Single Polaron Properties in Different Electron Phonon Models

Physical Review B, 2005

The polaron features due to electron-phonon interactions with different coupling ranges are investigated by adopting a variational approach. The ground-state energy, the spectral weight, the average kinetic energy, the mean number of phonons, and the electron-lattice correlation function are discussed for the system with coupling to local and nearest neighbor lattice displacements comparing the results with the long range case. For large values of the coupling with nearest neighbor sites, most physical quantities show a strong resemblance with those obtained for the long range electron-phonon interaction. Moreover, for intermediate values of interaction strength, the correlation function between electron and nearest neighbor lattice displacements is characterized by an upturn as function of the electron-phonon coupling constant.

European Physical Journal B, 2005

Polaron formation is investigated in a one-dimensional chain by taking into account both the local Holstein and the non-local SSH electron-phonon interactions. The study of the adiabatic regime points out that the combined effects of the two interactions are important mainly in the weak coupling regime. Thus, using the weak-coupling perturbation theory, spectral weights, effective masses, polaronic phase-diagram, and band structures are discussed. Contrarily to what happens in the Fröhlich and Holstein models, we find that the ratio between the coherent spectral weight and the mass renormalization ratio is greater than 1. Moreover, we show that the non-local electron-phonon interaction is responsible for the largest deviations of the band structure from the cosine shape of the free energy band.

Journal of Superconductivity and Novel Magnetism, 2012

When an electron interacts with phonons, the electron can exhibit either free electron-like or polaron-like properties. The latter tends to occur for very strong coupling, and results in a phonon cloud accompanying the electron as it moves, thus raising its mass considerably. We summarize this behaviour for the Holstein model in one, two and three dimensions, and note that the crossover occurs for fairly low coupling strengths compared to those attributed to real materials exhibiting conventional superconductivity.

Physical Review B, 2005

The energy of two-electron systems ͓exchange-coupled pairs of paramagnetic centers ͑D − centers͒ and bipolarons͔ is calculated for various distances between paramagnetic centers with regard to polaron effects for arbitrary coupling of electrons with a phonon field. Interaction of electrons with a phonon field is found by the Buymistrov-Pekar method. The calculations are made with a wave function ͑WF͒ in the form of expansion in Gaussians. Both the electronic correlations ͑direct dependence of the WF of a system on the interelectronic distance͒ and the permutation symmetry of the two-electron WF are taken into account. The lowest singlet 1 ⌺ g + and triplet 3 ⌺ u + terms are considered. Effects of electronic correlations are exemplified by the dependence of the energy and spatial distribution of the bipolaron WF on the distance between the centers of polaron polarization wells. A bipolaron corresponding to a two-center configuration is energetically unstable. The only minimum on the curve for the energy dependence of two polarons on the distance between the centers of their polarization wells corresponds to a one-center bipolaron configuration. For AgBr and AgCl we present the energies of the lowest singlet and triplet states of F 2 centers ͑ 1 ⌺ g and 3 ⌺ u terms͒ and those for 1 g and 1 u terms of F 2 + centers as a function of the distance between them ͑with a graph of various contributions into these energies͒. Control calculations performed for a hydrogen molecule with the use of a variational function suggested in the work yield the energies of the singlet and triplet states equal to −1.17416 and −0.78315 a.u. respectively, the equilibrium internuclear distance corresponds to R m = 1.4011 a.u. The contribution of phonons into the exchange interaction between paramagnetic centers has antiferromagnetic character. The exchange interaction caused by phonons is comparable in the order of magnitude with Coulomb exchange.

Physical Review B

We use the variational exact diagonalization to investigate the single polaron properties for four different dual models, combining a short-range off-diagonal (Peierls) plus a longer-range diagonal (Holstein or breathingmode) coupling. This allows us to investigate the sensitivity of various polaron properties both to the range of the diagonal coupling and to the specific diagonal coupling chosen. We find strong sensitivity to the range for all dual models as the adiabatic limit is approached; however, considerable sensitivity is observed for some quantities even in the antiadiabatic limit. Also, strong dependence of the results on the specific form of the diagonal coupling is observed everywhere in the parameter space. Taken together, these results suggest that a careful consideration must be given to the specific coupling and its proper range, when quantitative comparisons with experiments are sought.

Journal of Physics: Condensed Matter, 2004

The polaron features for long-range electron-phonon interaction are investigated by extending a variational approach previously proposed for the study of systems with local coupling. The ground-state spectral weight, the average kinetic energy, the mean number of phonons, and the electron-lattice correlation function are discussed for a wide range of model parameters focusing on the adiabatic regime and comparing the results with the short-range case (Holstein model). A strong mixing of electronic and phononic degrees of freedom for small values of the electron-phonon coupling constant is found in the adiabatic case due to the long-range interaction. Finally a polaron "phase diagram" is proposed.

2022

Monodeep Chakraborty, Sankeerth S. Narayan, Vigneshwaran R., and Mona Berciu 5 Centre for Quantum Science and Technology, Chennai Institute of Technology, Chennai, India-600037 Computer Science Engineering Department, Chennai Institute of Technology, Chennai, India-600037 Mechatronics Engineering Department, Chennai Institute of Technology, Chennai, India-600037 Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, Canada, V6T 1Z1 Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia, Canada, V6T 1Z4 (Dated: April 21, 2022)

Solid State Communications, 1993

In systems with strong electron-lattice coupling neither the electrons nor the phonons are any longer well defined quasi particles. What evolves ate new quasi particles : the small polarons. Electrons and phonons can be considered as the excitations of small polarons and can be tested by spectroscopic means. In principle small polarons can move through the lattice in a coherent fashion forming Bloch like states. Direct experimental verification of such states has remained till now ambiguous. We show here that an unequivocal proof for itinerant polarons is the appearance of a new branch of lattice modes. These modes correspond to the motion of the polaron induced local lattice deformations surrounding the charge carriers. They are expected to have large amplitudes and low frequencies as compared to the intrinsic optical modes in the system. These new modes should be detectable by inelastic neutron scattering and are expected to have a very specific lineshape quite distinct from ordinary phonons.

Journal of Physics: Condensed Matter, 1994

Polaron effects on the binding energy of a hydrogenic impurity in a semiconductor quantum well A Ercelebi and G Sualp-Recent citations Energy levels of magneto-optical polaron in spherical quantum dot-Part 1: Strong coupling A. J. Fotue et al-Electric and magnetic optical polaron in quantum dot-Part 1: strong coupling A. J. Fotue et al-Electromagnetic weak coupling optical polaron and temperature effect in quantum dot M. Tiotsop et al

Physics Letters A, 2000

We analyze electron-phonon correlation functions measured in 1D polaron ground states of the Holstein Hamiltonian using the Global-Local variational method. The spatial collapse of electron-phonon correlations is found to occur in concert with transition behavior in other polaron properties, providing mutually confirming evidence for a self-trapping line in 1D. The spatial extent of electron-phonon correlations is used to quantify polaron size, and is analyzed over a wide range of parameters. Distinct scaling behaviors are found to be characteristic of the region below the self-trapping transition and above it, contrary to some widely-held expectations and leading naturally to the notion of the polaron size as an order parameter for a self-trapping transition that becomes critical in the adiabatic limit. PACS numbers: 71.38.+i, 71.15.-m, 71.35.Aa, 72.90.+y 2 0 J = 9 J = 7 J = 6 J = 5 J = 4 J = 3 J = 2 J = 1 J = 0.5 J = 0.25