Effect of symmetry on the electronic DOS, charge fluctuations and   electron-phonon coupling in carbon chains
  A theoretical model is provided to address the parameters influencing the electronic properties of kink-structured carbon chain at 0K. It is studied by the principle of DFT and solving the numerical 1D time-independent Schr\"odinger equation of electron and phonon simultaneously. Two different lengths of branches A and B, are occupied alternatively to generate the asymmetric carbon chain. The ratio of the asymmetric branch length,RAB=A/B, plays an important role in the electronic density of states DOS around Fermi level Ef . The highest DOS(Ef) occurs if the RAB equals to 2 and while the Fermi level coincides with the Von-Hove singularity at RAB=3. The location of the singularity point relative to the Ef is controllable via branch length interestingly. By comparison with the symmetric case, tuning the branch length asymmetrically shows a stronger impact to shift the Ef to the singularity point. The numerical solution of the 1D time independent Schrodinger equation of phonon indicates that the kink reinforces the charge fluctuations but the fluctuations are minimized when the RAB goes up. Based on the simulation results, the electron phonon coupling of the carbon nanowire decreases with chain length. In comparison to the symmetric structure, the electron phonon coupling of the asymmetric carbon chain is higher. The maximum electron phonon coupling of the asymmetric carbon chain takes place at RAB=2 . However, the weakening of the electron phonon coupling is observed owing to ultrahigh concentration of kinks. The reduction of the electron phonon coupling of the carbon chain is occurred under pressure. 
C.H. Wong, J.Y. Dai, M.B. Guseva, V.N. Rychkov, E.A. Buntov, A.F.   Zatsepin
cond-mat.mtrl-sci