Metallic State of Heavily Doped

Models for the Metallic State of Heavily Doped Trans-(Cll)x- 

Tanner et al. have studied K doped trans-ifCYi) [14-15] and found that the oscillator strength of the doping induced IR active (IRAV) modes per dopant molecule is approximately the same both below and above the critical doping concentration. This result indicates that solitons, which are known to be the stable type of defect at low doping levels, remains stable even above the critical doping concentration. 

Another experimental evidence against the polaron lattice model for the metallic state of heavily doped trans-(CH)j comes from Electron-Energy-Loss Spectroscopy (EELS) data [21]. These data show levels spread well across the gap, which is more in agreement with the disordered incommensurate state than with the picture of narrow polaron bands in the gap. Band structure calculations using the Valence Effective Hamiltonian (VEH) technique [22] support this conclusion since it is shown that a large energy gap exists between the polaron bands in the band structure of the polaron lattice. On the other hand, experimental and theoretical results have been presented that support the polaronic metal state for doped polyaniline (emeraldine salt) [23]. 

Within the continuum model of Takayama, Lin-Liu, and Maki (the TLM model) [27], Dinter [28] has shown that a new type of superlattice exists for tranS (CH). This new type of lattice, which contains considerable dimerization, has a lower total energy than that of the soliton lattice for doping levels above 8%. The electronic band structure corresponding to this lattice configuration contains a partially filled band, i.e., a gapless metallic state exists for this type of lattice. A crossover from the soliton lattice to this new superlattice could therefore explain the onset of metallic properties in heavily doped trans-(CH)y, However, as pointed out by Dinter, calculations using the more realistic discrete SSH model have to be performed in order to check whether or not the new lattice is a mere artifact of the TLM model. 

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Several authors have discussed the role of disorder in obtaining a metallic state of heavily doped tra/i.y-(CH)x [16,17]. As discussed in Sec. 2, these studies all involve disorder which is much stronger than the one present in the well ordered samples that show a very abrupt transition into the metallic state [12-13], The disorder considered here is very weak and is expected to be present even... 

In the case of traw -polyacetylene (a degenerate polymer), band-structure calculations [126] indicate that a polaron lattice has a metallic band whereas a charged soliton lattice has no metallic band. An alternating polaron-charged soliton lattice [128] has been proposed for explaining the metallic properties of heavily doped states. 

In other words, the fundamental electronic structure of heavily doped conducting polymers is that of a metal. Since, however, polymeric systems are inherently disordered, states at the band tails are always localized and there exists a mobility edge that separates the region of the extended states in the interior of the band from the region of localized states. Whether the doped system is a metal or an insulator, then, is determined by the relative position of the Fermi energy with respect to the mobility edge. 

The presence of a Pauli-like term is associated with a nonzero density of states at the Fermi level it has been presented by different authors as evidence for metallic behavior. Before mentioning other possible interpretations, we would point out that the decomposition x = Xc + XP s not unambiguous. Indeed, in the case of poly acetylene in the heavily doped regime (y > 6%), the existence of Pauli susceptibility is well established [83], since in all the temperature range x is almost constant (Xp Xc)-But this is generally not the case in other compounds in which a significant Curie term remains present. 

At least in heavily doped polymers, the temperature-independent susceptibility is obsci-vcd in PT and P3AT (poly(3-alkylthiophenc)) doped with AsF(, [255,279, 282] PFc," [282] SO.iCF.r [295] CIO - [282,296] and BFj" [258], except for PT/P3AT-1T [255,297]. Possible reasons why it is not obseiwed in PT/P3AT-Ij arc (1) the ESR linewidth from the Pauli spins is too broad to observe by ESR and (2) the charge transfer from iodine to polymer is insufficient to fill a band gap. The situation with these systems is similar to the case of PPy on the metallic electronic states the electrical conductivity reaches 500 S/cm [298-300], the small... 

On going to polypyrrole we find that for heavily doped polypyrrole, the resistance is proportional to the logarithm of temperature in the temperature range 1 K to 1 mK. This behavior is appropriate for an amorphous metal [57]. This is supported by the temperature independence of paramagnetic susceptibility that is sometimes seen for heavily doped polypynole. Such a result is also inconsistent with spinless excitations such as bipolarons. Thus one can see various types of temperature behavior for charge transport in electroactive polymers in the dry state. 

Although heavily doped conducting polymers show clear signatures for a metallic density of states at Ep, their transport properties are not typical of a traditional metal. Instead, the electronic states at Ep are dominated by disorder. In this section, therefore, a brief review is given on the dielectric response of the disordered system in the context of the Anderson transition, both on the metallic and on the insulating side of the M-I transition, derived from the Kubo-Grreenwood formalism [1176]. 

In spite of the clear signatures of the metallic state, however, the heavily doped conjugated polymers do not exhibit traditional metallic behavior in transport [173] and optical properties [1155]. Instead, they show a negative temperature coefficient of the resistivity dp/dT < 0) the dc conductivity is activated with temperature, so that the dc conductivity decreases by several orders of magnitude as the temperature is lowered. Furthermore, the optical spectra do not show the Drude-like behavior expected for a typical metal in the infrared. Rather, an electronic pseudo-gap of about 0.1-0.2 eV has been observed, below which the optical conductivity is suppressed [1155]. These nonmetallic behaviors arise from the disorder of the sample, originating from a combination of molecular-scale disorder and mesoscale inhomogeneity. 

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