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Role of disorder in the two-site Holstein model with double exchange

Jayita Chatterjee

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

Using the perturbation method based on a variational phonon basis obtained by the modified Lang-Firsov (MLF) transformation, the two-site double-exchange Holstein model is studied in presence of a finite difference in bare site energies (ǫd=ǫ2-ǫ1). The polaronic ground-state wave function is calculated up to the fifth order of perturbation. The effect of ǫd (acts as a site-energy disorder) on the polaron crossover, polaronic kinetic energy and polaron localization are studied. Role of disorder on the properties of the double-exchange system is discussed.

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Using the perturbation method based on a variational phonon basis obtained by the modified Lang-Firsov (MLF) transformation, the two-site double-exchange Holstein model is studied in presence of a finite difference in bare site energies (ǫd=ǫ2-ǫ1). The polaronic ground-state wave function is calculated up to the fifth order of perturbation. The effect of ǫd (acts as a site-energy disorder) on the polaron crossover, polaronic kinetic energy and polaron localization are studied. Role of disorder on the properties of the double-exchange system is discussed.
The two-site two-electron Holstein model is studied within a perturbation method based on a variational phonon basis obtained through the modified Lang-Firsov (MLF) transformation. The ground-state wave function and the energy are found out considering up to the seventh and eighth order of perturbation, respectively. The convergence of the perturbation corrections of different orders to the ground state energy as well as to different correlation functions are investigated. The kinetic energy and the correlation functions involving charge and lattice deformations are studied as a function of electron-phonon (eee-ph) coupling for different values of adiabaticity parameter and Coulomb repulsion. The simultaneous effect of the eee-ph coupling and Coulomb repulsion on the kinetic energy shows interesting features.
The two-site single-polaron problem is studied within perturbative expansions using different standard phonon bases obtained through Lang-Firsov (LF), modified LF, and modified LF transformations with squeezed phonon states. The role of these convergent expansions using the above prescriptions in lowering the energy and in determining the correlation functions are compared for different values of the coupling strength. The single-electron energy, oscillator wave functions, and correlation functions are calculated for the same system. The applicability of different phonon bases in different regimes of the coupling strength, as well as in different regimes of hopping, is also discussed.
We look for an analytical method which can describe the Holstein model over the entire region of electron–phonon (e–ph) coupling strength. Considering a toy model of two sites the perturbation expansions are developed for the Holstein Hamiltonian using different standard phonon bases. It is found that the modified Lang Firsov phonon basis shows satisfactory convergence for almost the entire range of e–ph coupling from the antiadiabatic limit to the intermediate range of hopping. This method is used to study the magnetic transition and the small to large polaron crossover in a double exchange model with e–ph interaction. Implications of the results in the context of manganites are discussed.
The ground state and finite-temperature properties of polarons are studied considering a two-site and a four-site Holstein model by exact diagonalization of the Hamiltonian. The kinetic energy, Drude weight, correlation functions involving charge and lattice deformations, and the specific heat have been evaluated as a function of electron–phonon (e–ph) coupling strength and temperature. The effects of site diagonal disorder on the above properties have been investigated. The disorder is found to suppress the kinetic energy and the Drude weight, and reduces the spatial extension of the polaron. Increasing temperature also reduces the kinetic energy, Drude weight and the polaron size when the e–ph interaction is weak or intermediate. For strong coupling the effect of temperature is small but opposite. For sufficiently strong coupling the kinetic energy arises mainly from the incoherent hopping processes owing to the motion of electrons within the polaron and is almost independent of the disorder strength. The specific heat shows a peak in the intermediate range of coupling, and the peak is suppressed in the presence of disorder. From the coherent and incoherent contributions to the kinetic energy, the temperature above which the incoherent part dominates is determined as a function of e–ph coupling strength.