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Comptes Rendus Physique
Volume 17, n° 3-4
pages 357-375 (mars 2016)
Doi : 10.1016/j.crhy.2015.12.003
Novel superconducting phenomena in quasi-one-dimensional Bechgaard salts
Des nouveaux mécanismes de supraconductivité dans les sels de Bechgaard quasi-unidimensionnels
 

Fig. 1




Fig. 1 : 

(a) Side view of the TMTSF molecule (yellow and red dots are selenium and carbon atoms respectively, hydrogens not shown) and (TMTSF)2 PF6 Q1D structure seen along the b axis, courtesy of J.-C. Ricquier, IMN, Nantes. The yellow and green clouds around the atoms schematically present the real-space distribution of molecular orbitals responsible for electronic conduction. (b) Generic phase diagram for the   family [43] based on experiments on the sulfur compound (TMTTF)2 SbF6 . The ambient pressure for this compound is taken as the origin of the pressure scale. The horizontal tics correspond to a ∼5 kbar interval. All colored phases are long-range ordered. The curve between the 1D metal and charge localization marks the onset of 1D charge localization, which ends at around 15 kbar, slightly above (TMTTF)2 Br. The 1D to 2D deconfinement occurs on the continuous curve in the higher-pressure regime. The curve between 2D and 3D regimes defines the upper limit for the low-temperature 3D coherent domain. There exists a small pressure window around 45 kbar in this generic diagram, where SC coexists with SDW according to Refs. [44–46]. (TMTSF)2 ClO4 is the only compound to exhibit superconductivity under ambient pressure.


Fig. 2




Fig. 2 : 

First observation of superconductivity in (TMTSF)2 PF6 under a pressure of 9 kbar [15]. The resistance of the two samples is normalized to its value at 4.5 K.


Fig. 3




Fig. 3 : 

Diamagnetic shielding of (TMTSF)2 ClO4 at T =0.05 K for magnetic fields oriented along the three crystallographic axes, from Ref. [50].


Fig. 4




Fig. 4 : 

Critical fields of (TMTSF)2 ClO4 determined from the onset temperature of the c -axis resistance   for fields along the three principal axes with an indication of the Pauli limit at low temperature. The figure is taken from Ref. [54].


Fig. 5




Fig. 5 : 

(a) Temperature dependence of the specific heat of (TMTSF)2 ClO4 . We present data for two different single crystals, sample #1 (0.257 mg; blue circles) and sample #2 (0.364 mg; red squares). The broken curves are fitting results with the Sommerfeld–Debye formula C p /T =γ e +β p T 2 to the normal state data (T >1.3 K). Resulting fitting parameters are γ e =10.8±0.2 mJ/K2mol and β p =12.6±0.1 mJ/K4mol for sample #1, and γ e =10.6±0.4 mJ/K2mol and β p =9.8±0.2 mJ/K4mol for sample #2. (b) Electronic specific heat C el /T of the two samples.


Fig. 6




Fig. 6 : 

Phase diagram of  , governed by non magnetic disorder. The data are obtained by newly analysing the temperature dependence of resistivity reported in Ref. [62] (see text). Points with labels “R” refer to very slowly cooled samples in the R-state (the so-called relaxed state) with different   contents, whereas points with labels “Q” refer to quickly cooled samples in the quenched state. A sample with ρ 0 =0.27 Ωcm, i.e. beyond the critical defect concentration, is metallic down to the lowest temperature of the experiment. The continuous curve is a fit of Eq. (4) to the data with  .


Fig. 7




Fig. 7 : 

77Se Knight shift (a) and 1/T 1 vs T (b) for (TMTSF)2 ClO4 , for H //b and a , according to reference [103]. The sign of the variation of the Knight shift at T c depends on the sign of the hyperfine field. A linear temperature dependence of the relaxation rate is recovered at very low temperature, signaling the existence of unpaired carriers at the Fermi level.


Fig. 8




Fig. 8 : 

Possible gap symmetries agreeing with the different experimental results. The spin-singlet d -wave (or g -wave) symmetry is the only symmetry agreeing with all experiments (yellow columns on line).


Fig. 9




Fig. 9 : 

Schematic description of the Volovik effect in a superconductor with gap nodes or zeros. (a) Supercurrent flowing around magnetic vortices. Supercurrent velocity v s is perpendicular to the vortex direction, namely the direction of the magnetic field. (b) Quasiparticle excitation around gap nodes excited by the Volovik effect. (c) Quasiparticle excitation when the field is parallel to the Fermi velocity at a node. In such a situation, the excitation at this node is zero, since v s v F =0 at this node.


Fig. 10




Fig. 10 : 

(a)–(f) Observed in-plane field-angle dependence of the heat capacity of (TMTSF)2 ClO4 [55]. Blue curves in panels (a)–(c) are C /T obtained at 0.14 K and red curves in (d)–(f) are at 0.50 K. The black curves indicate C /T plotted against −ϕ . The difference between the colored and the black curves represents the asymmetry of the C (ϕ )/T curve. The curves in (g) are simulated results by calculating the density of states based on a simple Doppler-shift model with nodes at ϕ =±10deg [55]. The definition of the in-plane field angle ϕ is indicated at the bottom-right corner.


Fig. 11




Fig. 11 : 

(a) In-plane field-angle dependence of the heat capacity of (TMTSF)2 ClO4 near ϕ =0deg [55]. The arrows indicate positions of the observed kinks. (b) First and second derivatives of C (ϕ )/T . Anomalies at ϕ =±10deg corresponding to the kinks in C (ϕ )/T are easily seen. Calculated density of states N and their derivatives based on a simple Doppler shift model with nodes at ϕ n1 =−10deg and ϕ n2 =+10deg are plotted in (c) and (d).


Fig. 12




Fig. 12 : 

Schematic comparison between FFLO pair formations for (a) 3D or 2D Fermi surfaces and (b) Q1D Fermi surfaces.


Fig. 13




Fig. 13 : 

(a) Polar plot of the ϕ dependence of   at several magnetic fields. The red line indicates the new principal axis emerging above 3 T [54]. (b) Comparison of   for different samples [52]. The blue and red points indicate   of Sample #1 (very clean) and Sample #2 (moderately clean), respectively. Substantial difference is seen for |ϕ |>19deg, whereas the sample dependence is rather small for smaller field angles. This difference is attributed to the fact that the FFLO state, as well the field-induced 2D confinement for Hb , is very sensitive to impurity scatterings.


Fig. 14




Fig. 14 : 

SC phase diagram of (TMTSF)2 ClO4 obtained by the specific heat (filled points) and resistivity measurements (crosses) for (a) Ha , (b) Hb , and (c) Hc . Figures are made based on data in Refs. [54,55]. Notice that the vertical scale of the panel (c) is 20 time smaller than those of the other panels.


Fig. 15




Fig. 15 : 

Field dependence of 1/(T 1 T ) for Ha and Hb obtained by the NMR study on (TMTSF)2 ClO4 [103].


Fig. 16




Fig. 16 : 

Temperature dependence of the nuclear relaxation time multiplied by temperature versus temperature according to the data of Ref. [152]. A Korringa regime, T 1 T = const is observed down to 25 K. The 2D AF regime is observed below ≈15 K and the small Curie–Weiss temperature of the 9 kbar run is the signature of the contribution of quantum critical fluctuations to the nuclear relaxation. The Curie–Weiss temperature becomes zero at the QCP. These data show that the QCP should be slightly below 9 kbar with the present pressure scale. The inset shows that the organic superconductor (TMTSF)2 ClO4 at ambient pressure is very close to fulfill quantum critical conditions.


Fig. 17




Fig. 17 : 

A log–log plot of the inelastic longitudinal resistivity of (TMTSF)2 PF6 below 20 K, according to Ref. [153].


Fig. 18




Fig. 18 : 

Coefficient A of linear resistivity as a function of T c plotted versus T c /T c0 for (TMTSF)2 PF6 . T c is defined as the midpoint of the transition and the error bars come from the 10% and 90% points, and T c0 is defined as T c0 =1.23 K, the maximal T c under the pressure of 8 kbar in the SDW/SC coexistence regime. The dashed line is a linear fit to all data points excluding that at T c =0.87 K, according to Ref. [153].


Fig. 19




Fig. 19 : 

Calculated phase diagram of the quasi-one-dimensional electron gas model from the renormalization group method at the one-loop level [159]. Θ and the dash-dotted line defines the temperature region of the Curie–Weiss behavior for the inverse normalized SDW response function.

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