Trans-polyacetylene, the canonical conducting polymer with a degenerate bond-alternating ground state, exhibits intense doping-induced infrared-active vibrational (IRAV) absorption bands that the 1981 joint experimental–theoretical study of Etemad, Pron, Heeger, MacDiarmid, Mele, and Rice showed to be the vibrational signature of charged solitons — but only at dilute dopant concentrations. That work explicitly left open how these semi-localized soliton modes evolve as the dopant concentration increases through the insulator–semiconductor–metal transition, whether the one-electron/RPA (random-phase approximation) treatment remains valid at higher carrier densities or stronger Coulomb correlations, and how the parameter space (oriented samples, different dopant species, line-shape/inhomogeneous-broadening analysis) constrains the soliton model. Later work measured the heavily doped regime and found persisting, red-shifted, essentially unpinned IRAV modes coexisting with a ~1500 cm⁻¹ pseudogap, and produced competing theoretical scenarios (soliton lattice, doping-induced superlattice, disordered incommensurate charge-density wave) for the high-density state; however, no complete quantitative account — experimental or theoretical — of the IRAV frequencies, oscillator strengths, and line shapes across the full doping range, and of the underlying microscopic charge state, has been delivered. The surviving problem is to determine that evolution and the microscopic picture that reproduces it.

Background

Polyacetylene, (CH)x(CH)_x, is a conjugated polymer whose carbon chain in the trans configuration undergoes bond alternation — alternating short (double) and long (single) carbon–carbon bonds — which is the Peierls instability of a one-dimensional (1D) half-filled band: it opens an energy gap and makes the pristine polymer a semiconductor. Two degenerate alternation patterns exist (which bond is short), so domain walls between them are topologically allowed: such a wall is the soliton of the Su–Schrieffer–Heeger (SSH) coupled electron–phonon model. A charged soliton (spinless, charge ±e\pm e) reverses the bond-alternation phase over ~7 sites and creates a localized electronic state at mid-gap. Chemical or electrochemical doping (e.g. with iodine, AsF5_5, or alkali metals) injects carriers that are accommodated as charged solitons at low dopant concentration.

The lattice distortion of a charged soliton also generates new vibrational normal modes with unusually large infrared oscillator strength: doping-induced infrared-active vibrational (IRAV) modes, observed as strong absorption bands (notably near 1370 cm−11370\ \mathrm{cm}^{-1} and 900 cm−1900\ \mathrm{cm}^{-1} in lightly doped (CH)x(CH)_x). Mele and Rice computed these modes in a one-electron, random-phase-approximation (RPA) treatment of the π\pi-electron–phonon coupling, and the 1981 Phys. Rev. B 23, 5137 study (experiment by Etemad, Pron, Heeger, MacDiarmid; theory by Mele and Rice) combined Raman and infrared spectra of both (CH)x(CH)_x and fully deuterated (CD)x(CD)_x with those calculations, achieving quantitative, parameter-free agreement — including the isotope shifts — which provided specific spectroscopic evidence that doping produces charged solitons. The amplitude-mode description of Horovitz and co-workers later consolidated the relation between the resonant Raman lines and the induced IR activity as amplitude and phase modes of the dimerized chain, with the soliton-induced modes appearing as a pinned (in the dilute limit, dopant-pinned) version of the amplitude mode.

That study was, however, restricted to unoriented films and dilute concentrations. In the same journal issue, Mele and Rice (Phys. Rev. B 23, 5397) analyzed the semiconductor–metal (S–M) transition of doped polyacetylene itself, proposing a four-regime evolution with increasing dopant concentration: (I) solitons pinned at ionized impurity sites; (II) statistically fluctuating quasimetallic regions; (III) a dense band of localized states from an incommensurate charge-density wave disordered by the random impurity field, at which point the transition to metallic conduction occurs (predicted near ~10 at.% dopant in a strictly 1D theory, reduced below the ~5% observed experimentally once interchain coupling is included); and (IV) suppression of bond alternation at extremely high concentration. What this framework did not determine is the vibrational signature of that evolution — and that gap, together with the untested validity of the one-electron/RPA treatment at higher carrier density (where Coulomb correlations, interchain coupling, and disorder grow), is precisely the unresolved issue the dilute-limit IRAV study acknowledged: experiments extending the doping range, oriented samples, other dopant species, and line-shape analyses were called for to map the parameter space in which the soliton model holds.

Problem Statement

Determine how the soliton-induced infrared-active vibrational modes (IRAV modes) of doped trans-polyacetylene evolve as the dopant concentration increases from the dilute regime, where they quantitatively identify charged solitons (Etemad, Pron, Heeger, MacDiarmid, Mele, and Rice, Phys. Rev. B 23, 5137 (1981)), through the semiconductor–metal transition and into the heavily doped 'metallic' regime — and identify the microscopic charge state that produces them there. Concretely, the results that jointly serve this single objective are: (1) measurements of the IRAV frequencies, oscillator strengths, and line shapes as a function of dopant concentration across the transition (including the isotope comparison of (CH)x(CH)_x with (CD)x(CD)_x, different dopant species, and oriented versus unoriented samples), with line-shape analyses that separate inhomogeneous broadening from intrinsic mechanisms; and (2) a microscopic account — pinned charged solitons, soliton lattice, disordered incommensurate charge-density wave, or delocalized band carriers with a pseudogap — together with a quantitative theory of the vibrational spectrum that specifies the applicability and limitations of the one-electron/RPA treatment used at dilute doping once carrier density, Coulomb correlations, disorder, and interchain coupling become large, and that reproduces the measured evolution. The microscopic account and quantitative theory of (2) reproduce the measured evolution of the IRAV frequencies, oscillator strengths, and line shapes across the doping range, thereby fixing the parameter space within which the soliton model of doped trans-polyacetylene remains valid; the measurements of (1) are its empirical target.

References

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