Dynamical properties of small polarons

Abstract

On the basis of the two-site polaron problem, which we solve by exact diagonalization, we analyze the spectral properties of polaronic systems in view of discerning localized from itinerant polarons and bound polaron pairs from an ensemble of single polarons. The corresponding experimental techniques for that concern photoemission and inverse photoemission spectroscopy. The evolution of the density of states as a function of concentration of charge carriers and strength of the electron-phonon interaction clearly shows the opening up of a gap between single-polaronic and bipolaronic states, in analogy to the Hubbard problem for strongly correlated electron systems. In studying the details of the intricately linked dynamics of the charge carriers and of the molecular deformations which surround them, we find that in general the dynamical delocalization of the charge carriers helps to strengthen the phase coherence for itinerant polaronic states, except for the crossover regime between adiabatic and antiadiabatic small polarons. The crossover between these two regimes is triggered by two characteristic time scales: the renormalized electron hopping rate and the renormalized vibrational frequency becoming equal. This crossover regime is then characterized by temporarily alternating self-localization and delocalization of the charge carriers which is accompanied by phase slips in the charge and molecular deformation oscillations and ultimately leads to a dephasing between these two dynamical components of the polaron problem. We visualize these features by a study of the temporal evolution of the charge redistribution and the change in molecular deformations. The spectral and dynamical properties of polarons discussed here are beyond the applicability of the standard Lang-Firsov approach to the polaron problem.

Random resistivity network calculations for cuprate superconductors with an electronic phase separation transition

“…(2)), we can consider the grains as isolated entities with very weak intergrain coupling and a typical Fermi energy of a grain is much smaller than the bulk Debye energy, the so called anti adiabatic regime [44].…”

Polaron formation for nonlocal electron-phonon coupling: A variational wave-function study

“…It is worth to note that traditional variational approaches to the Holstein polaron problem uses the localized state (11) where only the on-site operator U (i) k (n) is applied. Thus we introduce in the expression of the trial wave-function the nearest-neighbor displacement operators U (i) k (n + 1) and U (i) k (n − 1), in order to take into account the dependence of the hopping integral on the relative distance between two adjacent ions.…”

“…In particular it has been shown that the self-trapping process, which lead to the formation of polarons, is not a phase transition, but just a continuous crossover with no broken symmetry. 7 In the case of the Holstein model, 8 where quantum vibrations interact locally with the electrons, the crossover from large to small polaron has been extensively studied by several numerical techniques [9][10][11][12][13][14][15] and variational approaches. [16][17][18] In particular all the ground state properties of the Holstein model can be described with great accuracy by a variational approach 18 based on a linear superposition of Bloch states that describe weak and strong coupling polaron wave functions.…”

Spectral properties of the 2D Holstein polaron

“…In the weak-coupling (adiabatic) limit, one expects (from scaling arguments) a quasi-free electron behaviour for D > 1, while in a 1D system the carrier state becomes polaronic at arbitrary small λ ("large" polaron). Previous exact diagonalization (ED) work has concentrated on the 1D case [8][9][10][11][12]21,[13][14][15][16][17], where, however, the calculations were limited to either very small clusters, rather weak EP coupling (λ < 1) or to the adiabatic limit (ω o = 0). On the other hand, the most interesting effects will be expected if the characteristic electronic and phononic energy scales are not well separated (λ ∼ 1; α ∼ 1).…”