Twin distortions of the Peierls instability

Abstract

It is proved analytically that a one-dimensional half-filled polymer chain is subject to two coupled spontaneous conformational relaxations, the well-known Peierls bond length alternation and a uniform bond contraction. These two coupled relaxations work cooperatively against the lattice elastic energy penalty so that all bonds alternate and contract less than the case when these two relaxations are independent. When the fully relaxed neutral chain is taken as reference, creating self-localized charge carriers upon doping results in spontaneous bond contraction within the self-localized domain where the undimerization is enforced. Numeric results based on the Su-Schrieffer-Heeger and extended Peierls-Hubbard models and ab initio calculations resolve a long-lasting puzzle observed by x-ray scatterings concerning of the initial zero slope and accompanied sharp knee in the strain response of trans-polyacetylene to the Na + dopant concentration. The demonstrated doping-induced polymer chain length variation mechanism has implications for ultrafast artificial muscle designs.A one-dimensional ͑1D͒ equally spaced metallic polymer chain of one electron per ionic site is unstable with respect to the spontaneous relaxation via optical phonons with the double Fermi wave vector, resulting in a dimerized insulating polymer chain. This is the Peierls instability, originally derived using the free-electron energy dispersion relation. 1 A more rigorous proof was given by Kennedy and Lieb 2 stating that such a dimerization is exact without additional symmetry breakdown, at least for the Su-Schrieffer-Heeger ͑SSH͒ type of Hamiltonians 3 in which the nearest-neighbor electron hopping integrals vary linearly with the distance. This work points to the existence of a ubiquitously coupled twin of the Peierls distortion, with validations from previously unresolved puzzling x-ray scattering data on Na + doped trans-polyacetylene. [4][5][6][7][8][9] Without loss of generality, 10 we follow Kennedy and Lieb 2 to focus on the SSH Hamiltonian. It is well recognized that the SSH Hamiltonian is subject to a spontaneous contraction. Explicitly, Su proposed a constant tension of 4␣ / to compensate such a undesired global contraction. 11 Later, Stafstrom and Chao 12 suggested a 2% correction to Su's term and attributed such a difference to the discrete energy spectrum of using a finite system. Vos et al. expressed the contraction as a function of the electron-phonon coupling coefficient for the perfectly dimerized case and obtained the sound speeds of acoustic and optical modes. 13 Nevertheless, we note that the chain length variation in the above mentioned arguments is independent of the polymer charge state; namely, if the neutral dimerized chain is taken as reference, no further chain length variations would be expected upon charge injections. In addition, Bishop et al. 14 observed local contractions at the soliton center via adiabatic exciton dynamics and attributed such local contractions to the coupling between moving solitons and acoustic ...

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