Phonon condensate in Landau-Pekar polarons and optical absorption due to their photoionization

Abstract

Quantum-field theory methods are applied to consider the state of the polarization field in a strongly-coupled large polaron (SCLP) and after its photodissociation. It is demonstrated that in the adiabatic approximation the polarization field in such a polaron coincides with the classical polarization field considered in Landau-Pekar theory up to small quantum fluctuations. However the state of this field after the polaron photodissociation is in principle different from that obtained in theories of Pekar and Emin. This results from the fact that as it is shown below the polarization field in a SCLP is a spatially inhomogeneous phonon condensate. If the charge carrier is removed from the SCLP on its photodissociation the phonon condensate decays into phonons. As any Bose-condensate, the phonon condensate is a superposition of states with different number of quanta where summands are phased up to small quantum fluctuations. Therefore decay of the phonon condensate at the SCLP photodissociation results in an essentially wider band in the absorption spectrum than that predicted by theories with classical consideration of the polarization: the position of maximum is 4.2Ep and the half-width 2.5Ep (3 Ep and Ep in Emin theory, respectively), where Ep is the polaron binding energy. The calculated band is in good conformity with mid-IR band in the optical conductivity spectra of complex oxides. The predicted ratio (approximately 4) of the maximum position of the band caused by the SCLP photoionization to the frequency of maximum of the band caused by phototransitions into polaron excited states calculated by other group is also in good conformity with experiments.