Organic Conductors and Superconductors

Molecular solids provide the opportunity to tailor a material with desired properties: by selecting and varying the building blocks and arrangement the targeted functionality can be achieved. Among them organic conductors are ideal model systems to investigate unconventional phenomena emerging from strong electron-electron interactions, including charge-ordered and Mott insulators, quantum spin liquids, unconventional superconductors, Fermi liquids and the effects of low dimensionality, such as the Luttinger liquid. The low energy scales allow us to cover the entire phase diagram with comparably small temperature and pressure scales.

Figure 1 (c)
Figure 1 Phase diagram of pristine Mott insulators. The temperature T and the electronic correlations U are normalized to the bandwidth W. For strong Coulomb interaction there is a gradual crossover upon cooling from a metallic like behavior to a more insulating behavior at the so-called quantum Widom line. At low temperatures the systems are Mott insulators. For weak correlations, close to the metal-insulator transition, such as in κ-(BEDT-TTF)2Cu2(CN)3 metallic quantum fluctuations are observed at low temperatures. Upon applying pressure, the materials enter the Fermi liquid phase where they become metallic and even superconducting at low temperatures.

The physics of strongly correlated materials is at the forefront of research in condensed matter physics, boosted by the discovery of high-Tc cuprates. The relationship between correlations and unconventional superconductivity, quantum spin liquid behavior and other exotic states of matter has been intensively debated. While at the level of model theories one can introduce quantitative criteria for the degree of correlation, such as the ratios U/W or V/W, where U and V are the on- and inter-site Coulomb repulsion, respectively, and W is the single-particle bandwidth, in most materials the single-band Hubbard model is not applicable.

Organic conductors provide a perfect laboratory to study and tune the effects of electronic correlations. The related energy scales are about two orders of magnitude smaller than in transition-metal compounds, such as vanadium oxides or cuprates, for instance. Thus, the effects of charge and spin localization can be accessed at significantly lower temperatures (1 – 100 K) and the bandwidth can be tuned by comparably small applied pressures (0.01 – 10 GPa) , providing access to so far inaccessible regions in the phase diagram.

Our main research interest focuses on the quasi two-dimensional (BEDT-TTF)2X as well as on the quasi one-dimensional Fabre and Bechgaard salts, (TMTTF)2X and (TMTSF)2X. In these charge transfer salts electrons are donated from the organic molecules to the anions X generating partially-filled bands on the organic molecules. Since the occupied anion bands are typically more than 1 eV (8000 cm-1) lower in energy, these systems provide the ideal framework to study the physics of the single band Hubbard model. In particular, our current investigations focus on materials exhibiting diverse unconventional phenomena, including Mott insulators, quantum spin liquids, superconductors, bad metals, Fermi liquids and Luttinger liquids.

We employ optical spectroscopy to study the effects of electronic correlations, such as the opening of a gap in the absorption spectrum in the course of a metal-insulator transition, covering a frequency range from 10 – 47000 cm-1.  Several optical cryostats and a pressure cell allow us to cover temperature, pressure and magnetic field ranges of 1.8 - 350 K, 0 - 2 GPa and 0 – 7 T, respectively. In addition, we provide dc transport facilities with essentially the same specifications, as well as electron spin resonance and SQUID magnetometry.

Figure 4 (c)
TOP: Figure 4 a Stack of equally spaced organic molecules with charge ρ = ρ0 = 1/2e per molecule, for instance. b The dimerization of the stack leads to alternating distances between adjacent molecules. c Charge ordering modulates the electronic charge ρ per molecule to ρ0 + δ and ρ0 − δ, as indicated by the gray values. d The charge disproportionation can be accompanied by a lattice dimerization; besides a (– + – +) pattern, the (– – + +) alternation is also possible in two different fashions: e (– – | + + | – – | + +) and f ( + – | – + | + – | – +). g In addition, the magnetic moments located at the molecular dimers can pair and form spin singlets. BOTTOM: Figure 3 The phase diagram of the quasi-one-dimensional TMTTF and TMTSF salts. For the different compounds the ambient-pressure position in the phase diagram is indicated. Going from the left to the right, the materials get less onedimensional due to the increasing interaction in the second and third direction. loc Localization, CO charge ordering, SP spin–Peierls, AFM antiferromagnet, SDW spin-density-wave, SC superconductor. The description of the metallic state changes from a one-dimensional Luttinger liquid to a two- and three-dimensional Fermi liquid. While some of the boundaries are clear phase transitions, the ones indicated by dashed lines are better characterized as a crossover. The position in the phase diagram can be tuned by external or chemical pressure.

Low-dimensional organic conductors are model systems for investigating the physics in reduced dimensions. In the metallic state of a one-dimensional solid, Fermi-liquid theory breaks down, and spin and charge degrees of freedom become separated. But the metallic phase is not stable in one dimension: as the temperature is reduced, the electronic charges and spins tend to arrange themselves in an ordered fashion due to strong correlations.

The competition of the different interactions is responsible for which broken-symmetry ground state is eventually realized in a specific compound and which drives the system toward an insulating state. Here, we review the various ordering phenomena and how they can be identified by optic and magnetic measurements. While the final results might look very similar in the case of a charge density wave and a charge-ordered metal, for instance, the physical cause is completely different. When density waves form, a gap opens in the density of states at the Fermi energy due to nesting of the one-dimension Fermi surface sheets. When a one-dimensional metal becomes a charge-ordered Mott insulator, on the other hand, the short-range Coulomb repulsion localizes the charge on the lattice sites and even causes certain charge patterns. There are interesting similarities and conceptional differences of these phenomena. Particular emphasis of our research is on collective phenomena that are inherently present as soon as ordering breaks the symmetry of the system.

Figure 1 (c)
Figure 1. (a)–(c) The optical conductivity of (TMTTF)2X with the anion X = SbF6 (TCO = 157 K), AsF6 (TCO = 102 K) and PF6 (TCO = 67 K) (top down) recorded along the c direction for different temperatures. The conductivity was shifted for clarity. Below TCO, the _28(b1u) mode splits in two components. (d) Temperature dependence of the split _28(b1u) mode for (TMTTF)2X with X = SbF6, AsF6 and PF6. (e) 2__(T) as estimated from the difference of the two resonance frequencies.

We explore the experimental aspects of electronic ferroelectricity and related electrodynamics in the one-dimensional (TMTTF)2X and TTF-CA, and in the most prominent phases of two-dimensional (BEDT-TTF)2X molecular charge-transfer solids.

By now it is well understood that electronic ferroelectricity is established in (TMTTF)2X and TTF-CA, as well as in α-(BEDT-TTF)2I3 and the relaxed state of θ-(BEDT-TTF)2RbZn(SCN)4. Macroscopic electric polarization arises due to valence instability in TTF-CA and long-range charge order in the others; and is stabilized by a subtle interplay of Coulomb forces and structural changes. The charge disproportionation was evidenced by a variety of experimental techniques including NMR, x-ray and neutron diffraction, Raman and infrared vibrational spectroscopy and optical second harmonic generation; they probe the local order as well as the global symmetry.

Remarkably, even when non-equivalent bonds are already present in the native structure, additional structural changes set in and enhance the breaking the inversion symmetry. Type and magnitude of changes differ for these compounds ranging from dimerization in TTF-CA and changes of dihedral angles in α-(BEDT-TTF)2I3, changes of dihedral angles accompanied by doubling of the unit cell in θ-(BEDT-TTF)2RbZn(SCN)4 to an uniform anion shift as a whole in the (TMTTF) salts. The role of cation-anion hydrogen bond interactions have been also suggested for (TMTTF)2X and α-(BEDT-TTF)2I3. Taken together experimental data and current theoretical approaches, there are clear indications that the stabilization of electronic ferroelectricity takes place by a cooperative process between Coulomb interactions and coupled molecular cation-anion subsystems.

The electrodynamic properties demonstrating the ferroelectric nature of the charge-ordered state include: a Curie-like peak of the dielectric constant and its characteristic dispersion, strong non-linear effects, switching, polarization hysteresis and ultra-fast dynamics. Polarization hysteresis, commonly taken as a basic piece of evidence for ferroelectricity has only been observed in TTF-CA. The missing evidence in the other systems may be due to either relatively high conductivity or to a low breakdown field; certainly more efforts are needed to clarify this issue.

Optical nonlinearity and ultra-fast photo-response observed in TTF-CA, and in α-(BEDT-TTF)2I3 and θ-(BEDT-TTF)2RbZn(SCN)4 strongly support an intrinsic electronic origin of the ferroelectricity. Effects include the light-induced melting of the charge-ordered state and creation of metallic domains within extremely short times at the level of pico- to femtoseconds and decay back to the original state. A quantitative difference observed in photo-induced dynamics among these systems can be correlated with different structural changes involved in the formation of the ferroelectric state. On the other hand, dc electric field-induced effects such as negative differential resistance and switching happen within much longer, i.e. millisecond time scales and thus can hardly be explained by melting. One of the plausible mechanisms involves the domain wall dynamics; this issue remains to be explored further. The formation of ferroelectric domains was visualized by electro-reflectance and optical second harmonic generation interferometry in TTF-CA and α-(BEDTTTF)2I3; their presence was invoked in interpretation of the dielectric response at lower temperatures, away from the charge-ordering phase transition in (TMTTF)2X, TTF-CA and α-(BEDT-TTF)2I3.

The dielectric response features a Curie peak with negligible dispersion at the charge ordering and neutral-to-ionic phase transition temperature and a characteristic response at lower temperatures. Pre-transitional effects are also observed in α-(BEDT-TTF)2I3 and relaxed state of θ-(BEDT-TTF)2RbZn(SCN)4 up to room temperatures. Anomalous features of the dielectric response indicate the critical role of random potential arising due to internal heterogeneity. It may influence the scale at which charge order develops thus, for example, affecting the formation of a Curie peak at the phase transition, and even resulting in relaxor ferroelectricity in nominally pure single crystals, as observed for (TMTTF)2X and TTF-CA. Importantly, for the best single crystals, estimates of charge disproportionation deduced from the Curie constant strongly deviate from well-established values for (TMTTF)2X and TTF-CA, while they are close to them for α-(BEDT-TTF)2I3 and θ-(BEDT-TTF)2RbZn(SCN)4. These findings are intriguing and call for further considerations.

Finally, we have taken a look at the electrodynamical properties of two most challenging materials κ-(BEDT-TTF)2Cu[N(CN)2]Cl and κ-(BEDT-TTF)2Cu2(CN)3 suggested as candidates for a molecular multiferroic and quantum spin liquid, respectively. These systems display an anomalous dielectric response in the absence of structural changes and with no evidence for charge disproportionation within the dimers. A polarization hysteresis and bistable resistance are also reported for κ-(BEDT-TTF)2Cu[N(CN)2]Cl. Advanced experimental probes and theoretical approaches are required to achieve a very much needed breakthrough in understanding of these phenomena.

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