Statics and dynamics of the Holstein and Jahn-Teller polarons.

摘要

Based on a recently developed variational method, we explore the properties of the Holstein polaron (HP) on an infinite lattice in D dimensions, where 1 ≤ D ≤ 4. We present the most accurate ground state energy (with no small parameter) to date for polaron problems. It is found that the crossover to large effective mass of the higher-dimensional polaron is much sharper than the 1D polaron. The correlation length between the electron and phonons decreases significantly as the dimension increases. In addition, the E ⊗ e Jahn-Teller polaron is studied and compared with the HP. Only quantitative differences are found (when hopping matrices are diagonal) except that the optical conductivity sigma(o) in the antiadiabatic regime. We also calculate sigma(o) in the adiabatic regime and compare with experiments of colossal magnetoresistance manganites.; As for the dynamics, we study the formation process of a polaron quasiparticle from a bare electron. We calculate the distribution of the electron and phonon density, lattice deformation, the electron-phonon (el-ph) correlation functions in real space, and the exchange of energy between the electron and phonons as functions of time.; The polaron-formation time is considered as the dephasing time of the continuum of unbound-phonon excited states in the spectra, which depends on the phonon frequency and the el-ph coupling strength. As el-ph coupling increases, qualitative changes in polaron formation occur when the one-phonon polaron bound state is formed. It is found that a potential barrier between the quasi-free and heavy polaron state exists in both 2D and 3D. Our results provide insight into fast-optics experiments on polarizable media.; Finally, finite-temperature transport of the HP is numerically studied based on quantum coherent dynamics. In the strong-coupling regime, we obtain a thermally enhanced Drude weight with an activation energy E a ≈ o0. A semiclassical picture suggests that thermal fluctuation of the lattice could localize all the eigenstates at high temperature, so the localized polaron can only diffuse in concord with lattice motion. As a result the resistivity is proportional to temperature and it can exceed the Ioffe-Regal limit without saturation. In addition, the temperature dependence of sigma(o) is calculated and it agrees well with experiments.