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1.1 Introduction

In general, organic solids are insulators. However, there have been extensive and intensive efforts in materials science and technology to make them conductive. The family of organic solids, starting from insulators, has widened to include organic semiconductors, organic conductors, and organic superconductors. The distinctions between them are based on the band structure of the materials as well as the electron occupancy of these bands. In 1954, the first organic semiconductor was discovered and the conductivity reached 10−3 S/cm [1]. This illustrates a new direction for the synthesis of organic conductors, when organic material was first doped with an electron donor or acceptor as a charge-transfer complex. In the 1960s, a conducting organic solid was first achieved with the charge-transfer complex of TCNQ [2]. The organic/metal product TTF-TCNQ was obtained in 1973 [3] and the first organic superconductor TMTSF2·PF6 was discovered in 1980 [4–6]. After that, the critical temperature of organic superconductors quickly increased from 0.6 to 18 K. In 1991, the electron-transfer superconductor A3C60 was discovered with superconducting transition at 33 and 35 K [7, 8], respectively and eventually single-component molecular metals were synthesized in 2001 [9].

Organic conductors are critical for electronic applications as they are as efficient as metals but lighter and more flexible. Scientists working on organic electronics want to improve the conductivity, stability, and tailorability of highly conjugated organic semiconductors and conductors. The way to challenging high performance optical and electronic organic devices is to understand the processes that determine charge transport of organic molecular and polymeric materials. Small molecules can also be grown as single crystals as model systems to demonstrate the intrinsic electronic properties. This chapter focuses on the charge transport of organic materials, and some prototype organic solids are also discussed.

1.2 Crystal Engineering of Charge-Transfer Complexes

One way to produce the organic conductors is to use charge-transfer reactions from donor to acceptor and the produced crystal is called a charge transfer complex (salt) [10]. The formation of the charge transfer complex is through hybridization between the HOMO (highest occupied molecular orbital) of the donor and the LUMO (lowest unoccupied molecular orbital) of the acceptor. Scientists’ efforts from the 1960s led to the organic acceptor 7,7,8,8-tetracyanoquinodimethane (TCNQ) [11] and the donor tetrathiafulvalene (TTF) [12, 13] (Fig. 1.1a, b).The first stable organic conductor TTF-TCNQ was synthesized in 1973 [3]. In 1978, the derivative of TTF, combining a conjugated TTF unit and ethylene group, BEDT-TTF, (Fig. 1.1d) was synthesized, showing a two-dimensional layer in the crystal and contributing most of the organic superconductor properties as κ-(BEDT-TTF)2Cu[N(CN)2]Cl, T c = 13.2 K [14]. With regard to this, most organic conductors were synthesized by the charge transfer reaction until the new superconductor Ni(dmit)2 (Fig. 1.1e) was synthesized in 2001 [9]. In this single molecular conductor, the gap between HOMO and LUMO is so small that it can form partially filled bands. The characterization of conducting organic material is carried out for a high-quality single crystal because the crystal defect traps the carrier inside the material. Electrocrystallization is a powerful method for obtaining high quality organic conductors and superconductors.

Fig. 1.1
figure 1

Molecular structure of some organic donors and acceptors

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The charge carrier transport properties of organic solids have been investigated extensively and can be used to investigate and optimize the structure-property relations of the materials used in existing optoelectronic devices and to predict the ideal materials for the next generation of electronic and optoelectronic devices. The electronic properties are controlled by weak interactions between the π-units (donor: TTF, BEDT-TTF; acceptor: Ni(dmit)2). The interaction between π-units and transition metal counterions as π–d interaction plays an important role in the physical properties. For example, when a π-unit was put in one column or two-dimensional layer, within the orbital overlap between neighbor π-unit as an S…S contact at distance less than 3.6 Å (sum of Van der Waals value of S), the channel for the conduction electron resulted. The crystal showed semiconductive metallic to superconductive behavior.

Polytypism and polymorphism are popular in charge-transfer complexes because of the assembly of molecular crystals in crystal engineering. For example, the charge-transfer complexes of BEDT-TTF and I3 – with compositions of 2:1, 3:2, and 3:5 and the charge-transfer salts of BEDT-TTF and FeCl n–4 with composition of 2:1, 3:2, 1:1, and 1:2 are examples of polytypism. Depending on the donor arrangement of the BEDT-TTF molecule, more than ten arrangement modes known as α, β, γ, κ, λ, δ, …, etc., were observed [15], displaying different transport properties. Regarding polymorphism, in charge-transfer complexes, α-(BEDT-TTF)2I3 shows metal–insulator transition at 150 K, β-(BEDT-TTF)2I3 and γ-(BEDT-TTF)2I3 show superconductivity at 7 and 6 K, respectively. Mott insulator β′-(BEDT-TTF)3(FeCl4)2 and metal δ-(BEDT-TTF)3(FeCl4)2 have also been investigated.

The conductivity of crystal and charge-transfer complexes is controlled by the arrangement of π-units and crystal structures, respectively. For example, β-(BEDT-TTF)2I3 shows metal to superconductor transition at 6 K, β-(BEDT-TTF)3[CrMn(C2O4)3] shows as metallic to 2 K. α-(BEDT-TTF)2I3 shows metal to insulator transition at 150 K, and metal to insulator transition was observed at 150 K in α-(BEDT-TTF)3[CrMn(C2O4)3]. Conductivity could be influenced by counterions when the arrangement of π-units remained the same. For example, a metallic to insulator transition at 200 K is observed in θ21-(BEDT-TTF)3Ag6.4I8 with σrt = 50 S/cm, and θ21-(BEDT-TTF)3[Cu2(C2O4)3](CH3OH)2 is a semiconductor with σrt = 4 S/cm. Conductivity can be influenced by the guest solvent molecules. For example, in (BEDT-TTF)4(H3O)Fe(C2O4)3 in solvent, T c = 7.0 K is observed when the solvent is C6H5CN and 4.0 K when solvent is C6H5Br. As the donor arrangement remained the same as δ-phase with the counteranion of GaCl4 –, room-temperature conductivity increased from 0.1 to 1 S/cm when solvent molecules C6H5Cl intercalated into an anion sheet. Some of the crucial factors relating to conducting molecular solids are as follows.

1.2.1 Charge Transfer Salts of AB Type

One of the highlights at this stage is the TTF-TCNQ, which is one-dimensional (1D) charge-transfer conducting salt with a Peierls transition at low temperature and synthesized between the π-electron molecules: the electron donor TTF and the acceptor TCNQ [3, 13]. The ratio of the TTF and TCNQ is 1:1. As a donor, TTF has four sulfur heteroatoms which can easily donate electrons when combining with the acceptor molecule. TCNQ, as an acceptor, can be easily reduced to form an anion radical TCNQ−. The conductivity of this salts reaches σ = 1.47 × 104 (S/cm) at around 60 K, where a metal to insulator phase transition was also observed [3] and the metallic behavior was confirmed by polarized reflection spectroscopy [16]. The divergent peak (σMAX > 106 S/cm) of conductivity at 58 K in a TTF-TCNQ crystal was reported [17] and the conductivity was found to originate from the fluctuations of Frohlich superconductivity, which is based on the coupled electron–phonon collective mode in a 1D system [18]. This metal to insulator phase transition is attributed to the fluctuation of charge density waves by impurities or lattice instability [19]. After this discovery, Scientists synthesized many types of derivatives of TTF and TCNQ such as TSeF-TCNQ [20], HMTSF-TCNQ [21], and TMTSF-DMTCNQ [22], which show metallic conductivity at very low temperatures. AB type charge transfer salts have generally demonstrated insulating ground states because of the instability of metallic states intrinsic for 1D systems.

1.2.2 Charge Transfer Salts of A2B Type

More conductive states have been found in charge transfer salts of the A2B type compared to the AB type. In 1980, the first superconductor (TMTSF)2PF6 at 0.9 K under 12 kbar was discovered [6, 23]. This transition originated from the spin density wave (SDW) and occurs at 12 K [24–26], an antiferromagnetic ordering being observed by using NMR [27] and static magnetic susceptibility measurements [14]. In the vast (TM)2X family (see Fig. 1.1c), scientists mainly found two isostructural groups: selenium TMTSF salts which are metals with a formally 3/4-filled conduction band and sulfur TMTTF salts which are close to the Mott–Hubbard insulating state because of the high anisotropy, dimerization, and on-site Coulomb repulsion [28]. X in  (TM)2X can be several possible anions such as (TMTSF)2PF6, (TMTSF)2AsF6, (TMTSF)2SbF6, and (TMTSF)2TaF6 which show the metal–insulator transition at 11–17 K below that of the SDW state [24–26]. (TMTTF)2PF6 and (TMTTF)2SbF6 undergo superconducting transitions at 1.8 K under 54 kbar and 2.6 K under 61 kbar, respectively [29, 30]. Moreover, the superconducting phase transition of (TMTSF)2ClO4 was observed at ambient pressure down to 1 K [31]. Figure  1.2 shows the phase diagram of (TM)2X [23]. This diagram suggests various different phases such as normal metals, superconductors, spin-density-wave states, spin-Peierls state, and antiferromagnetic state as a function of decreasing pressure. Although the band structure of (TMTSF)2PF6 is calculated to have a quasi 1D Fermi surface, intermolecular Se…Se contact was observed between the TMTSF stacks [32]. Scientists found the way to synthesize 2D organic conductors from (TMTSF)2PF6 by increasing the bandwidth and dimensionality [33].

Fig. 1.2
figure 2

Generalized phase diagram for: TM2X [23]

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The one-dimensional A2B systems may be unstable in the insulating state and the ideal 2D A2B systems superconductor was first made from β-(BEDT-TTF)2ReO4 at 2 K under 4 kbar [34]. β-(BEDT-TTF)2I3 at 1.4 K at ambient pressure [27, 35, 36] and κ-ET2Cu(NCS)2 at 10.4 K [35], and recently β’-ET2ICl2 showed the highest T c among organic superconductors at 14 K under 82 kbar [37, 38]. BEDT-TTF as a donor, was first synthesized in 1978 [14]. The π-electron orbitals of the donor aromatic rings overlap to form a conducting band. This BEDT-TTF molecule forms various phases with various anions. Figure 1.3 shows the four different donor planes of the BEDT-TTF compound. The β-type organic BEDT-TTF salts were known very early because of their superconducting state at ambient pressure—e.g., (BEDT-TTF)2IBr2 at 2.7 K and (BEDT-TTF)2AuI2 at 3.8 K [32, 39]. β′ and β″ types are similar to the β type whereas the molecular stackings are different. Figure 1.4 shows the phase diagram of the θ phase family θ—(BEDT-TTF)2MM′(SCN)4 (M = Rb, Tl, Cs, M′ = Co, Zn) concerning the charge ordering phenomenon [40, 41]. The electronic state, including insulators, superconductors, and metals, is parameterized by the dihedral angel between columns [40]. In the phase diagram, the metallic phase is reduced with increasing dihedral angle. All compounds become insulators at low temperature.

Fig. 1.3
figure 3

Schematic view of some molecular configurations of the BEDT-TTF compound

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Fig. 1.4
figure 4

Universal phase diagram of θ-type BEDT-TIF compounds [40, 41]

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The α-type BEDT-TTF salts are similar to the θ phase and show a weak dimerization. There are two different kinds of typical groups in α-type BEDT-TTF salts. One is the family of α-(BEDT-TTF)2MHg(SCN)4 (M = K, Rb, Tl, NH4) in which K, Rb, and Tl compounds produce the SDW below 10 K [38] and NH4 salt shows a superconductivity at 1.15 K [42]. Another group is α-(BEDT-TTF)2X (X = I3, IBr2, ICl2, etc.). Material α-(BEDT-TTF)2I3 undergoes an MI transition at 136 K [41, 43, 44]. Charge-ordering phenomena were found in NMR experiments [45]. After the success of the 1D TMTSF and 2D BEDT-TTF salts, scientists made efforts to synthesize many new 3D molecular superconductors such as K3–C60 with T c = 18 K [46] and Cs2RbC60 with the highest T c = 33 K [47].

1.2.3 Charge Ordering in Organic ET Compounds

The family of 2D organic conductors (ET)2X is known to exhibit a variety of interesting electronic properties. The theoretical studies of Kino and Fukuyama developed a systematic way to understand the diversity in their ground state properties [48]. Another interesting conclusion of Kino and Fukuyama is that α-type compounds show an insulating state with charge transfer in their notation (charge ordering) [49]. Arising from a strong correlation, the charge ordered (CO) state is one of the typical ground states of molecular conductors. As to the electron correlation phenomenon, it draws growing attention to understanding the organic conductor’s low temperature properties [49–52]. Charge ordering can be understood as self-organization of localized charge carriers. For example, in the charge-ordered state of a one-dimensional system with a quarter-filled conduction band, the localized charge carriers occupy or do not occupy the lattice site individually. If the conduction band is not filled completely, charge disproportionation can be observed. Charge order in organic conductors was first suggested in the 1D dimensional system (DI-DCNQI)2Ag [53]. It was shown that below 220 K, 13C-NMR spectra are split. Nonequivalent differently charged molecules appear along the chain axis and the ratio is 3:1 below 130 K. U is the on-site Coulomb repulsion and V is the nearest neighbor interaction. The inter-site Coulomb repulsion V is the driving force for charge ordering to occur as well as the onsite Coulomb repulsion U [49, 50]. If V exceeds a certain value, the charges arrange themselves with a long enough distance to minimize the influence of the V. The extended Hubbard model is a good description of the relevant energies [49, 54–56].

Here we discuss the charge ordering state using quarter-filled systems. Figure 1.5 shows the two cases [56]: (1) dimer Mott–Hubbard insulator such as 1D MEM-TCNQ2 and 2D κ-(BEDT-TTF)2X, λ-BETS2X and (2) Wigner crystal type charge ordering such as DI-DCNQI2Ag and TMTTF2X, 2D θ-(BEDT-TTF)2X, and α-(BEDT-TTF)2X [57]. In the first case, because of the strong dimerization, the single electron occupies the bonding state of each dimer. The Mott insulating state is realized because of this strong effective Coulomb interaction within a dimer. In the second case, however, inter-site Coulomb interaction, V plays an important role, and the charge-ordered state called the Wigner crystal is realized on the lattice. In the absence of a dimerization structure of the 2D system such as α, θ, and β″ type compounds, several types of a CO state which is called stripe type CO state are found as a ground state [58]. Electrons stay apart from each other if the kinetic energy is rather small compared to the Coulomb interaction. Moreover, the anisotropy in the transfer integrals is also important for the arrangement of the localized charges. Figure 1.6 shows the different pattern of CO.

Fig. 1.5
figure 5

a Dimer Mott–Hubbard insulator. b Wigner crystal type charge ordering [56]

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Fig. 1.6
figure 6

a Horizontal stripe. b Vertical stripe. c Diagonal stripe

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The charge-ordered state has been studied by means of NMR [59], XRD [60], and vibrational spectroscopy [61–65]. The NMR spectrum shows a splitting or broadening depending on the distribution of carrier density. The first CO was found in (DIDCNQI)2Ag by 13C-NMR measurement [53]. The spin/charge configuration of (TMTTF)2X (X = SCN, Br, PF6, AsF6) was also confirmed by NMR experimentally [66–70] and theoretically [71]. (TMTTF)2PF6 and (TMTTF)2AsF6 undergo a spin-Peierls transition [72, 73], whereas (TMTTF)2 SCN [66] and (TMTTF)2Br [67] have 1010 type ordering and CO was directly confirmed as the splitting of signals into charge-rich site and charge-poor sites at low temperature by 13C-NMR [69]. In 2D systems, θ-(BEDT-TTF)2RbZn(SCN)4, θ-(BEDT-TTF)2CsZn(SCN)4, and α-(BEDT-TTF)2I3 were investigated and were found to be in CO states at low temperature and in CD state at high temperature by NMR [45, 59, 74–80]. In the case of α-(BEDT-TTF)2I3, the ratio of the effective charges are also estimated from the amplitude of the curves [45, 78], and the horizontal stripe CO pattern predicted theoretically [49] was confirmed from experimental results not only by 13C-NMR but also by X-ray [81, 82] and IR/Raman spectroscopy [63, 64, 83]. Among the various techniques for charge ordering research, vibrational spectroscopy such as IR/Raman can be one of the powerful methods [84, 85]. In vibrational spectroscopy, most charge-sensitive modes for BEDT-TTF molecule are the stretching modes ν3, (Raman active), the in-phase ν2 (Raman active), and out-of-phase ν27 (infrared active) (Fig. 1.7) [86]. The ν2 and ν3 modes include the stretching vibrations of the central C=C bond and the symmetric ring C=C bond. The ν27 mode corresponds to the stretching vibration of the anti-symmetric ring C=C bond. In these three sensitive modes, ν3 is more strongly perturbed by electron-molecular-vibration interaction than by molecular charge. Therefore, it is inappropriate to use υ3 for estimating the fractional charge on molecules. ν2 and ν27 are mainly perturbed by molecular charge, have a linear relationship between the frequency and the charge on the molecules, and can be used to calculate the fractional charge in charge ordering state at low temperature [83]. The linear relationship between the frequency and site charges is shown in Fig. 1.7: ν2(ρ) = 1447 + 120(1 − ρ) and ν27(ρ) = 1398 + 140(1 − ρ) [83]. Vibrational spectroscopy was first applied to the study of charge-ordering in θ-(BDT-TTP)2(SCN)4 [85]. θ-(BEDT-TTF)2RbZn(SCN)4 undergoes the CO–CD phase transition at 200 K. The assignments for ν2 modes which split into two and ν3 modes which split into four were performed based on the 13C-substituted sample by IR/Raman spectroscopy [64]. Based on this assignment, the horizontal stripe was confirmed. The horizontal stripe of the CO pattern was also reported by analyzing the electronic transition in the infrared region [87]. The same IR/Raman method was applied to the study of charge ordering in α-(BEDT-TTF)2I3 below and above 136 K from ambient pressure to 3.6 GPa [63]. The splitting of ν2 indicates the charge disproportionation caused by charge localization and it formed the horizontal CO stripe perpendicular to the stacks.

Fig. 1.7
figure 7

Frequencies of the υ2 and υ27 modes plotted as a function of the charge ρ on the BEDT-TTF molecule [83]

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1.3 Magnetism in Charge Transfer Salt

Naturally, magnetism relates closely with conductivity. Classic magnetism is found in charge-transfer complexes such as the long-range ferromagnetic ordering at 4.5 K in insulator (NH4)2[Ni(mnt)2]·H2O [88]. Recently, quantum magnetism as spin liquid was observed in molecular insulators κ-(BEDT-TTF)2[Cu(CN)3] and EtMe3Sb[Pt(dmit)2]2 with spin on π-units [89–92]. The conductivity of a charge-transfer complex of TCNQ was studied before the discovery of the TTF series of organic superconductors, and the room-temperature conductivity of (5,8-dihydroxyquinolineH)(TCNQ)2 reached 102 S/cm in 1971 [93]. When TCNE was used as ligand, the conducting magnet was produced. In 1991, the room-temperature ferrimagnet V(TCNE)2(CH2Cl2)0.5 was discovered [94]. It was a semiconductor with σrt = 10−4 S/cm [95]. It is one of the best examples of combined magnetism and conductivity in a molecule-based conducting magnet. When TCNE, TCNQ, and its derivatives were used as coordination ligands, a large number of molecule-based conducting magnets, including dynamic conducting magnets, were obtained. No metal product was found [96–98].

There are two sources of magnetism in coordination compounds: one is the interaction between cation and anion through weak interactions such as antiferromagnetic ordering at 3.0 K in (C2H5)4NFeCl4, the other comes from magnetic interaction between metal ions in a counter-anion such as oxalate-bridged Cr3+ and Mn2+ ions in (C4H9)4N[CrMn(C2O4)3]. This shows ferromagnetic ordering at 6 K [99, 100]. Magnetism in charge-transfer salt was also influenced by the arrangement of donor and counter-anion in the crystal, such as β′-(BEDT-TTF)3(FeCl4)2 and δ-(BEDT-TTF)3(FeCl4)2. β′-(BEDT-TTF)3(FeCl4)2 shows antiferromagnetic transition at 2.7 K and δ-(BEDT-TTF)3(FeCl4)2 at 4.8 K [101].

1.4 Dual-Functional, Multifunctional Molecular Crystals

Endowing the molecular conductor with magnetism or certain optical properties produces dual-functional molecular crystals such as the magnetic conductor [102], the magnetochiral conductor [103], and the single-molecular magnet with luminescence [104]. Combining the magnetic or photonic building block with conducting π-unit is one of most popular way to approach the goal.

Supramolecular chemistry is the key to designing new dual-functional, multifunctional molecular conductors. The functional units are synthons, and the arrangement and weak interaction between π-units decide the conductivity.

The magnetic conductor is the hottest research area in dual-functional molecular crystals because of the close relationship between magnetism and conductivity in organic superconductors and between molecular conductors and molecular magnetism. In the phase diagram of the inorganic superconductor, the diamagnetic superconductor is close to the antiferromagnetic insulator. An antiferromagnetic insulator could become a diamagnetic superconductor after hole or charge doping.

The antiferromagnetic Mott insulator attracts attention because of their potential for conversion into a superconductor after carrier-doping.

Top-down is another way to obtain dual-function, multifunction material. The intercalation of alkali metal into layered compounds, such as intercalated graphene, can produce a superconductor with transition temperatures ranging from 0.14 [105] to 11.5 K [106]. When alkali metal was intercalated into an isomer of graphene–C60, the superconducting transition temperature reached higher than 50 K. Intercalated compound of aromatic compounds have recently been studied, and new materials with superconducting transition temperatures of about 30 K (18 K [107]; 5 K [108]) have been obtained. More exciting results can be obtained when the crystal structures are confirmed. (One of the shortcomings of the top-down approach is that it is always difficult to obtain high-quality single crystals.)

When an electric field, magnetic field, ultrabright laser, or high-pressure is applied to a single crystal, the energy state may be modified. Thereby (electric) field-induced organic superconductor doping with hole or electron is obtained when gate voltage is changed in a field-effect-transistor. The electric-field-induced superconductor was observed in the inorganic layer compound MoS2 [109, 110], the (magnetic) field-induced reaction being obtained when the intra-magnetic field inside the crystal from spin-orbital coupling as a π–d interaction was compensated by application of a magnetic field. Irradiation of the crystal under a laser could change the electronic structure of the crystal as an injection of energy, and laser-induced metallic reaction was observed in (EDO-TTF)2PF6 [111]. This indicates the possibility of modulating the conductivity state with photo-irradiation.

High-pressure was one of the most powerful and the earliest method used to increase interactions between molecular π-units; it could suppress the metal–insulator transition by Peierls transition, charge-ordering, charge-localization, or Fermi nesting in organic compounds when the temperature decreased. Now the pressure of 200 GPa can be achieved with a diamond cell. However, the crystal is sensitive to pressure, so the experiments should be carried out carefully and slowly, step by step [112]. Bottom-up is a powerful method to obtain material with controllable designed properties. Magnetic conductors were synthesized by combining conducting organic π-units with magnetic inorganic coordination anions as organic–inorganic hybrids. Zero-dimensional anions, such as FeCl4 –, MnCl4 2–, CoCl4 2–, and CuCl4 2–, could produce π–d interaction between donor and anion through S…Cl contact in charge-transfer salts. Charge-transfer salts with strong π–d interaction showed negative magnetoresistance around 4.2 K [113, 114], magnetic-field-induced superconductivity was observed in λ-BETS2FeCl4 with Jπd = 17.7 K [115], and by diluting Fe with Ga as Fe/Ga alloy in λ-BETS2Fe0.40Ga0.6Cl4 with insulator metal superconductor modulation by an applied magnetic field [116]. The band engineering method succeeded on charge-transfer salts of β′-(BEDT-TTF)3(FeCl4)2. A strong π–d interaction was observed in β′-(BEDT-TTF)3(FeCl4)2 with Jπd = 25.82 K, so it is a Mott insulator.

A one-dimensional anion, such as [Fe(C2O4)Cl2 –] n , was used as counter-anion for a magnetic conductor. In ammonium salts of [Fe(C2O4)Cl2 –] n , a broad maximum for low-dimensional antiferromagnetism was observed at around 20–50 K, some of them showing long-range magnetic ordering as spin canting. In TTF[Fe(C2O4)Cl2], the strong π–d interaction between TTF dimer and [Fe(C2O4)Cl2 –] n produced a three-dimensional antiferromagnetic ordering at 19.8 K [117]. The weak ferromagnetic conductor with metallic properties to 0.6 K was obtained with BETS stacks in a two-dimensional κ′-phase, hysteresis with a loop of 150 Oe being observed at 150 Oe. The bifurcation of ZFCM/FCM at 4.5 K suggested a long-range magnetic ordering [118]. In the charge-transfer salt (BEDT-TTF)[Fe(C2O4)Cl2](CH2Cl2), BEDT-TTF dimer and CH2Cl2 coexisted in a donor layer, this being a semiconductor as is TTF[Fe(C2O4)Cl2] [119].

The single molecular magnet (SMM) and single chain magnet (SCM) are of great interest as quantum magnets to chemists. They could be used as counterions to synthesize charge-transfer salts with TTF or dmit units [120] or to connect TTF units to coordination ligands to form coordination compounds [121]. An excellent way to obtain a magnetic conductor is to merge TTF and dmit units into one unit as a single-component compound. Antiferromagnetic transition was observed at 110 K produced by Fermi nesting [122].

Molecular magnets provide abundant magnetic units for dual-functional molecular crystals with magnetism and conductivity. In 1992, (Bu4N)[CrMn(C2O4)3] was reported to have ferromagnetic transition at 5.5 K [100]. It was not until 2001 that the first organic-inorganic hybrid dual-functional molecular crystal as charge-transfer salt of (BEDT-TTF)3[CrMn(C2O4)3] was reported with magnetism from layered anions and conductivity from donors as the β-phase in β-(BEDT-TTF)2I3, respectively [102]. The charge-transfer salt α-BETS3[CrMn(C2O4)3] shows ferromagnetic transition at 5.5 K and a metal-to-semiconductor transition at 150 K [123]. These two crystals have incommensurate structures, and the donor and anion structures were determined separately.

When homometallic honeycomb anion [Cu2(C2O4) 2–3 ]n was used as counter-anion, the high-quality single crystal (BEDT-TTF)3[Cu2(C2O4)3](CH3OH)2 was obtained. By means of the Jahn–Teller distortion of Cu2+, a distorted honeycomb anion was formed. The donor arrangement belongs to the θ21-phase, and when BEDT-TTF was replaced with BETS the isostructural compound was obtained. This is different from charge-transfer salts of heterometallic honeycomb anions where high-quality crystal structures are obtained from single crystal X-ray diffraction experiments [124, 125]. The spin-orbital coupling of Cu2+ produces spin frustration in these crystals. The frustration factor f is larger than 60, at least when the conductivity and susceptibility were measured above 1.8 K. Experiments at lower temperatures may bring some exciting results [126].

1.5 Relationship Between Organic Superconductors and Inorganic Superconductors: Resonating Valence-Bonding Solids and Jahn–Teller Distortion

Organic superconductors are important in the study of superconductors, not only because of their conductivity but also their magnetism. Research on the organic superconductor covers a wide area including the conductivity of insulators, semiconductors, conductors, and superconductor, and magnetism from classic magnets to quantum magnets.

After the discovery of the superconductor, people were confused by the mechanism of superconductivity for decades. Designing new superconductor systems is still a challenge for chemists. In 1986, Muller discovered the first high-temperature superconductor Ba x La5–x Cu5O5(3–y) with an onset temperature of 30 K from his initial exploration of the Jahn–Teller effect in the presence of spin-orbital coupling in perovskite material [127, 128]. The Jahn–Teller polaron in superconductors was confirmed by the observation by scanning tunnel microscopy. After that, Jahn–Teller distortion could be used to interpret the superconductivity in new inorganic superconductors, such as octahedral Co2+ in Na x CoO2(H2O) y and tetrahedral Fe2+ in La–O–Fe–As (iron pnictide) [129]. Because Jahn–Teller distortion could be observed from crystal structure with bond-length of coordination polyhedron, it could be treated as distorted octahedral or tetrahedral coordination environments in the crystal structure.

Another investigation of high-temperature superconductor was carried out by Anderson in 1987 who looked at resonating valance bonding in solids relating to the electron structure [130]. He introduced Pauling’s valance bond theory from chemistry into condensed state material as valance bond solids (VBS) and proposed the spin frustration state in the triangular lattice in 1973 to be a resonating valance bond (RVB) state [131–135]. Then he developed his theory by the discovery of high-temperature cuprate superconductors and proposed the possibility that a copper pair was formed by coupling of spin in the spin liquid state. Carrier doping on parent antiferromagnetic La2CuO4, Na2CoO2, and LaFeAs produced a new superconductor intermediate by spin fluctuation. The two-dimensional antiferromagnetic correlation as spin frustration or antiferromagnetic ordering came from the resonant valence-band state [136]. So at first, an extended (infinite) coordination polymer is needed, such as the Cu–O plane in cuprate, Co–O plane in Na x CoO2(H2O) y , and Fe-As plane in iron pnictides. This guarantees the transportation channel for the carrier in the solid. Then the Jahn–Teller distorted transition metals with their variable valances should exist. From the structure point of view, a two-dimensional extended metal-O layer is the key to these materials. The conducting layer behaves as an acceptor, so the high-temperature superconductor acts as a charge-transfer salt. Because the superconductivity was first discovered in the ceramic phase in these systems, it always takes time to confirm the composition and growth of high-quality single crystals with the critical ratio of atoms. This is the main difference between organic and inorganic superconductors. In research on organic superconductors, the high quality and clear crystal structure is always the first step. For example, a series of candidates for quantum spin liquids was discovered in charge-transfer complexes with π-units in a κ-phase arrangement. In these compounds, interactions between donor pairs are isotropic and produce a resonating valence state. The first quantum spin liquid with triangular lattice was observed in a charge-transfer salt with κ-phase donor arrangement κ-(BEDT-TTF)2Cu2(CN)3 and confirmed by specific heat and ESR experiment [92, 137]. It is a Mott insulator and could be superconductive at 3.9 K under 0.06 GPa [138]. Such a Mott insulator, β′-(BEDT-TTF)2ICl2, shows T c = 14.2 K under 8.2 GPa [37]. The charge-transfer salt (C2H5)(CH3)3Sb[Pd(dmit)2]2 was found to be another quantum spin liquid with triangular lattice [91]. A third one was discovered in a single component compound with κ-phase arrangement, κ-H3(cat(cat-EDT-TTF)2 [139]. The Kagome lattice is another ideal model to spin liquid; when people were looking for coordination compounds with kagome lattice, the weak interactions between organic molecule formed a kagome lattice in [EDT-TTF-CONH2]6[Re6Se8(CN)6] [140] and antiferromagnetic spin fluctuation was observed. This was earlier than the first coordination compound with kagome lattice Zn0.33Cu0.67(OH)6Cl2 [141, 142].

The single component organic conductor and superconductor is an important area in organic superconductor technology. Apart from the calculation of band structure, the theory of the resonating valance bonding state could be useful in explaining this system. The weak interaction between molecules from supramolecular chemistry forms a resonating valence bonding state. So the crystal could show semiconductor, conductor, and superconductor properties. The Jahn–Teller distortion originating from metal coordination compounds now extends to organic chemistry as representative of energy degeneracy. The International Symposium on the Jahn–Teller effect, which was initiated by Prof. Muller, is held every 2 years. He combined the RVB with the Jahn–Teller effect in inorganic superconductors, and it is also suitable for use with organic superconductors [129]. The research area can be expanded after the combination of inorganic superconductor units and molecular crystals [23, 143].

1.6 Summary

Organic materials have received considerably more attention than inorganic-based materials for use in modern optoelectronic devices, such as organic solar cells, light-emitting diodes, and field effect transistors, because of their low-cost, easy deposition, and wide variety and tailorable or tunable properties. This chapter focuses on the charge transport of organic materials, and some prototype organic solids are also discussed. Organic superconductors can be obtained from organic conductors, semiconductors, and insulators under suitable conditions at low temperatures. These materials therefore still represent a challenging and exciting research field for the near future.