Purely electronic instabilities versus Peierls instabilities in semi-metallic 1D atomic chains

In 1929 Peierls hypothesized that a semi-metallic linear chain of equally spaced single electron atoms is unstable due to electron-phonon coupling at T=0: periodic lattice distortions along the longitudinal mode of vibration lead to the opening of an electronic band gap, lowering the symmetry of the lattice and stabilizing a semiconducting ground state. The origin of the symmetry breaking and of the formation of a charge density wave (CDW) state, was thus directly linked to the ionic displacement.

Here we study two equidistant semi-metallic linear chains, the (hypothetical) hydrogen chain and the carbon chain (carbyne), by means of accurate ab initio calculations based on quantum Monte Carlo and density functional theory (DFT). For both chains we find that the CDW state is more stable than the metallic phase even without any lattice distortion. This means that the ground state is electronically unstable. In DFT we show that the presence of the electronic instability is directly related to the non-locality of the Hartree-Fock exchange term that appears in the hybrid functionals. These results suggest that in 1D semi-metals there exists a pure electronic instability that opens a gap, leading to a CDW phase which is prior to Peierls distortion.