J O U R N A L DE PHYSIQUE page C3-775 Colloque C 3 , supplément au n°6, Tome 44, juin 1983 ORGANIC SUPERCONDUCTORS D. : THREE YEARS ONLY ! Jérôme Laboratoire 91405 Orsay, de Physique France des Solides, Université Paris-Sud, Résumé - Cet a r t i c l e présente une vue d'ensemble d'un domaine en expansion rapide : l e s supraconducteurs o r g a n i q u e s . Nous i n s i s t o n s plus p a r t i c u l i è r e ment sur l e s nombreux r é s u l t a t s expérimentaux qui indiquent une r e l a t i o n é t r o i t e entre p r o p r i é t é s physiques de ces matériaux et l a t h é o r i e des conduct e u r s unidimensionnels. A b s t r a c t - This a r t i c l e attempts to g i v e an overview on the r a p i d l y expanding f i e l d of organic superconductors. I t emphasizes e s p e c i a l l y the numerous expérimental data which suggest that One-Dimensional Physics i s c l o s e l y r e l a t e d to t h e i r physical p r o p e r t i e s . The présent survey of Organic Superconductivity in the (TMTSF)?X s é r i e s emphasizes some p a r t i c u l a r l y important data which cannot "be l e f t out of trie i n t e r p r é t a t i o n ( 1 ) . Furthermore, we wish to c l a r i f y the l i n k s e x i s t i n g between the expérimental data and the b a s i c f e a t u r e s of Quasi-One-Dimensional conductors, namely ( i ) the i n t e r p l a y between superconducting and d i e l e c t r i c (SDW o r CDW) ground s t a t e s , ( i i ) the e x i s t e n ce o f a broad température région where quantum and c l a s s i c a l f l u c t u a t i o n s of the order parameter a r e important and ( i i i ) the strong s e n s i t i v i t y of long range order to random p o t e n t i a l s breaking the interchain phase cohérence. I - BAND STRUCTURE ANISOTROPY Before d i s c u s s i n g the low température p r o p e r t i e s of the (TMTSF)2X family we show how the normal s t a t e (high température) p r o p e r t i e s a r e a f f e c t e d by the anisotropy of the interniolecular o v e r l a p i n t é g r a i s . The stacking d i r e c t i o n ( a - a x i s ) i s o b v i o u s l y the d i r e c t i o n along which the o v e r l a p between near neighbour molecular o r b i t a l s is the s t r o n g e s t . However because of short Se Se contacts i n t e r m o l e c u l a r o v e r l a p i s a l s o s i g n i f i c a n t along the t r a n s verse b - d i r e c t i o n . The t r a n s v e r s e c - d i r e c t i o n along which stacks of TMTSF molécules are separated from each other by X anions represents a d i r e c t i o n of weak interchain coupling. The conductivity anisotropy at room température is r e l a t e d to the band s t r u c t u r e anisotropy by the r e l a t i o n ( 2 ) : V°b • ( a t a / b t b> 2 <!> where a = 3.6 Â and b = 77 Â are the l a t t i c e parameters of weak dimerization of the molécules along the stacking axis high t e m p é r a t u r e ) . Hence using a / a h = 25 of Greene et a l . e q . ( l ) , t / t % 10. Other aroups ( 1 ) have reported a / a % from eq. ( 1 ) t / t 30. a a D a a D (TKTSF^X neglecting the ( t h i s i s j u s t i f i e d at ( 3 ) one finds from ( 2 - 4 ) x 10 r e q u i r i n g 2 b The anisotropy in the b-c plane i s l e s s problematic : both from conductivity ( 4 ) and c r i t i c a l f i e l d s a n i s o t r o p i e s ( 3 ) one obtains t h / t % 30. S i n g l e c r y s t a l r é f l e c tance studies ( 5 ) reveal the e x i s t e n c e of a strong r é f l e c t a n c e of (TMTSF)2X a t low température even with the l i g h t p o l a r i z e d along the t r a n s v e r s e b - d i r e c t i o n provided the frequency i s smaller than a plasma edge of ^ 1000 c m - . c 1 Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol/1983002 J O U R N A L DE PHYSIQUE C3-776 The a n a l y s i s of the o p t i c a l data ( 6 , 7 ) y i e l d s again t /% % 10. Furthermore, the c a l c u l a t i o n of the o v e r l a p i n t é g r a i s ( 8 ) leads to a comparable a to b anisotropy namely t / t = 12 with t = 0.14 eV and t = 0.012 eV at room température in (TMTSF^ClO/j. With a band s t r u c t u r e anisotropy of about 10, the Ferai s u r f a c e cannot reasonably d i s p l a y closed o r b i t s unless a d d i t i o n a l f o l d i n g of the s u r f a c e is p r o v i ded by a change of the p e r i o d i c i t y (occurence of a SDW s t a t e at low température f o r example). a a D a D The observation of a plasmon e x c i t a t i o n in a Q - l - D conductor with the l i g h t p o l a r i zed perpendicular to the chains r e q u i r e s some cohérence of the é l e c t r o n motion from chain to chain. The condition to be f u l f i l l e d i s ( 2 ) : H/ T / / < Zirfc (2) According to e q . ( 2 ) the smearing of the Ferai s u r f a c e due to a f i n i t e intrachain é l e c t r o n time T / / must be smaller than the warping due to a small energy d i s p e r s i o n along the t r a n s v e r s e d i r e c t i o n . A t r a n s v e r s e plasma edge with the l i g h t p o l a r i z e d along the b - a x i s is observed in (TffTSF)2AsF5 ( 5 ) at low température. However when the l i g h t is p o l a r i z e d along the c - a x i s the r é f l e c t a n c e of the c r y s t a l remains low down to the i n f r a r e d région with no sign of any Drude l i k e behaviour. The FS smearing should l i e t h e r e f o r e in between the warpings due to both c and b - a x i s c o u p l i n g s , namely 2irt <Ç $— c < 2tt t (3) fa V/ Hence an upper l i m i t of tu derived from e q . ( 3 ) with t -13 c 'v 0.3 meV is about 4 x 10 s At room température, tu is derived from the Drude f i t of the l o n g i t u d i n a l r é f l e c ­ tance spectrum ( 5 ) i . e . tu 3 x 10 s. T h e r e f o r e , the f a c t o r 10 increase of the conductivity between 300 K and 4.2 K in (TMTSFJgCKty implies T / / ( 4 . 2 K ) % 3 x l O - s (with 0.5 c a r r i e r / m o l é c u l e and m % m ) as long as the low température conduction is a t t r i b u t e d to a s i n g l e - p a r t i c l e conduction mechanism. - 1 5 3 12 0 - 1 2 An é l e c t r o n s c a t t e r i n g time of 3 x 1 0 s would be about ten times longer than the upper l i m i t derived from the absence of plasma edge in the c - d i r e c t i o n . Hence the assumption of s i n g l e - p a r t i c l e conduction at low température is not c o n s i s t e n t with the optical r é f l e c t a n c e data of the (TMTSF)2X s é r i e s . As f a r as the b - a x i s is concerned e q . ( 3 ) leads to a lower l i m i t T / / > l O - ^ s (with t ^ 10 meV). The Drude f i t of the l o n g i t u d i n a l plasma edge f o r (TMTSF)2PF at 25 K gives ( 9 ) T / / % 10" s in f a i r agreement with the lower l i m i t d é r i v a t i o n . D 1,1 6 Summarizing, o p t i c a l data show that the low température é l e c t r o n motion is cohérent in the ( a - b ) plane but d i f f u s i v e along the c - a x i s . The p i c t u r e of ( a - b ) planes,weakkly coupled along the c - d i r e c t i o n is a l s o supported by the i n t e r p r é t a t i o n of the nuclear spin l a t t i c e r e l a x a t i o n f i e l d dependence ( 1 0 ) . Experiments show that the f i e l d of 10 kOe corresponds to a c r o s s - o v e r between a l o w - f i e l d régime with l / T ^ f i e l d independent ( I O T ^ p < 1) and a h i g h - f i e l d régime (aieT^TJ > 1) where l / T r ^ l o g i j j ( i o is the é l e c t r o n Larmor frequency and I/T^D i the ( a - b ) plane to plane hopping rate. E e e s The plane to plane hopping r a t e can be derived by the theory of the in low-dimensional conductors ( 2 ) which gives : relaxation (4) 2D Using the expérimental v a l u e s , 1 / T = 2.10 s , T X 1 0 " s at low température ( 1 1 ) , e q . ( 4 ) gives t % 1 meV. Such a weak interchain coupling along the c d i r e c t i o n is c o n s i s t e n t with the c r y s t a l s t r u c t u r e of the (TMTSF^X s é r i e s . 1 1 c _ 1 _1 C3-777 Fi g. 1 - A schematic view of the warped Fermi s u r f a c e at low température in zéro magnetic f i e l d showing d i f f u s i v e é l e c t r o n motion in the c - d i r e c t i o n ( * / / c the cohérent motion in the b - d i r e c t i o n | (H/T / T > t ) a n d // In summary o p t i c a l r é f l e c t a n c e and NMR data show the cohérence a t short distance of the é l e c t r o n motion along b at low température. However the a to b band a n i s o tropy does not a l l o w to consider a c l o s e d Fermi s u r f a c e ( t h i s s i t u a t i o n would r e q u i r e t / t k % 2 ) . Very c r u d e l y , the Fermi s u r f a c e of the conducting s t a t e looks l i k e a warped plane as sketched in f i g u r e 1. a II - INTERPLAY BETWEEN SUPERCONDUCTIVITY AND MAGNETISM. The e x i s t e n c e of a common border l i n e between a SDW semiconducting ground s t a t e and the superconducting s t a t e is now well e s t a b l i s h e d in the ( T , P ) phase diagram of (TMTSF)2X s a l t s ( 1 ) f o r which no extra p o t e n t i a l with periodicity 2kp opens a gap at the Fermi l e v e l . Typical r e p r é s e n t a t i v e s of thèse Systems are s a l t s of anions with hexahedral symmetry PF6, ASF5... However,a compétition between superconductivity and a SDW s t a t e i s a l s o observed under c e r t a i n circumstances in (TMTSF)2C104 : a s a i t with t e t r a h e d r a l anions. I f (TMTSF)2C104 is cooled at a slow enough r a t e down to hélium température a s o - c a l l e d r e l a x e d ( R ) - s t a t e is obtained (12,13).C104 ions o r d e r uniformly below 24 K ( 1 4 ) . Such ion o r d e r i n g with a wave-vector 4kp does not a f f e c t the density of s t a t e s at the Fermi l e v e l . The R - s t a t e undergoes a t r a n s i t i o n towards a superconducting s t a t e below 1.2 K without any up-turn of the r e s i s t i v i t y below 5 K as i t i s observed in f a s t - c o o l e d samples ( 1 5 , 1 6 ) . The superconducting o r d e r (with n e a r l y complète f l u x expulsion f o r t r a n s v e r s e f i e l d s and zéro r e s i s t i v i t y ) i s destroyed by the a p p l i c a t i o n of a magnetic f i e l d exceeding the upper c r i t i c a l f i e l d H ^ . At H > H , the r é s i s t a n c e i s f i n i t e and s t r o n g l y r i s i n g with magnetic f i e l d but no o s c i l l a t i o n s of the nagnetoresistance can be observed unless the f i e l d i s l a r g e r than a "turn-on" f i e l d which dépends c r i t i c a l l y on the o r i e n t a t i o n of the c r y s t a l ( 1 6 , 1 7 , 1 3 ) . The"turn-on" f i e l d corresponds to a phase transition induced by the applied field. c 2 : : The phase diagram ( T , H ) of the R - s t a t e of (TMTSF)2C104 (with H / / c ) i s d i s p l a y e d in f i g u r e 2. The high f i e l d s t a t e which becomes s t a b l e at f i e l d s l a r g e r than % 50 kOe is semimetallic with a low density of s t a t e s at the Fermi level (19) and a closed Fermi s u r f a c e ( 1 7 ) . Moreover, S e NMR studies (20) have c l e a r l y e s t a b l i s hed the magnetic nature of the h i g h - f i e l d s t a t e . Internai magnetic f i e l d s due to the onset of a SDW suppress the Se NMR l i n e of the h i g h - f i e l d s t a b i l i z e d s t a t e . In a d d i t i o n , proton (21) and sélénium (20) r e l a x a t i o n experinents show a l s o the e x i s t e n c e of a narrow peak of 1/T-, r e l a t e d to the magnetic c h a r a c t e r of the phase 7 7 C3-778 J O U R N A L DE P H Y S I Q U E T M T S F Cl 2 5 0 U ( R .state) Fig. 2 - Phase diagram of (TMTSF) C10 ( R - s t a t e ) . The phase t r a n s i t i o n l i n e has been drawn from data of Shubnikov-de Haas, s p é c i f i e heat and NMR experiments. The shaded portion in low f i e l d s corresponds to the superconducting s t a t e . 2 — 4 Conductor UJ ce -> No magnetism < ce Fermi s u r f a c e o p e n 4 SDW ' S e m i metql 20 40 MAGNETIC 60 FIELD 80 kOe // C t r a n s i t i o n . An estimate of the c a r r i e r density of the h i g h - f i e l d phase derived from the period of the Shubnikov de-Haas o s c i l l a t i o n s leads to n <\, 1 0 - / m o l e c u l e ( 1 7 ) 2 In summary, the h i g h - f i e l d s t a t e i s semimetallic and magnetic whereas the phase s t a b l e at lower f i e l d s i s non-magnetic and h i g h l y conducting. The i n t e r p l a y between s u p e r c o n d u c t i v i t y and magnetism i s an e s s e n t i a l property of the microscopic d e s c r i p t i o n of 1-D conductors ( 1 ) . However a remarkable f e a t u r e of f i g u r e 2 i s the e x i s t e n c e of a wide f i e l d domain extending from % 1 kOe to % 50 kOe at zéro température where n e i t h e r superconducting nor magnetic long range order i s achieved a t low température. We wish to emphasize that such an absence of long range o r d e r is not expected in the theory of Q - l - D conductors. This f a c t i n d i c a t e s some l i m i t a t i o n s of the présent mode!s to understand the p r o p e r t i e s of the (TMTSF)2X f a m i l y . III - PRECURS0R EFFECTS Several expérimental s t u d i e s have shown that N(Ep) of o r g a n i c superconductors is s t r o n g l y a f f e c t e d a t low température by the proximity of the superconducting phase. For example, the c o n t r i b u t i o n to the s p é c i f i e heat l i n e a r in température is magnetic f i e l d dépendent ( 2 2 ) . In (TMTSF)2C104, C/T increases from 10 to 20 mJ/ mole.K between Hc2 1 kOe and 20 kOe. Furthermore the thermal c o n d u c t i v i t y of (TMTSF)2C104 (23) shows a s i g n i f i c a n t drop below 50 K which is i n t e r e s t i n g f o r two reasons : ( i ) In the same température région O Q Q i s s t r o n g l y enhanced (24) and reaches ^ 3 x 10 (ficm) at 4.2 K. Thus one could expect heat to be c a r r i e d by the é l e c t r o n s according to the Wiedemann-Franz law K / a = LT. ( i i ) The drop of K is s t r o n g l y suppressed by the a p p l i c a t i o n of a magnetic f i e l d (23). Therefore in terms of the W-F law t h i s f i e l d dependence of K i s very s t r i k i n g since opposite f i e l d dependences a r e observed f o r a and K. 2 % 5 _1 e The s e n s i t i v i t y to a magnetic f i e l d suggests that the drop of K i s r e l a t e d to a decrease of N(Ep) which can be p a r t l y suppressed by the a p p l i c a t i o n of a magnetic f i e l d . Various s p e c t r o s c o p i c techniques have provided an estimate of the energy width of the d é p r e s s i o n . Schottky tunneling performed on (TMTSF)2PF6 (25) under 11 kbar or on (TMTSF)2C104 ( 2 6 ) at ambient pressure point to an approximate width of 2 A "U ( 3 - 4 ) meV. L i k e w i s e , f a r - i n f r a r e d r é f l e c t a n c e of (TMTSF)2C104 r e v e a l s at 2 K a sharp o p t i c a l absorption threshold ( s e n s i t i v e to magnetic f i e l d ) around the same energy range of % 3.8 meV ( 2 7 ) . 0 C3-779 Although a drop of the DC conductivity i s expected a t low température according to the FIR d a t a , t h i s i s e x a c t l y the opposite s i t u a t i o n which i s observed experiment a l l y . Furthermore, a study of a ( w ) (28) provides a low and magnetic f i e l d independent conductivity of about 2000 (ficrn) f o r u > 30 c m . Since the de conductivity reaches % 3 x 1 0 ( n c m ) " at hélium température and i s a l s o s t r o n g l y magnetic f i e l d dépendent the e x i s t e n c e of a narrow c o l l e c t i v e mode is expected at zero-frequency (Au ^ 1-2 c m ) . -1 5 - 1 1 - 1 III - INFLUENCE OF RANDOM POTENTIALS Non-magnetic impurity p o t e n t i a l s which u s u a l l y have very l i t t l e e f f e c t on superconductivity of metals play a c r u c i a l r ô l e in the s t a b i l i t y of the long range ordered superconductivity of the (TMTSF)2X s é r i e s . The superconducting s t a t e of (TMTSF)2C104 i s suppressed by d i s o r d e r of the conducting chain in the (TMTSF)i_ (TMTTF) )oC104 s o l i d s o l u t i o n (29) with x > 0.2 %. Disorder on the anion chain i s a l s o e f f i c i e n t since superconductivity is removed by £ 3 t of Re04 in the System (Tf'!TSF)2(C104)i_ (Re04)j. ( 3 0 ) . O r i e n t a t i o n a l d i s o r d e r is présent in the metastable quenched ( Q ) - s t a t e of (friTSF)2C104 according to X-ray d i f f u s e s c a t t e r i n g data (14) and enhanced entropy a t low température r e l a t i v e to the R-state ( 1 3 ) . Frozen-in CIO4 d i s o r d e r in (TMTSF)2C104 ( Q - s t a t e ) governs the balance between SDW and superconductivity ( 1 5 ) . With f a s t quenching times a semiconducting (SDW) s t a t e i s observed below 4 K with no f u r t h e r t r a n s i t i o n a t lower températures ( 3 1 ) . For intermediate cooling r a t e s , the SDW s t a t e e s t a b l i s h e s below X 4 K but superconduct i v i t y is recovered at a température T ^ 0.9 K lower than the c r i t i c a l température of the R-state ( 1 6 ) . x x x IV - C0NCLUDING REMARKS The expérimental study of (TMTSF)2C104 shows c l e a r l y a dépression of the density of s t a t e s of the Fermi l e v e l occuring below 25 K or so. In the same température i n t e r v a l a gap becomes o b s e r v a b l e in the frequency dependence of the conductivity below 30 c m . However a zero-frequency c o l l e c t i v e mode ( o f width % 1-2 c m ) grows as the System i s cooled down to 4.2 K. The DC conductivity at 4.2 K i s l a r g e r than 10 (ficm) and a l s o s t r o n g l y diminished by the a p p l i c a t i o n of a magnetic f i e l d perpendicular to the conducting chain a x i s . - 1 5 - 1 -1 Can we consider magnetic f l u c t u a t i o n s towards SDW o r d e r i n g as the o r i g i n of both the collective-mode and the pseudo-gap since in some cases of the (TMTSF^X family a SDW ground s t a t e i s s t a b i l i z e d ? We i n f e r that such an i n t e r p r é t a t i o n is very u n l i k e l y f o r the f o l l o w i n g reasons : ( i ) There are no d é t e c t a b l e signs of magnetism at low température in the R-state of (TMTSF)2C104 as shown from NMR (12) and EPR data ( 1 5 ) . Both techniques a r e known to be very s e n s i t i v e to the onset of magnetism. Whenever SDW f l u c t u a t i o n s c o n t r i b u t e to the nuclear s p i n - l a t t i c e r e l a x a t i o n r a t e t h i s e f f e c t is r e s t r i c t e d to a very narrow température domain at the onset of SDW o r d e r i n g ( 1 2 ) . ( i i ) Commensurability of the SDW's would prevent f l u c t u a t i o n s from c o n t r i b u t i n g to the de conduction ( 3 2 ) , e s p e c i a l l y at very low température when kT < u>p-j (where iop-j is the pinning energy of the commensurate SDW). ( i i i ) Whenever a SDW s t a t e i s observed in the (TMTSFJoX s é r i e s i t is f u r t h e r s t a b i l i z e d by the a p p l i c a t i o n of a magnetic f i e l d (33) whereas the dépression of N ( E r ) i s suppressed under f i e l d ( 2 3 ) . ( i v ) The very l a r g e magnetoresistance of the conducting s t a t e of (TMTSF)2C104 ( R - s t a t e ) or (TMTSF^PFg under pressure (34) cannot be i n t e r p r e t e d in terms of small pockets of c a r r i e r s on the Fermi s u r f a c e since no magnetic i n s t a b i l i t y i s detected by EPR or NMR. However superconducting f l u c t u a t i o n s in a System of veakly coupled chains provide a q u a l i t a t i v e understanding to the l a r g e magnetoresistance above the superconducting t r a n s i t i o n ( 3 5 ) . n n The p r o p e r t i e s of the (TMTSF)2X reveal several f e a t u r e s c l o s e l y connected to the behaviour of 1-D Physics. In p a r t i c u l e r as f a r as superconductivity i s concerned, the phase t r a n s i t i o n a t T i s not d i r e c t l y r e l a t e d to the strenght of the p a i r i n g i n t e r a c t i o n 2 A between é l e c t r o n s within each chain. I n s t e a d , T involves the amount of interchain tunneling coupling and consequently k T « 2 A . At e l e v a t e d temperac 0 c c 0 J O U R N A L DE PHYSIQUE C3-780 tures (T > T£ where kT£ % 2 A ) the superconducting response function d i v e r g e s f o l l o w i n g the 1-D laws X ^ . Q ^ T Y where y i s defined by the 1-D t h e o r y . In the high T domain the t r a n s v e r s e cohérence length Ç remains s m a l l e r than the i n t e r chain d i s t a n c e . I f a Landau-Ginzburg functional i s used to d e s c r i b e the f r e e energy of the System in terms of the o r d e r parameter ( 1 ) , the r e g i o n T > T£ corresponds to an energy F(A) with a s i n g l e minimum a t A = 0. In t h i s température régime the f l u c t u a t i o n s a r e c h a r a c t e r i z e d by a l o c a l f i n i t e amplitude of A (ampli tude f l u c t u a t i o n s ) . At low températures T < T£ the divergence becomes 3-D l i k e , i 3D ^ ( " ç ) and d . In t h i s température domain the f r e e energy présents minimum at | Â | but the phase of the o r d e r parameter i s not f i x e d . There i s no r e s t o r i n g f o r c e a c t i n g a g a i n s t v a r i a t i o n s of the phase. This is the phase f l u c t u a tion régime where the o r d e r parameter c o r r é l a t i o n function i s given by < A ( x ) A " ( 0 ) > = | A | e x p - x / Ç ( T ) with % 1/T. 0 _ x X T T - 1 0 2 A treatment of the onset of long range o r d e r a t T in a System where short range order of i n d i v i d u a l chains is s t r o n g l y developped has been given r e c e n t l y by Schulz and Bourbonnais (36) i n c l u d i n g z e r o - p o i n t motion of the phase quantum e f f e c t s ) . Furthermore i t i s shown that in s p i t e of the well e s t a b l i s h e d 1-D f l u c tuations with the r e l a t e d pseudo-gap in the density of s t a t e s at the Fermi l e v e l the c r i t i c a l région a s s o c i a t e d with the 3-D o r d e r i n g at T i s q u i t e narrow, in agreement with the sharpness of the t r a n s i t i o n detected by r é s i s t i v e or s p é c i f i e heat techniques. With the mode! of quantum phase f l u c t u a t i o n s scattering from non-magnetic i m p u r i t i e s i n c r e a s e s the quantum c h a r a c t e r and t h e r e f o r e acts to decrease the 3-D o r d e r i n g température in marked c o n t r a s t to the usual BCS theory. c c F i n a l l y expérimental data i n t e r p r e t e d in terms of the présent d e s c r i p t i o n of superconductivity in Q - l - D conductors suggest that s h o r t - r a n g e superconducting order on i n d i v i d u a l chains develops a l r e a d y at f a i r l y high températures, of the order of 20-30 K p o s s i b l y . This short survey of Organic Superconductors three y e a r s only a f t e r t h e i r discove ry has shown the broad v a r i e t y of s t r i k i n g phenomena observed in the (TMTSF^X f a m i l y . 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