Holstein polaron: The effect of coupling to multiple-phonon modes

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.

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)

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.

Physica B-condensed Matter, 2009

The transition from band to hopping conductivity of small polaron is examined within Holstein's molecular crystal model. The conditions under which each of these mechanisms prevail are formulated in terms of the values of the coupling constant S and adiabatic parameter B. Particular attention was paid to the possible influence of the polaron induced modification of phonon spectrum.

Journal of Physics: Condensed Matter, 2004

An analytical variational method is applied to the molecular Holstein Hamiltonian in which the dispersive features of the dimension dependent phonon spectrum are taken into account by a force constant approach. The crossover between a large and a small size polaron is monitored, in one, two and three dimensions and for different values of the adiabatic parameter, through the behavior of the effective mass as a function of the electron-phonon coupling. By increasing the strength of the inter-molecular forces the crossover becomes smoother and occurs at higher e-ph couplings. These effects are more evident in three dimensions. We show that our Modified Lang-Firsov method starts to capture the occurence of a polaron self-trapping transition when the electron energies become of order of the phonon energies. The self-trapping event persists in the fully adiabatic regime. At the crossover we estimate polaron effective masses of order ∼ 5 − 40 times the bare band mass according to dimensionality and value of the adiabatic parameter. Modified Lang-Firsov polaron masses are substantially reduced in two and three dimensions. There is no self-trapping in the antiadiabatic regime.

Physical Review B, 2006

We study the effects of lattice type on polaron dynamics using a continuous-time quantum Monte-Carlo approach. Holstein and screened Fröhlich polarons are simulated on a number of different Bravais lattices. The effective mass, isotope coefficients, ground state energy and energy spectra, phonon numbers, and density of states are calculated. In addition, the results are compared with weak and strong coupling perturbation theory. For the Holstein polaron, it is found that the crossover between weak and strong coupling results becomes sharper as the coordination number is increased. In higher dimensions, polarons are much less mobile at strong coupling, with more phonons contributing to the polaron. The total energy decreases monotonically with coupling. Spectral properties of the polaron depend on the lattice type considered, with the dimensionality contributing to the shape and the coordination number to the bandwidth. As the range of the electron-phonon interaction is increased, the coordination number becomes less important, with the dimensionality taking the leading role.

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.

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, 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.

Journal of Luminescence, 1994

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