(Color online) Eigenspectrum for , , . The continuum represents single phonon continua and the breather band or phonon bound state due to “impurities” in the upper branch of the spectrum.
(Color online) (a) The variation of the energy gap is shown plotted against the impurity content of . The curve becomes asymptotic around the critical point of the impurity. It is thought that for LiNbO3 type ferroelectrics, there is such a transition point at which working with a practical device will be easier. (b) The bound state energy EBS vs α, showing the transition point according to analytical calculations.
(Color online) (a) The width of the single phonon continua (Wph ) plotted against the Landau coefficient. (b) The magnitude of Wph plotted against the percent impurity, showing a transition at a critical point of impurity.
(Color online) The hopping coefficient plotted against the Landau coefficient .
The variation of |Wph|, | |, and with .
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