Quarter-filled bands

The nomenclature for band filling is that a filled band has two electrons (or holes) per site (with spin up and spin down) a half-filled band has only one electron (or hole) per site a quarter-filled band has one electron (or one hole) per two sites. 

In Fig. 4 we show the molecular structures of [M(mnt)2] and perylene and the general scheme of the crystal structure of the a phases. The conduction band of the perylene system is a three-quarter-filled band, whereas the dithiolate chains are either Mott-Hubbard insulators or closed shell. The members of this series cover a number of the situations described above. 

The intra- and interchain Coulomb interactions between electrons on the TCNQ chains are the subject of extensive study. For a quarter filled band the on-site and nearest neighbour interactions 1 eV and 1 eV are considered in the framework of the extended Hubbard model. The interchain Coulomb... 

If the bond-length-dependent Hiickel model is used for three-quarter or one-quarter filled bands, the result is surprising at first. A one-dimensional chain with 104 atoms, each bonded by a single bond is used. Three-quarter occupancy can be achieved by occupying the lowest 78 MOs by two electrons and leaving the rest empty. A band gap at the Fermi level opens up, but it is smaller than in the case of half-filled bands p = 0.12 eV, if Ipol = 3 eV. 

Another instance where spin state is important and has a direct bearing on structure is in one-dimensional systems. Just as in Section 13.2 where we showed how a half-filled band usually results in a pairing distortion, so similar reasoning suggests that a quarter-filled band should result in a tetramerization 13.72. However, if the distorted arrangement is magnetic then dimerization is the process that is favored 13.73. Again prediction of the mode of distortion is not at all easy. 

Figure 3.15(IV) shows the electronic band structure and Fermi surface of t-(EDO-S,5-DMEDT-TTF)2-(AuBr2)i(AuBr2)o,75 [407]. The Fermi surface is star-like shaped inside the Brillouin zone. For a hypothetical three-quarters filled band the Fermi surfaces touch the Brillouin zone, i.e. the structure is similar to that of Figure 3.12(d). Similar structures were found for other T-phases of Table 3.13 [326,391],...

Within a one-electron description (i.e., U = 0, U being the on-site Coulomb repulsion [2,3], regular conducting TCNQ chains with p = electron per molecular site correspond to quarter-filled electronic bands. Consequently, the Fermi wave vector is in this case kF = n/4d, d being the spacing parameter between adjacent sites, and the chains are metallic. This is the case, for instance, for MEM(TCNQ)2 and TEA(TCNQ)2. Note that in these two salts the cations MEM+ and TEA+ are diamagnetic and do not participate in electrical conduction. 

On the whole it is better to resort to safer methods of heating. The simplest procedure is to employ a small water bath. This may consist of a 250 ml Pyrex beaker, three-quarters filled with water and covered with a lead or galvanized iron plate (Fig. 11.22) drilled with two holes to accommodate a test-tube and a centrifuge tube. It is a good plan to wind a thin rubber band... 

The power law coefficient can also be derived from the optical response at frequencies co greater than the Hubbard gap since then the frequency dependent conductivity is governed by inter Hubbard sub-band transitions and becomes CT(a)) = (with n = 2 for the quarter-filled situation). This is markedly... 

TMTSFfjPF and CIO4 both give the exponent — 1.3 in the power law frequency dependence in the low temperature range (10-20 K) of the 2D intermediate phase. This exponent leads to A p = 0.23 in case of a quarter-filled 1-D band [96]. 

With regard to Q-(TCNQ)2 and Ad-(TCNQ)2, Bulaevskii et al, have pointed out that the observed nonmonotonic temperature dependence of their susceptibilities suggests complete charge transfer and a quarter-filled TCNQ conduction band in those materials. Theodorou (unpublished) has extended a simpler version of the above theory to arbitrary filling and has demonstrated that the exponent 0< increases as the filling decreases, as is observed for the sequence NMP-TCNQ, Ad-(TCNQ)2/ and Q-(TCNQ)j. 

Geometry optunizatiou by semi-empirical methods gives the bonding pattern seen in Figure 16.5. Each N atom corresponds to one CH unit in polyacetylene (PA). In PA, each CH unit contributes one % orbital and one electron. The valence band is half filled and the systan PA is therefore subject to Peierls distortiou. In (SNj, on the other hand, the sp hybridized S atom contributes two electrons to the jt-system. The jt-system of (SN)x is therefore three-quarters filled and not subject to auy Peierls distortion. However, three-quarter filling leads to other peculiarities, as we will see next. 

The decrease in conductivity in polytoluidines can be attributed to their electronic structure. The electronic structure of polytoluidines, like PANI, corresponds to that of a metal with the highest occupied band three quarters filled. The observation of Pauli paramagnetism in polytoluidines [39,40] reveals the existence of a degenerate electronic structure with a finite density of states at the Fermi energy as in PANI [117]. Note that PANI also typically does not exhibit the traditional signatures of metallic transport due to a combination of... 

The thermopower data for various types of doped PANl are shown in Figs. 2.51a and 2.51b [172,193]. The room temperature value is approximately 10 /itV/K with small variations ( 2 p.V/K) depending on the details of the process for casting the film. The magnitude and positive sign of 5(7) are similar to those obtained from a number of partially doped p-type conducting polymers [89-92]. The positive sign of the thermopower is consistent with the calculated band structure of the metallic emeraldine salt, a three-quarter-filled tt band with one hole per... 

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