Two-Site Polaron Problem: A Perturbation Approach With Variational Basis States

Das, Anindita; Chatterjee, Jayita

doi:10.1142/s0217979299004070

Cited by 14 publications

(38 citation statements)

References 11 publications

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“…4(a-d) we have shown the ground-state wave functions of the d oscillator for different values of e-ph coupling for both the ordered and disordered cases considering that the electron is located at site 1. The results for the ordered case have been discussed in previous works [15,20,22] the additional shoulder, which appears (at the right side of the main peak) for the ordered case, is absent in presence of disorder; (iii) for strong coupling (g + = 2.0) though the wavefunction around the main peak is identical for both cases, the additional small broad peak, observed for the ordered case, is not found for the disordered case. The first feature indicates that the on-site polaronic deformation is larger for the disordered case; while the second feature may be due to the reduced retardation effect.…”

Section: Resultsmentioning

confidence: 52%

“…Now one has to make a choice of λ so that the perturbation corrections are small and perturbative expansion becomes convergent. Here we will follow the procedure of our previous work [15] to find out the variational phonon basis as a function of e-ph coupling. Minimizing the unperturbed ground state energy E (0) 0 with respect to λ we obtain…”

Section: Formalismmentioning

confidence: 99%

“…For convenience we will refer to the difference in site energies as disorder strength because it partly mimics the role of disorder in larger systems. Another aspect of choosing a two-site Holstein model is that almost exact results may be obtained for such a system with the perturbation method [15] using a modified Lang-Firsov (MLF) basis [16]. For the Holstein model the interaction is very short-ranged and the essential physics relating polaronic behavior for a larger system is similar to that in a two-site system.…”

Section: Introductionmentioning

confidence: 99%

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Effect of different site energies on polaronic properties

Chatterjee¹,

Das²

2005

Eur. Phys. J. B

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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 single polaron Holstein model is studied in presence of a difference in bare site energies (ǫ d =ǫ2-ǫ1). The polaronic ground-state wave function is calculated up to the fifth order of perturbation. The effect of ǫ d (acts as a site-energy disorder) on the polaron crossover, polaronic kinetic energy, oscillator wavefuncion and polaron localization are studied. Considering a double-exchange Holstein model with finite ǫ d , role of disorder on the properties of the double-exchange system is also discussed.

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Section: Resultsmentioning

confidence: 52%

Section: Formalismmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effect of different site energies on polaronic properties

Chatterjee¹,

Das²

2005

Eur. Phys. J. B

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“…1 shows the phase diagram for the four possible spin orders for our system, in the g − vs J plane. To study the polaronic character one calculates the static correlation functions n 1 u 1 0 and n 1 u 2 0 , where u 1 and u 2 are the lattice deformations at sites 1 and 2 respectively, produced by an electron at site 1 [8]. The locations of the large polaron region (A) and the small polaron region (B) are indicated in the g − vs J phase digram ( Fig.…”

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confidence: 99%

Polaronic heat capacity in the Anderson-Hasegawa model

2003

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An exact treatment of the Anderson -Hasegawa two -site model, incorporating the presence of superexchange and polarons, is used to compute the heat capacity. The calculated results point to the dominance of the lattice contribution, especially in the ferromagnetic regime. This behavior is in qualitative agreement with experimental findings. 1 The Anderson-Hasegawa (AH) model [1] is a two-site realization of the basic idea of double -exchange (DE) proposed by Zener [2] almost fifty years ago. In the DE scenario a localized spin is visualized to be strongly 'Hund's rule' coupled to an itinerant spin at the same site governed by strength J H , whereas the itinerant spin can tunnel from site to site accompanied by a 'hopping integral' t. Because of large J H the itinerant spin is polarized along the localized spin, and as it hops to a neighboring site, it carries with it the memory of its spin polarization, thereby polarizing the neighboring local spin as well. Thus transport is correlated with spin ordering of localized moments, leading to concomitant metal-insulator transition and magnetic ordering.

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“…In this work we will follow a method based on variational phonon basis [15] which is promising for Holstein [16][17][18] and related models [19] to predict the correct results up to intermediate range of hopping ðtÞ ðtpo 0 where o 0 is the phonon frequency) [17]. The importance of a variational phonon basis in predicting accurate results has been proved for a two-site system over the entire range of e-ph couplings [17]. Our previous study [19] on the 'two-site' DE model with a single polaron as a function of e-ph couplings reveals that the FM to AFM crossover does not coincide always with the polaron crossover.…”

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confidence: 99%

Role of the superexchange interaction in magnetic transition and polaron crossover

Chatterjee¹,

Das²

2004

Physica B: Condensed Matter

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The Hubbard-Holstein model is studied including double-exchange interaction and superexchange interaction using a variational phonon basis obtained through the modified Lang-Firsov transformation followed by the squeezing transformation. The kinetic energy, polaron crossover and magnetic transition are investigated as a function of electron-phonon (e-ph) coupling and electron concentration for different values of antiferromagnetic superexchange interaction ðJÞ between the core spins. The polaron crossover, magnetic transition and the suppression of ferromagnetic transition with J are discussed for the model. rRecently, the interest in the double-exchange (DE) model [1] has grown considerably with the discovery of very large negative colossal magnetoresistance (CMR) [2] and anomalous magnetotransport properties in doped manganites [3], namely in R 1Àx A x MnO 3 (where R ¼ La; Pr and A ¼ Ca; Sr; Ba). Ferromagnetism (FM) in these compounds (for xB0:220:4) is believed to be due to the DE mechanism which operates when local Mn-ion spins are strongly coupled by Hund's rule with the spins of the itinerant electrons occupying a narrow band. However, the experimental results [3] in manganites, namely the sharp change in resistivity near T c and the physics of CMR, cannot be explained by the DE alone [4]. Millis suggested the lattice polaron effects due to strong electronphonon (e-ph) interaction as a necessary extension [5]. R. oder et al.[6] also examined the combined effect of e-ph interaction and DE on T c using the variational wave function techniques. In fact, the contribution of the lattice polaron to carrier mobility was pointed out earlier by Goodenough [7]. Several theoretical models have been proposed based on lattice-carrier coupling [6,[8][9][10][11]. Many experiments [12] indicate evidence of strong lattice-electron coupling in manganese oxides [12] which shapes the properties of manganites crucially. Moreover, small to large polaron crossover ARTICLE IN PRESS

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Two-Site Polaron Problem: A Perturbation Approach With Variational Basis States

Cited by 14 publications

References 11 publications

Effect of different site energies on polaronic properties

Effect of different site energies on polaronic properties

Polaronic heat capacity in the Anderson-Hasegawa model

Role of the superexchange interaction in magnetic transition and polaron crossover

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