Holstein polaron in the presence of disorder

¹  Department of Physics and Astronomy, University of British Columbia - Vancouver, BC, Canada, V6T 1Z1
²  Cross-Correlated Materials Research Group (CMRG), ASI, RIKEN - Wako 351-0198, Japan
³  Russian Research Centre “Kurchatov Institute” - 123182 Moscow, Russia
⁴  Department of Applied Physics, University of Tokyo - 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan

Received: 5 November 2009
Accepted: 20 January 2010

Abstract

Non-local, inhomogeneous and retarded response similar to that observed in experiments is studied theoretically by introducing the Inhomogeneous Momentum Average (IMA) approximation for single-polaron problems with disorder in the on-site potential and/or spatial variations of the electron-phonon couplings and/or phonon frequencies. We show that the electron-phonon coupling gives rise to an additional inhomogeneous, strongly retarded potential. This potential describes essential physics ignored by ”instanteneous” approximations. The accuracy of IMA is demonstrated by comparison with single-impurity results from the approximation-free Diagrammatic Monte Carlo (DMC) method. Its simplicity allows for easy study of many problems that were previously unaccessible.