Driving forces behind the distortion of one-dimensional monatomic chains: Peierls theorem revisited

Abstract

The onset of distortion in one-dimensional monatomic chains with partially filled valence bands is considered to be well-established by the Peierls theorem, which associates the distortion with the formation of a band gap and a subsequent gain in energy. Employing modern total energy methods on the test cases of lithium, sodium and carbon chains, we reveal that the distortion is not universal, but conditional upon the balance between distorting and stabilizing forces. Furthermore, in all systems studied, the electrostatic interactions between the electrons and ions act as the main driving force for distortion, rather than the electron band lowering at the Fermi level as is commonly believed. The main stabilizing force which drives the chains toward their symmetric arrangement is derived from the electronic kinetic energy. Both forces are affected by the external conditions, e.g. stress, and consequently the instability of one-dimensional nanowires is conditional upon them. This brings a new perspective to the field of one-dimensional metals, and may shed new light on the distortion of more complex structures.

Role of Coulomb correlations in the charge density wave of CuTe

“…Electronic instability, however, widely understood as the origin of a Peierls transition, has been challenged 10,11,23,24 . As the dimension of interatomic connection increases, the susceptibility peak feature becomes weaken, and other mechanisms such as electronphonon interaction become important in the realization of a Peierls-type structural, or CDW transition.…”

High-Throughput Design of Peierls and Charge Density Wave Phases in Q1D Organometallic Materials

“…Irrespective of the band gap modulation, all 33 Peierls materials undergo geometric distortions deviating from the 1U structure, augmented by a net drop in the total energy (Figure 3a). These results are to be viewed in light of the original statement by Peierls [2,5] ing the net gain in potential energy to the relative displacement of atoms from their symmetric 1U positions, τ : ∆E = −τ 2 log(τ ). Hence, the overall gain in the thermodynamic stability is a system-specific, non-local property; the structure of the highly rigid σ-networks of B 3 C 2 H 2 M (M=K/Rb/Cs) are the least distorted in the Peierls phase showing essentially no net change in E f from the 1U to the Peierls phase.…”

“…Recent studies based on first-principles calculations have unequivocally established that opening of the energy gap on the zone-edge is one of the many parts of the total energy; which, in some cases, may even be cancelled with other contributions from the band structure [5]. Generalizing both gap-opening and gap-closing cases, the dynamic instability characterized by a soft phonon mode constitutes a necessary condition for PT, while a metallic band (ε g = 0) in the 1U phase, a sufficient one.…”

The Lennard Jones Potential Revisited -- Analytical Expressions for Vibrational Effects in Cubic and Hexagonal Close-Packed Lattices

“…A good example for symmetry breaking is the so-called Peierls distortion (Jahn-Teller effect). 73,74 A local form of symmetry breaking happens when the Einstein frequency becomes zero and the square root in Eq. ( 14) or (15) vanishes.…”