Anomalous quantum cri/cality linking an/ferromagne/sm and superconduc/vity in organic metals

Transcription

1 Anomalous quantum cri/cality linking an/ferromagne/sm and superconduc/vity in organic metals C. Bourbonnais NQS2011, Kyoto, November 2011 Coll. A. Sedeki N. Doiron- Leyraud S. René De Cotret L. Taillefer P. Auban- Senzier D. Jerome

2 Outline 1. Organic conductors: what are they? 2. (TMTSF) 2 PF 6 : paradigm for AF - SC proximity 3. Normal state : anomalous quantum cri/cality 4. RG to Quasi- 1D electron gas : AF- SC interference and ext. quantum cri/cality 5. Conclusion

3 TMTSF or TMTTF Donors e- Acceptors e- Perylene BEDT-TTF Etc. DMTCNQ

4 Bechgaard salts Series: one- chain ca/on- radical salts (TMTSF) 2 X X = PF 6, AsF 6, ClO 4,... (radicals, δ=0.5e) Quasi- 1D Fermi surface 1 hole/2 mol + weak dimeriza/on ~ 1/2- filled band Γ

5 Resis/vity vs T P= 1bar D. Jerome, H. J. Schulz, Adv. Phys. 31, (1982) P=12 kbar ~ 12 K K. Bechgaard et al., Solid State Comm. 33, 1119 (1980) AF - SC proximity D. Jerome et al., J. Phys. Lee. 41, L95 (1980).

6 N. Doiron- Leyraud, P. Auban- Senzier et al., Phys. Rev. B 80, (2009)

7 Normal phase: NMR T 1 1 : probing spin fluctuations S. Brown et al., 2008 Also, F. Creuzet et al., J. Phys. Lee. 45, (1984); Synthe/c Metals 19, 277 (1987); T 1 1 T (FL) Wu et al., PRL 94, (2005) T 1 1 T T +Θ Curie- Weiss enhancement

8 Anomalous T 1 1 enhancement (T 1 T ) 1 ξ 2 (d = 2) ξ (T +Θ) 1/2 No Fermi liquid recovery T 1 1 T (Korringa law)

9 T 1 1 CW enhancement vs T c 13 C NMR (TMTSF) 2 PF 6 (T 1 T ) 1 = C 0 + C T +Θ C vs T c : SDW fluct. correlated to pairing (T c ) Y. Kimura et al., PRB 84, (2011).

10 Anomalous scaeering: linear resis/vity AT + BT 2 ~T 2 ʹ ρ(t ) AT + BT 2 ʹ Fermi Liquid T 2 at P c ʹ N. Doiron- Leyraud, P. Auban- Senzier et al., Phys. Rev. B 80, (2009); EPJB, , 23 (2010); P.Auban- Senzier et al., J. Phys: Cond. Mat. 23, (2011).

11 Anomalous scaeering: linear resis/vity ρ(t )=AT + BT 2 - Link between scaeering and pairing N. Doiron- Leyraud, P. Auban- Senzier et al., Phys. Rev. B 80, (2009)

12 Quantum Cri/cality and the phase diagram T NFL T 1 1, ρ T NFL ρ at + bt 2 SDW P c FL T 1 1 T ρ T 2 P SDW P c (T 1 T ) 1 (T +Θ) 1 SCd P c FL ρ T 2 P Landau- Ginzburg- Wilson paradigm NFL FL at P > P c at T 0 Quantum order parameter (SDW) fluct. (e- h) Hertz, Millis (1976,1993) Moriya, Ueda (1990,2002), Abanov et al., (2003) NFL FL at P > P c Role of SC? Excita/ons? (e- h + e- e) Shio in the QCP paradigm

13 Mechanism of the transi/ons - SDW state From 1 H NMR lineshape T. Takahashi et al., J.Phys. Soc. Jpn 55, 1364 (1986). J. M. Delrieu et al., J. Physique 47, 839 (1986). 13 C NMR : M. Misawa et al., (2010) L. Ducasse et al., J. Phys. C. Solid State Phys. 18, L947 (1985). SDW modula/on wave vector q 0 (NMR) : the best calculated nes/ng vector q 0 (0.5 a*, 0.24 b*) Mechanism for SDW order: Nes/ng of the Fermi surface + repulsive interac/ons

14 Quasi- 1D electron gas model : SDW - SC phases g 1, g 3 g 1 χ σ g 3 D ( ) ( ) q 0 g 2 T SDW ( ) g 2 quasi- 1D Fermi surface V.J. Emery et al., Phys. Rev. Lee. (1982))

15 Many- body physics of the q- 1D electron gas (interference of pairings) q 0 q 0 e-h pairing e-h e-e e-e pairing χ 0 P (0,T) ln P E F max{ T,4t } χ 0 C(0,T) ln E F T C P C P etc. DW- Cooper pairing mixing present at every order

16 Scaling theory (RG) of both pairing channels l = + g 1,2 C P k- resolved flow of scaeering amplitudes P + + l = + g 3 Singulari/es T scales for instabili/es via P χ SDW (T ; g 2,g 3 ) { χscd (T ; g 1,g 2 ) T(K) 10 2 SDW fluct. induce d- wave pairing (Interference) Instability lines vs nes/ng altera/ons ( pressure ) SDW 10 0 SCd t' b (K) C.B. & A. Sedeki, PRB 80, (2009) C.Nickel et al., Phys. Rev. Lee. 95, (2005) R.Duprat & C.B., Eur. Phys. J. B, 21, 219(2001)

17 Normal phase: extended Curie Weiss regime T(K) 10 2 Θ SDW C-W 10 0 SCd t' b (K) C. B. and A. Sedeki, PRB 80, (2009) - d- Cooper pairing boosts (interferes construc/vely with) SDW - Enhancement Fits a Curie- Weiss law χ SDW (q 0 ) (T +Θ) 1

18 Impact on the normal phase : NMR RG S. Brown et al., ( ) T 1 1 C 0 T + C T T +Θ P>P c T(K) 10 2 Θ SDW C-W 10 0 SCd b (K) C. B. and A. Sedeki, PRB 80, (2009) t' N. Doiron- Leyraud et al., Phys. Rev. B 80, (2009); EPJB (2010)

19 Two- loop RG : one- parccle self- energy l Σ + = + + One-particle spectral quantities : z(k ),A(k F (k ),ω),m,τ 1 k,..

20 spond to a fit to Eq. (18) of the marginal liquid theory at k =0. Quasi- par/cle weight vs T and pressure phase digram. We see from Fig. 5 that not too far from t at the intermediate t =26.8K, z(k )exhibitsasignificative decay in the metallic state extending far above the critical domain, comprising the entire Curie-Weiss z (k = 0) T [K] regime of spin1 correlations. The amplitude of the z decay correlates with the one of SDW fluctuations in the 0.8 normal phase as t is tuned away from t.whent is far upward, at K, for instance, one has T c =0.12K Tc, and a very weak 0.4 temperature dependence is found for z above T c,whichisveryclosetothatofafermiliquid 0.2 (Fig. 5). t t t If we now concentrate 0 on the Curie-Weiss temperature interval, T c < T T CW, we see that the z decay at T [K] k =0forinstance,canbeseenasaresultoflogarithmic corrections that conform to the expression, T(K) Fermi liquid component is forming a z(±π/2) constant (Fig. 6 and Figs B. Renormalization of transverse The corrections produced by the generate the new term, z ( k ), in propagator (14) (see also App. A). z (k ) z (k, ω ν=0 )affects the tra Θ electron spectrum and then deforms According to (14), the modification o ergy issdw of the form, δε C-W (k )=z(k )z even function of k can be decompos series SCd δε (k )= t 0 + δt t' b (K) cos k + δt δt cos 3k +. The series coefficients consist of corre z 0 (k ) z(k )= 1+g(k )ln(t CW /T ), Marginal (18) Fermi icalliquid potential (Varma(t et 0 ), al., the PRL first (89))(δt ), s (δt )..., nearest-neighbors hoppin ( linear scaeering transverse rate direction. in temperature) Here δt which is compatible with the phenomenology proposed,asw harmonics are new terms of the spec by the marginal Fermi liquid theory for the quasiparticle self-energy in two dimensions. 48 RG flow. It turns out, however Recovery of a Fermi liquid Herein z 0 the (k large )= t theor total small correction T c limit δε is very accu z(k,t CW )isthequasi-particleweightatthecutoff temperature T CW =10K,andg(k )isthesquareofanef- existing form of the transverse part o which involves δt and δt alone; th fective coupling constant normalized by πv F. etc.., are vanishingly small and can

21 Normal phase quasi- par/cle scaeering rate l Σ + = + + One- par/cle self- energy : τ 1 ( ρ),z,... Within the Curie- Weiss domain: C. B. and A. Sedeki, C. R. Physique 12, 532 (2011), A. Sedeki and C.B. (2011)

22 Anisotropy of the scaeering rate above T c a π 3π/4 π/2 π/4 0 π/4 π/2 3π/4 π k τ 1 k a(k )T + b(k )T 2, x x π x x π x x x x (k ) Follows the SCd gap not the hot spots on the FS c.f. H- Tc, Tl 2 Ba 2 CuO 6+x, Abdel Jawad et al.,prl 99, (2007). τ 1 an (φ) a(φ)t φ

23 On the nature of the normal state above T c T(K) 10 2 Θ Interfering e- e & e- h pairings : 10 0 SDW C-W DisCnct electron liquid (NFL) Extended QC region SCd t' b (K) T c 1K SCd NFL... t 100 K 1D:LL T E F 3000 K SDW

24 Summary SDW + SC dome under pressure C- W SDW fluctua/ons ( T 1 1 ) vs T c Linear resis/vity correlated with T c RG of Q- 1D electron gas at T t,t Interfering Cooper pairing with SDW: T(K) 10 2 Θ t - T SDW T c - Extended Curie- Weiss domain - Not a Fermi liquid at low T : T 1 - Extended quantum cri/cality ,τ 1,z,... SDW C-W SCd t' b (K)

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26 BaFe 2 (As 1- x P x ) 2 Ba(Fe 1- x Co x ) 2 As 2 75 As F.L. Ning et al., Phys. Rev. Lee. 104, (2010) Y. Nakai et al., Phys. Rev. Lee. 105, (2010)