Corrections of Electron-Phonon coupling for Second-Order Structural Phase Transitions

TL;DR

This paper refines the understanding of electron-phonon interactions in second-order structural phase transitions by incorporating nuclear kinetic energy and position, providing more accurate free energy calculations and insights into symmetry breaking effects.

Contribution

It introduces a modified Hamiltonian treatment that includes nuclear kinetic energy and position, improving upon previous models for electron-phonon coupling in phase transitions.

Findings

Nuclear corrections are minor but significant for symmetry breaking.

Derived more accurate free energy expressions using canonical ensemble.

Estimated shifts in transition temperature due to nuclear effects.

Abstract

Structural phase transitions are accompanied by a movement of one nucleus (or a few) in the crystallographic unit cell. If the nucleus movement is continuous, a second order phase transition without latent heat results, whereas an abrupt nucleus displacement indicates a first order phase transition with accompanying latent heat. In this paper an Hamiltonian including electron-phonon coupling (EPC) as proposed by Kristoffel and Konsel\cite{Kristoffel1973} is taken. Contrary to their treatment, both the kinetic energy of the nucleus and its position are treated. The interaction of the many electron system with the single nucleus is taken into account by the Born-Oppenheimer approximation and perturbative expressions for the free energies are derived. The nuclei corrections due to the entangled electrons are found to be minor, but highlight the importance of the symmetry breaking at low temperature. Furthermore the free energy for a canonical ensemble is computed, whereas Kristoffel and Konsel used a grand canonical ensemble, which allows to derive more stringent bounds on the free energy. For the zero-order nucleus correction the shift of the phase transition temperature by evaluating the free energy is deduced.