Polaron Physics - Momentum Average Approximation




The formation of a composite object (the polaron) when an electron interacts with the lattice deformations (phonons) is a problem studied for decades in condensed matter physics. Even so, there is no exact solution for the simplest model -- the Holstein Hamiltonian.  Most of the analytical approaches were based on asymptotic limits (weak-strong coupling), while numerical solutions are computationally intensive due to the infinite size of the Hilbert space (Monte Carlo, exact diagonalization, etc).

    A new analytical method -- the Momentum Average approximation (MA), has been developed in the group of Prof. Mona Berciu. This method is computationally fast and exact in the asymptotic limits and accurate for all electron-phonon coupling strengths. While all the sum rules are accurate, the spectral function can be readily calculated within this approximation.
Using the Momentum Average approximation, I considered problems that were previously even hard to solve, such as the existence of multiple phonon branches, ZO phonons in graphene, phonons in the presence of spin-orbit coupling and the effect of surfaces states on the polaron.


For details on MA see:

1. Green's function of a dressed particle, Mona Berciu 
   Phys. Rev. Lett.  97, 036402 (2006)
2. The Green's function of the Holstein polaron, Glen L. Goodvin, Mona Berciu, and George A. Sawatzky
    Phys. Rev. B  74, 245104 (2006)
3. Systematic improvement of the Momentum Average approximation for the Green's function of a Holstein polaron, Mona Berciu and Glen L. Goodvin
   Phys. Rev. B  76, 165109 (2007)


   

Multiple phonons
Europhysics Lett. 80, 67001 (2007)

    We accurately show the interplay between two phonon branches in the formation of the polaronic state. The Momentum Average approximation is very useful in this situation, the phonon space increases such that other numerical methods become prohibitive.

   


Polarons in graphene
Phys. Rev. Lett. 100, 256405 (2008)

    We show that in rippled graphene, modeled by out-of-plane optical phonons, Dirac quasiparticles are well defined even for large electron-phonon coupling.


           



Polarons and spin-orbit coupling
    We consider the effect of the Rashba spin-orbit coupling on the polaron. We find that by increasing the spin-orbit interaction the transition from large to small polaron can be tuned. In addition, one of the spin-polarized bands becomes heavier. We show that within the Momentum Average approximation one can accurately find the off-diagonal part of the self-energy.