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arXiv:cond-mat/9911404 · Physical review. B, Condensed matter

Effective mass of the E⊗e Jahn-Teller polaron in comparison with the Holstein polaron

Yasutami Takada

Published Apr 1, 2000• 16 citations
arXivHTMLPDF

Abstract

Based on an exact expression for the self-energy of the Jahn-Teller polaron, we find that symmetry of pseudospin rotation makes the vertex correction much less effective than that for the Holstein polaron. This ineffectiveness brings about a smaller effective mass ${m}^{*}$ and a quantitatively different large-to-small polaron crossover, as examined by exact diagonalization in a two-site system. In the strong-coupling and antiadiabatic region, a rigorous analytic expression is found for ${m}^{*}.$

DOI
10.1103/physrevb.61.8631

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Based on an exact expression for the self-energy of the Jahn-Teller polaron, we find that symmetry of pseudospin rotation makes the vertex correction much less effective than that for the Holstein polaron. This ineffectiveness brings about a smaller effective mass m∗{m}^{*}m∗ and a quantitatively different large-to-small polaron crossover, as examined by exact diagonalization in a two-site system. In the strong-coupling and antiadiabatic region, a rigorous analytic expression is found for m∗.{m}^{*}.m∗.
We study the crossover from quasi-free electron to small polaron in the Holstein model for a single electron by means of both exact and self-consistent calculations in one dimension and on an infinite coordination lattice. We show that the crossover occurs when both strong coupling (λ > 1) and multiphonon (α 2 > 1) conditions are fulfilled leading to different relevant coupling constants (λ) in the adiabatic and (α 2 ) antiadiabatic region of the parameters space. We also show that the self-consistent calculations obtained by including the first electron-phonon vertex correction give accurate results in a sizeable region of the phase diagram well separated from the polaronic crossover.
The properties of the polaron and bipolaron are explored in the one-dimensional Jahn-Teller model with dynamical quantum phonons. The ground-state properties of the polaron and bipolaron are computed using a recently developed variational method. Dynamical properties of the ground state of a polaron are investigated by calculating the optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega}).$ Our numerical results suggest that the Jahn-Teller and Holstein polarons are similar. However, in the strong-coupling regime qualitative differences in $\ensuremath{\sigma}(\ensuremath{\omega})$ between the two models are found and discussed. The influence of the electron-phonon coupling and the electrostatic repulsion on the bipolaron binding energy, bipolaron masses, and correlation functions is investigated.
The crossover from quasi-free electron to small polaron in the Holstein model for a single electron is studied by means of both exact and self-consistent calculations in one dimension (1D) and on an infinite coordination lattice in order to understand the role of dimensionality in such a crossover. We show that a small polaron ground-state occurs when both strong coupling (λ>1) and multiphonon (α 2 >1) conditions are fulfilled, leading to different relevant coupling constants (λ) in adiabatic and (α 2 ) anti-adiabatic region of the parameter’s space. We also show that the self-consistent calculations obtained by including the first electron-phonon vertex correction give accurate results in a sizeable region of the phase diagram well separated from the polaronic crossover. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
We derive an effective polaronic interaction Hamiltonian, exact to second order in perturbation, for the spinless one-dimensional Holstein model. The small parameter is given by the ratio of the hopping term (t)(t)(t) to the polaronic energy $({g}^{2}{\ensuremath{\omega}}_{0})$ in the whole region of validity for our perturbation; however, the exception is the regime of extreme antiadiabaticity $(t∕{\ensuremath{\omega}}_{0}\ensuremath{\leqslant}0.1)$ and small electron-phonon coupling (g<1)(g<1)(g<1) where the small parameter is $t∕{\ensuremath{\omega}}_{0}$. We map our polaronic Hamiltonian onto a next-to-nearest-neighbor interaction anisotropic Heisenberg spin model. By studying the mass gap and the power-law exponent of the spin-spin correlation function for our Heisenberg spin model, we analyze the Luttinger liquid to charge-density wave transition at half filling in the effective polaronic Hamiltonian. We calculate the structure factor at all fillings and find that the spin-spin correlation length decreases as one deviates from half filling. We also extend our derivation of polaronic Hamiltonian to ddd dimensions.
We study the impact of the many-body effects on the phonon spectral function of Holstein polaron in one-dimension in the antiadiabatic regime by incorporating the contributions from the electron self-energy and vertex corrections within a weak-coupling approach that respects the charge-conserving Ward identity. We find that while the polaronic spectral weight is suppressed due to contribution from the electron self-energy, on the other hand, the same is enhanced due to contribution from the vertex corrections. While strength of both the contributions increases with increasing the wave vector ($\q$) of phonons, they nearly cancel each other for the small-$\q$ modes so that the polaronic spectral weight is weakly affected due to the many-body effects. For the large-$\q$ modes near the zone boundary, the net many-body correction is dominated by the contribution of the electron self-energy which increases faster in comparison to that of the vertex corrections with increasing the wave vector thereby resulting in a significant suppression of the polaronic spectral weight. We find that while the weak-coupling perturbative approach provides a reliable estimation of the impact of the many-body effects deep inside the antiadibatic regime, the renormalization of quasiparticle spectrum must be taken into account for an accurate estimation when the phonon energy approaches the electronic bandwidth.
A path-integral representation for the Jahn-Teller polaron (JTP) is constructed. It leads to a perturbation series that can be summed exactly by the diagrammatic quantum Monte Carlo technique. The ground-state energy, effective mass, spectrum, and density of states of the three-dimensional JTP are calculated with no systematic errors. The band structure of JTP is found to be similar to that of the Holstein polaron. The mass of JTP increases exponentially with the coupling constant. At small phonon frequencies, the spectrum of JTP is flat at large momenta, which leads to a strongly distorted density of states with a massive peak at the top of the band.