(The lower dimensional, all purpose, solid state, Hubbard Model testing... platform)
Organic conductors are materials made of relatively large organic molecules, about 20 atoms each. Their history started in 1964 when Bill
Little (Stanford U.) suggested that the critical temperature of superconductors could be increased and he applied his theory to a polymer
chain. Although his orginal idea did not produce a high temperature superconductor, a new class of crystalline organic conductors was discovered.
Most materials composed of organic molecules are normally not metals because of hybridization, which leaves their conduction and valence bands
filled. This property was first overcome by combining planar organic molecules with nonorganic anions (ClO4, PF6 etc.) which serve as acceptors or donors thus resulting in the appearance of partially filled
conduction and/or valence bands. Such materials are called charge transfer salts. In 1981 Bechgard synthesized (TMTSF)2ClO4 (see diagram below), the first organic material that was superconducting at ambient pressure. Although, it has a relatively low superconducting transition temperature (1.2 K), the interest in superconductivity and other rather unusual properties
in organic materials exploded after this discovery.
Since 1981, over 700 organic conductors have been synthesized,
over 150 of which are superconducting. During this time the superconducting transition temperature in these materials has risen
from 1.2 K to 12.6 K (13.2 K under pressure). Also in this time period, a number of other interesting electronic states have been observed in organic
conductors including charge density waves (CDW), spin density waves (SDW), field induced spin density waves (FISDW, of course), spin liquids, and the
quantum Hall effect. In addition, more traditional quantum oscillation effects that are found in metals, such as
the de Haas-van Alphen effect, the Shubnikov-de Haas effect, and angular magnetoresistance oscillations, are greatly enhanced in organic conductors. The study of all the ground state properties is greatly enhanced by the determination of the electronic properties of these materials through the
measurement of quantum oscillations. This has caused at least one theoretician to remark that "organic conductors are a laboratory of solid state physics." Some excellent monographs describe the discovery and development of organic superconductors,1, 2 as well as an excellent collection of articles,3 and review articles.4
Because organic conductors are complicated organic salts, they have many free parameters that can be adjusted to carefully fine tune their chemical structure. Consequently their electronic sucture can also be esily adjusted and fine tuned. In addition, their electronic structure is unique because they have low Fermi energies and are electronically very clean, making it easy to study the intricacies of their Fermi surfaces through the observation of quantum oscillations. The low Fermi energy makes high magnetic field experiments more interesting due to the impact of the magnetic energy on the Fermi surface structure. As an example, Ef = 7.0 eV for Pb, whereas Ef for a typical organic is approximately 0.01 eV (50 T ~ 0.003 eV).
So what makes organic conductors such interesting superconductors? The organic conductors are low dimensional, low carrier density superconductors. That sounds a lot like the high temperature cuprates!
In fact both families of superconductors, as well as others such as the pnictides and heavy Fermion superconductors are well described by the Hubbard Model. The Hubbard model in its simplest form considers the balance between Coulomb repulsion, U, and inter site hopping amplitudes, t, to predict transitions between metallic and insulating states.
Fig. 1. Phase diagram for κ-(ET)2Cu[N(CN)2]Cl, from S. Lafebvre et al.,5 that shows the complex phase diagam of ground states that exist in one material as a function of temperature and pressure.
The hopping amplitude t, also called the hopping integral, is directly related to the bandwith, W, and, it is common to see the parameter U/t or U/W as a measure of a material's location in a phase diagram determined by the Hubbard model. With additions that consider geometry (frustration) and spin, the rich phase diagrams such as Fig. 1 can be generated. The organic superconductors are unique because they are rich quantum systems that are tunable via pressure and chemical substitution to form many of the interesting ground states mentioned above and described by the Hubbard Model. In particular, they have one of the few true spin liquid ground states, which is tunable with higher pressure into a superconducting state. In addition, unlike the cuprate superconductors, which also can be described by the Hubbard model, most organic conductors are stoichiometric and have a fixed band filling of one half, yet they are very compressible and have many chemical substitutions that continuously or incrementally change the band structure respectively. The incremental changes in the band structure cause the ratio of U and t to change, and the topology of the spin exchange, which taken together covers a wide range of the phase space described by the Hubbard model. The organics have modest critical temperatures which translate into accessible critical magnetic fields so that the entire phase diagram can be investigated. Thus the organic conductors cover a wide range of the Hubbard parameters to study them is the phase transitions between and the charge order in the resulting ground states. For a good discussion of the Hubbard model as it applies to crystalline organic metals and magnets see the reviews by Powell and
McKenzie.6, 7
Read on to see the remarkable similarities between families of unconventional superconductors.
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1T. Ishiguro, K. Yamaji, G. Saito, Organic Superconductors, 2nd Ed., Springer, (Berlin, Heidelberg, New York, 1998). 2Naoki Toyota, Michael Lang, Jens Mùˆller, Low-Dimensional Molecular Metals, Springer, (Berlin, Heidelberg, New York, 2007). 3 Andrei Lebed, The Physics of Organic Superconductors and Conductors, Ed. Springer, (Berlin, Heidelberg, New York, 2008). 4Singleton, J.; Mielke, C. Quasi-two-dimensional organic superconductors: A review. Contemp. Phys.43, 63 (2002). 5S. Lafebvre et al., Phys. Rev. Lett., 85, 5420 (2000). 6B. J. Powell and Ross H. McKenzie, "Strong electronic correlations in superconducting organic charge transfer salts,Strong electronic correlations in superconducting organic charge transfer salts," J. Phys.:Condens. Matter18, R827 (2006). 7B. J. Powell and Ross H. McKenzie, "Quantum frustration in organic Mott insulators: from spin liquids to unconventional superconductors," Rep. Prog. Phys.74, 056501 (2011).
