Semiclassical approach to calculating the influence of local lattice fluctuations on electronic properties of metals

Abstract

We propose a semiclassical approach based on the dynamical mean-field theory to treat the interactions of electrons with local lattice fluctuations. In this approach the classical ͑static͒ phonon modes are treated exactly, whereas the quantum ͑dynamical͒ modes are expanded to the second order and give rise to an effective semiclassical potential. We determine the limits of validity of the approximation, and demonstrate its usefulness by calculating the temperature dependent resistivity in the Fermi-liquid to polaron crossover regime ͑leading to ''saturation behavior''͒ and also isotope effects on electronic properties including the spectral function, resistivity, and optical conductivity, problems beyond the scope of conventional diagrammatic perturbation theories.

Semiclassical action based on dynamical mean-field theory describing electrons interacting with local lattice fluctuations

“…This give rise to interesting isotope effects on electronic properties as discussed in Ref. 15 and in Sec. V.…”

“…For the Holstein model this has been done in Ref. 15. The idea is to expand the difference S eff ϪS class to second order in (1Ϫ␦ nm )W( n Ϫ m ), i.e., to leading order in the nondiagonal part of the electron-phonon interaction.…”

“…On the other hand, semianalytical techniques have the advantage of being instructive and of being extensible to more realistic model systems of conduction-electrons coupling to local lattice distortions including may be even electron-electron interactions. These approaches [12][13][14][15] rely on a detailed analysis of the effective action based on the dynamical mean-field theory.…”

“…Here, we extend a ''semiclassical'' approach 15 recently introduced by one of the authors to general models of electrons in degenerate orbital states coupling to Jahn-Teller distortions. The classical ͑static͒ phonon modes are treated exactly and the quantum ͑dynamical͒ modes are expanded to second order.…”

Benchmarkings for a semiclassical impurity solver for dynamical-mean-field theory: Self-energies and magnetic transitions of the single-orbital Hubbard model

“…Including the quantum fluctuation to recover the correct Fermi-liquid behavior is not easy. 32,43,44 Although, it is not exact, it will be shown below that the semiclassical method gives good estimates of the important physical quantities.…”