Numerical study of the E⊗e Jahn-Teller polaron and bipolaron

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.

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.

Arxiv preprint arXiv:0904.1711, 2009

We investigate the bipolaronic crossover and the pairing transition for a two-orbital model with Jahn-Teller coupling to a two-fold degenerate phonon mode. The evolution from weak to strong coupling is reminiscent of the behavior of the single-band Holstein model: The polaron crossover in which the electrons and phonons become strongly entangled occurs for a weaker coupling than the binding of bipolarons, which gives rise to a metal-insulator transition. Interestingly, a single bipolaronic transition takes place also when the two bands have significantly different bandwidths, as opposed to the case of repulsive Hubbard-like interactions for which an orbital-selective Mott transition has been reported. This behavior is related to the inter-orbital nature of the Jahn-Teller coupling.

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)

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.

Intrinsic "local textures" are becoming a leitmotiv of complex electronic materials, including high-T c superconductors. Here we discuss signatures of nonlinear dynamics in the context of small polarons through various correlation functions which measure correlated structural and optical properties of a system. It is shown that energy-resolved correlation functions can be used to probe length and time scales in a unique fashion. These methods are applied to a polaron-tunneling problem which not only serves as a prototype for nonlinear and nonadiabatic behaviour in the presence of coupled electronic and lattice degrees of freedom, but may also be relevant to describing aspects of local electronic and structural dynamics in high-T c superconducting materials.

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.

Physical Review B, 2004

We introduce a variational wave-function to study the polaron formation when the electronic transfer integral depends on the relative displacement between nearest-neighbor sites giving rise to a non-local electron-phonon coupling with optical phonon modes. We analyze the ground state properties such as the energy, the electron-lattice correlation function, the phonon number and the spectral weight. Variational results are found in good agreement with analytic weak-coupling perturbative calculations and exact numerical diagonalization of small clusters. We determine the polaronic phase diagram and we find that the tendency towards strong localization is hindered from the pathological sign change of the effective next-nearest-neighbor hopping.

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.

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

Physical Review B, 2005

We present the numerically exact ground state energy, effective mass, and isotope exponents of a one-dimensional lattice polaron, valid for any range of electron-phonon interaction, applying a continuous-time Quantum Monte Carlo (QMC) technique in a wide range of coupling strength and adiabatic ratio. The QMC method is free from any systematic finite-size and finite-time-step errors. We compare our numerically exact results with analytical weak-coupling theory and with the strongcoupling 1/λ expansion. We show that the exact results agree well with the canonical Fröhlich and Holstein-Lang-Firsov theories in the weak and strong coupling limits, respectively, for any range of interaction. We find a strong dependence of the polaron dynamics on the range of interaction. An increased range of interaction has a similar effect to an increased (less adiabatic) phonon frequency: specifically, a reduction in the effective mass.

2m and the Born-Oppenheimer HamiltonianĤ BO (R) [4,5].Ĥ BO (R) depends on the nuclear configurationR, and for a fixed R, ⟨R|Ĥ BO (R) |R⟩ =Ĥ BO (R) is an electronic operator. This is particularly useful in the adiabatic regime (slow phonons), where the change in phonon coordinates 4.1 Publication: Finite-temperature density-matrix renormalization group method for electron-phonon systems: Thermodynamics and Holstein-polaron spectral functions 43 ... 4.1 Publication: Finite-temperature density-matrix renormalization group method for electronphonon systems: Thermodynamics and Holsteinpolaron spectral functions

The Journal of Chemical Physics, 1997

In this paper we revisit from a contemporary perspective a classic problem of polaron theory in one dimension using a new variational approach generalizing that of Toyozawa, based on delocalized trial states including mixed gobal and local exciton-phonon correlations. Polaron structure is represented by variational surfaces giving the optimal values of the complete set of exciton and phonon amplitudes for every value of the joint exciton-phonon crystal momentum. Characteristic small polaron, large polaron, and nearly free phonon structures are identified, and the manner in which these compete and/or coexist is examined in detail. Through such examination, the parameter space of the problem is mapped, with particular attention given to problematic areas such as the highly quantum mechanical weak-coupling regime, the highly nonlinear intermediate-coupling regime, and to the self-trapping transition that may be said to mark the onset of the strong-coupling regime. Complete energy bands are presented in illustrative cases, and the principal trends in the ground-state energy, polaron bandwidth, and effective mass are identified. The internal structure of our variational Bloch states is examined for qualities that might reflect the typical characteristics of solitons, finding some intriguing qualitative comparisons, but little that bears close scrutiny.

2013

Noninteracting itinerant electrons in a solid occupy Bloch one-electron states. Phonons are collective vibrational excitations of the crystal lattice. The basic electron-phonon (EP) interaction process is the absorption or emission of a phonon by the electron with a simultaneous change of the electron state. From