A variational approach is used to investigate consequences of electron-phonon interactions between a charge carrier and multiple (specifically two) phonon branches. Phase diagrams are obtained and the nature of the transition from undressed to dressed phases of the carrier is studied with their help. No sharp transition between singly dressed and doubly dressed phases occurs. The effective carrier bandwidth, reduced by strong coupling to the high-frequency branch is found to be stable with respect to small to intermediate values of additional coupling to the low-frequency branch. This finding lends support to transport calculations based on the idea that carriers in a polaron band are dressed by one phonon mode and scattered by another.
V. M. Kenkre and P. E. Parris, "Variational Considerations in the Study of Carrier Transport in Organic Crystals," Physical Review B: Condensed Matter and Materials Physics, American Physical Society (APS), Jan 2004.
The definitive version is available at http://dx.doi.org/10.1103/PhysRevB.70.064304
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