Phonon coupling in tunneling systems at zero temperature: An instanton approach

Abstract

We have found a new method for dealing with phonon modes in path integrals. Using it and an instanton calculation, we have developed a detailed theory of the tunneling event in the presence of phonons. This theory generalizes the traditional methods (truncating the energy spectrum of the defect, treating it as a discrete "spin" system) which are valid only in the weakly coupled low-mass regime. Most atomic tunneling will be described by an "effective mass" for the defect due to coupled lattice motion; we use (KCl:Li+) as an example of this "slow-flip" regime. A physical picture describing electrons which are strongly coupled to phonon modes (i.e., self-trapped and polaronic electrons) is presented, but the instanton machinery does not simplify in this regime and direct calculation is necessary. We present a study of Anderson's negative-U centers to elucidate this type of tunneling. We also use a two-parameter model to distinguish the domains of validity for the truncation, self-trapped, and effective-mass regimes.