Ab Initio Study of the Structural Phase Transition in Cubic Pb_3GeTe_4

TL;DR

This study uses first-principles calculations and Monte Carlo simulations to investigate the structural phase transition in cubic Pb_3GeTe_4, providing insights into the transition temperature and underlying atomic displacements.

Contribution

It introduces a first-principles based model Hamiltonian for Pb_3GeTe_4 and analyzes its thermodynamics, advancing understanding of phase transitions in disordered Pb_{1-x}Ge_xTe.

Findings

Transition temperature for the model is approximately 620K.

Unstable modes involve off-centering of Ge ions and neighboring Te displacements.

The model provides a basis for understanding the transition in disordered systems.

Abstract

In the substitutionally disordered narrow-gap semiconductor Pb_{1-x}Ge_xTe, a finite-temperature cubic-rhombohedral transition appears above a critical concentration $x \approx 0.005$. As a first step towards a first-principles investigation of this transition in the disordered system, a (hypothetical) ordered cubic Pb_3GeTe_4 supercell is studied. First principles density-functional calculations of total energies and linear response functions are performed using the conjugate-gradients method with ab initio pseudopotentials and a plane-wave basis set. Unstable modes in Pb_3GeTe_4 are found, dominated by off-centering of the Ge ions coupled with displacements of their neighboring Te ions. A model Hamiltonian for this system is constructed using the lattice Wannier function formalism. The parameters for this Hamiltonian are determined from first principles. The equilibrium thermodynamics of the model system is studied via Metropolis Monte Carlo simulations. The calculated transition temperature, T_c, is approximately 620K for the cubic Pb_3GeTe_4 model, compared to the experimental value of T_c \approx 350K for disordered Pb_{0.75}Ge_{0.25}Te. Generalization of this analysis to the disordered Pb_{1-x}Ge_xTe system is discussed.