The complex β-(meso-DMBEDT-TTF)₂AsF₆ is isostructural to the complex β-(meso-DMBEDT-TTF)₂PF₆ both at 298 K and 30 K. At 298 K, the crystallographically independent molecules are one donor and a half anion. Below 70 K, the unit cell is doubled, so that there are two crystallographically independent donors and one anion; the equivalent donors (D^0.5+ D^0.5+) in a dimer at 298 K are transformed to the charge-disproportionated donors (D^0.65+ D^0.35+), which are in the charge—rich D^0.65+ and the charge—poor D^0.35+ states (Figure 2, Table 1). Between dimers, two charge—rich D^0.65+D^0.65+ and two charge—poor D^0.35+D^0.35+ are adjacent, such as in ··D^0.65+)(D^0.65+D^0.35+)(D^0.35+·· in the stacking direction, and construct the checkerboard-type charge-ordered state. Although the charge-ordered patterns of the PF₆ and the AsF₆ complexes are similar, the degree of charge disproportionation is relaxed from D^0.75+D^0.25+ for the PF₆ complex to D^0.65+D^0.35+ for the AsF₆ complex. As an anion size increases from PF₆⁻ to AsF₆ ⁻, the unit cell volume at 298 K gets larger from 906(2) ų [4] to 914.3(7) ų and the dimerization ratio r2/ r1 decreases from 2.74 to 2.12 at 298 K (Table 2). As a result, the degree of the charge split is reduced from D^0.75+D^0.25+ to D^0.65+D^0.35+. In the charge-ordered state, both kinds of dimerization ratio of the AsF₆ complex (r2/r1 = 1.94, r4/r3 = 1.34) are smaller than those of the PF₆ complex (2.01, 1.39). With a lowered temperature, the reduction rate of the dimerization ratio{[(r2/r1) (30 K)]/[(r2/r1) (298 K)] = 0.92 and [(r4/r3) (30 K)]/[(r2/r1) (298 K)]} = 0.63 for the AsF₆ salt is also smaller than those (0.73 and 0.51) for the PF₆ salt.

In order to elucidate the electronic state at 298 K, the correlation parameters W_U/ΔE [W_U: upper band width, ∆E: on-site Coulomb repulsion energy = 2 * (intradimer transfer energy)] of the obtained β-(meso-DMBEDT-TTF)₂X (X = PF₆, AsF₆) at 298 K are shown in Table 3. The parameters W_U/ΔE are calculated to be 1.11–1.23, which is comparable to those of κ-(BEDT-TTF)₂X {1.24 for X = Cu(NCS)₂ [11,12,13], 1.11 for Cu₂(CN)₃ [13]}. Therefore, the complexes β-(meso-DMBEDT-TTF)₂X (X = PF_6, AsF₆) might be in the dimer state at 298 K.

Moreover, the enhancement of the mid-infrared conductivity hump in the optical spectra for β-(meso-DMBEDT-TTF)₂PF₆, which originates from a transition between lower and upper Mott Hubbard bands, demonstrates experimentally that the complex is in the dimer state from room temperature to 75 K [14]. Since the lower bandwidth of β-(meso-DMBEDT-TTF)₂X is wider than that of κ-(BEDT-TTF)₂X, the gap between the upper and lower bands (Eg) is 0–0.02 eV and the complex β-(meso-DMBEDT-TTF)₂PF₆ shows weak metallic behavior from room temperature to 75 K at an ambient pressure (Figure 1, [4,7]). Below 75 K, the dimer optical peak stops growing and the charge-ordering band starts to increase [14].

Figure 3 shows the temperature dependences of resistivities under an ambient and a pressurized condition for β-(meso-DMBEDT-TTF)₂AsF_6. This complex with 0.1 ohm cm at 300 K exhibits weak metallic behavior down to 90 K and is transformed into the insulating state. Compared with β-(meso-DMBEDT-TTF)₂PF₆ [4,7], the resistivity at room temperature is similar, 0.1 ohm cm, but the metal- insulator transition is broader. The rapid increase of the resistivity was suppressed under 0.19 GPa and a distinct resistivity drop at 4.2 K was observed under 0.38 GPa. As pressure is applied, the temperature of the resistivity drop decreases monotonically with −4.7 K/GPa, which is similar to that of β-(meso-DMBEDT-TTF)₂PF₆, −4.5 K/GPa [7]. As shown in Figure 4, the resistivity drop under 0.38 GPa was suppressed by applying a magnetic field and proved to be the superconducting (SC) transition. This magnetoresistance reached +32% just above the transition temperature of 4.6 K under 9 T, which might have been due to the Pauli Blockade originating from CO [15], similar to the case of β-(meso-DMBEDT-TTF)₂PF₆ [7].

Figure 5(a) shows the temperature dependence of resistivity under pressure below 30 K. The analysis of ρ T^α was carried out under several pressures in the temperature range of 2 < T < 20 K. The exponent α is 2 when the electronic state is in the Fermi liquid nature. Near the superconducting state, α is calculated to be 1.3 under 0.9 GPa. The power α increases almost linearly with application of pressure. The pressure dependence is dα/dP = 0.6 K/GPa, which is much faster than those of (TMTTF)₂X (X = PF₆, AsF₆) with 0.15–0.19 K/GPa [16]. The system at 1.5 GPa is non-Fermi liquid (NFL) with α = 1.7 and might be realized to be the Fermi liquid above 2.5 GPa if the linear extrapolation of the pressure dependence is assumed.

The phase diagram of β-(meso-DMBEDT-TTF)₂AsF₆ is elucidated in Figure 5(b). At an ambient pressure, the insulating state below the transition temperature is the checkerboard-type charge-ordered state. Upon the application of pressure, the metal-insulator transition temperatures are lowered and the distinct superconducting transition appears under 0.38–0.9 GPa at 4.2–1.9 K. For both complexes β-(meso-DMBEDT-TTF)₂X (X = PF₆ [7] and AsF₆), the SC states compete with the charge-ordered states over certain pressure ranges.

Under ambient pressure, the dimer state of the titled complexes is developed with lowering temperature and is suddenly transformed into the checkerboard-type charge-ordered state with accompanying metal-insulator transition around 75–90 K. In order to clarify the electronic state of β-(meso-DMBEDT-TTF)₂X (X = PF₆ and AsF₆), the measurements of static magnetic susceptibilities were carried out as shown in Figure 6. The static magnetic susceptibilities at 300 K for β-(meso-DMBEDT-TTF)₂X (X = PF₆ and AsF₆) are 5.5 × 10⁻⁴ and 5.3 × 10⁻⁴ emu mol⁻¹, respectively. These values are similar to those of the electron-correlated molecular conductors, such as the dimer-Mott molecular conductors κ-(BEDT-TTF)₂X {X = Cu(NCS)₂, Cu[N(CN)₂]Br, Cu[N(CN)₂]Cl}, 4.2–4.5 × 10⁻⁴ emu mol⁻¹ [17], and the charge-ordered conductor, θ-(BEDT-TTF)₂RbZn(SCN)₄, 6.0 × 10⁻⁴ emu mol⁻¹ [18]. With lowering temperatures, the susceptibilities decrease gradually and drop from 4.7–4.5 × 10⁻⁴ emu mol⁻¹ around 80 K to 3.1–2.7 × 10⁻⁴ emu mol⁻¹ around 60 K. The susceptibility of the PF₆ complex below 80 K was well fitted by the following, as shown by the solid line in Figure 6:

The contributions of ST₁, L₂, and Curie₁ denote the susceptibilities based on a singlet-triplet model [19], a two-dimensional Heisenberg model [20], and Curie law. The drop of the susceptibility below 80 K is mainly fitted by the singlet-triplet model. Recently, Okazaki and Terasaki et al. reported that the infrared imaging measurements of several samples indicated the inhomogeneity of the charge-ordered and the dimer states even below 80 K [14]. The contribution of the dimer state by the two-dimensional Heisenberg model showed good agreement with the experimental data. At low temperatures, the 0.6% Curie contribution (S = 1/2 and g = 2) is due to the impurity. The behaviors of the PF₆ and AsF₆ complexes are similar. The measurements of magnetic susceptibilities indicate that the ground state would be the spin-gapped state, which is consistent with the behavior by the NMR measurement [21].

In Section 2.1, the checkerboard-type charge ordering in the PF₆ and AsF₆ complexes is described. The charge disproportionation is usually caused by the electron-electron repulsion in the closest donor pair [2]. In this case, the dimer (D^0.5+ D^0.5+) at 298 K is transformed into the charge-disproportionated pair (D^0.65+D^0.35+) to construct ··D^0.65+)(D^0.65+D^0.35+)(D^0.35+·· in the stacking direction below 70 K. This charge distribution induces not only the checkerboard-type charge ordering with accompanying lattice modulation, but also the spin-singlet state at the same transition temperature. This spin-gapped state, namely the two-dimensional Spin Peierls state, is the origin of the checkerboard-type charge ordering and the characteristic feature of the strong electron-phonon coupling for molecular materials.

The electronic state of the titled complexes can be discussed by the spin-singlet paired-electron crystal (PEC) model in the two-dimensional strongly correlated quarter-filled band on the anisotropic triangular lattice [22] [Figure 2]. In the moderate or strong spin and charge frustrated region, the checkerboard-type charge-ordering, wherein the pairs of the charge-rich sites are separated by the pairs of the charge-poor sites, affords the spin-singlet state. The phase diagram as a function of onsite and intersite Coulomb interactions as well as the electron-phonon coupling is also discussed in this model. Moreover, it is speculated that the spin-bonded pairs of the PEC can become mobile for stronger frustration, giving rise to a paired-electron liquid. The titled complexes seem to be explained by the PEC model. The appearance of the checkerboard-type charge ordering in the two-dimensional quarter-filled band on the anisotropic triangular lattice at 70 K affords the spin-gapped state by the static magnetic susceptibility and the NMR measurements at low temperatures. The transfer integrals of charge-rich sites [r3 = 18.2 (the PF₆ complex) and 18.7 × 10⁻² eV (the AsF₆ complex)] are larger than those of charge-poor sites (r1 = 12.6 and 12.9 × 10⁻² eV) in the charge-ordered and spin-gapped state for β-(meso-DMBEDT-TTF)₂X (X = PF₆ and AsF₆), respectively (Table 2). Under the pressurized condition, both complexes exhibit superconductivity, which was attributed to a paired-electron liquid. The PEC model can be applied for not only β-(meso-DMBEDT-TTF)₂X (X = PF₆ and AsF₆), but also thiospinel CuIr₂S₄ [23] with the charge-ordered and the spin-dimerized transition at 230 K, and triclinic EtMe₃P[Pd(dmit)₂]₂ [24] with the charge-ordered and the spin-gap transition.