 2 =0.7 U=0.3 e V P=1bar, P=1.5kbar, P=3kbar et P=4kbar Our calculation ĸ-(ET) 2 Cu[N(CN) 2 ]Br [H. Mayaffre94] R. Louati, Phys. Rev. B 2000 P=4kbar P=1bar
Bandwidth effect on 1/T 1 T : The pressure acts on the bandwidth and also on the nesting (t 1 /t 2 ) Louati et al., Phys. Rev. B 62, 5957 (2000) T* T* increases with pressure
Self-energy corrections Calculation of the Green functions of the antiferromagnetically correlated electron system. GG0G0 G0G0 + Self-energy within RPA approximation (Q) k’+Q k’-Qk’ U U RPA k’k’ k’+Q … = U U U = = G0G0
Spin fluctuations ε k+Q = - ε k χ RPA (Q,ω) is maximum for a Q vector correcponding to the : best nesting k belongs to the Fermi surface
qzqz qxqx Magnetic susceptibility (bande 1) qzqz best nesting [Louati et al, Phys. Rev B (2000)]
qzqz qxqx Magnetic susceptibility (bande 2) qzqz qxqx [Louati]
Quasi-particules Imaginary part of the self-energy : Inverse of q-p life time kk A(k, U = 0 A(k, EkEk U > 0 E k real part of the green function pole : q –p energy
Pseudogap formation for C and B points There is a critical value of U for which the pseudogap opens No pseudogap at A; different behaviours at different points of the FS ; C is a hot spot Self energy calculation :hot spots at best nesting points C point B 1 point A point C B A
Imaginary part of the self-energy Anisotropic behaviour of the FS Life time in A higher than in C. C A
U The quasi-particule has a shorter life time C A B2B2 Point C Point B 2 Imaginary part of the self-energy
Point C C C is more affected by both band fluctuations C is a affected by e-e scattering The quasi-particule is vanishing Spin fluctuations of the band 1Spin fluctuations of the band 2 Spin fluctuations of both bands t 1 / t 2 =0.4
Density of states
Density of states calculation : Important pseudogap effect 30% reduction of the density of states near the Fermi level Band 2 T=50 K EFEF
Comparison with experiments 30% reduction of the magnetic susceptibility at 50 K in agreement with NMR experimental data of the susceptibility : pseudogap effect The results fit well the 1/T1T temperature dependence Good agreement with optical measurements (Dressel 2008) Good agreement with the estimation of the life time from magneto-transport data (J. Singleton PRL, 2007) Possible explanation of absence of quasi-particles in parts of the FS.
Superconducting pairing due to inter-band interaction Pairing of electrons from the band 2 mediated by spin fluctuations from the band 1 : d-wave paring
Supraconductivité non homogène : Diagrammes de phases bar k-(ET)2N(CN)2Cl S. Lefebvre et al., Phys. Rev. Lett. 85, 5420 (2000). Yoneyama et al., J. Phys. Soc. Jpn. (2004). k-(h8-ET) 1-x (h8-ET) x ] 2 Cu[N(CN)2]Br Phase segregation Hydrostatic pressure Chemical pressure
Su et al. (1998) Tc versus disorder Cooling rate Irradiation J. Analytis et al. PRL (2007)
The Model J0J0 J1J1 J2J2 SC Josephson couplings Insulator fluctuations Time dependent Ginzburg-Landau equation+ critical superconducting fluctuations
Our results κ(BEDT-TTF)2Cu(SCN)2
Conclusion Interpretation of the normal state properties by a spin fluctuation effect Mechanism for superconducting coupling Explanation of the coexistence region as a segregation phase ( Josephson coupling)