Abstract
We calculate the spectral properties of the one-dimensional Holstein
and breathing polarons using the self-consistent Born approximation.
The Holstein model electron-phonon coupling is momentum independent
while the breathing coupling increases monotonically with the phonon
momentum. We find that for a linear or tight binding electron
dispersion: i) for the same value of the dimensionless coupling the
quasiparticle renormalization at small momentum in the breathing
polaron is much smaller, ii) the quasiparticle renormalization at
small momentum in the breathing polaron increases with phonon
frequency unlike in the Holstein model where it decreases, iii) in
the Holstein model the quasiparticle dispersion displays a kink and a
small gap at an excitation energy equal to the phonon frequency
$\omega_0$ while in the breathing model it displays two gaps, one at
excitation energy $\omega_0$ and another one at $2\omega_0$. These
differences have two reasons: first, the momentum of the relevant
scattered phonons increases with increasing polaron momentum and
second, the breathing bare coupling is an increasing function of the
phonon momentum. These result in an effective electron-phonon
coupling for the breathing model which is an increasing function of
the total polaron momentum, such that the small momentum polaron is in
the weak coupling regime while the large momentum one is in the
strong coupling regime. However the first reason does not hold if
the free electron dispersion has low energy states separated by large
momentum, as in a higher dimensional system for example, in which
situation the difference between the two models becomes less
significant.
