Ab initio study of the ferroelectric transition in cubic

In the substitutionally disordered narrow-gap semiconductor (Formula presented) a finite-temperature cubic-to-rhombohedral transition appears above a critical concentration (Formula presented) As a first step towards a first-principles investigation of this transition in the disordered system, a (hypothetical) ordered cubic (Formula presented) 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 (Formula presented) 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, (Formula presented) is approximately 620 K for the cubic (Formula presented) model, compared to the experimental value of (Formula presented) for disordered (Formula presented) Generalization of this analysis to the disordered (Formula presented) system is discussed.