Mass of a lattice polaron from an extended Holstein model using the Yukawa potential

Abstract

Renormalization of the mass of an electron is studied within the framework of the Extended Holstein model at strong coupling regime and nonadiabatic limit. In order to take into account an effect of screening of an electron-phonon interaction on a polaron it is assumed that the electronphonon interaction potential has the Yukawa form and screening of the electron-phonon interaction is due to the presence of other electrons in a lattice. The forces are derived from the Yukawa type electron-phonon interaction potential. It is emphasized that the early considered screened force of Refs. [7,18,19,22] is a particular case of the force deduced from the Yukawa potential and is approximately valid at large screening radiuses compared to the distances under consideration. The Extended Holstein polaron with the Yukawa type potential is found to be a more mobile than polaron studied in early works at the same screening regime.A model of a polaron with a long-range "density-displacement" type force was introduced by Alexandrov and Kornilovitch in Ref. [1]. The model by itself represents an extension of the Fröhlich polaron model [2] to a discrete ionic crystal lattice or extension of the Holstein polaron model [3] to a case when an electron interacts with many ions of a lattice with longer ranged electron-phonon interaction. Subsequently, the model was named as the extended Holstein model (EHM) [4]. The model was introduced in order to mimic high − T c cuprates, where the in-plane (CuO 2 ) carriers are strongly coupled to the c-axis polarized vibrations of the apical oxygen ions [5]. In the last decade the model was successfully applied to cuprates [4,[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] as well as to semiconducting polymers [25,26]. Kornilovitch in Ref.[6] studied the ground state energy, effective mass and polaron spectrum with the help of continuous-time Quantum Monte Carlo algorithm. An anisotropy of polaron's mass due to electron-phonon interaction, groundstate dispersion and density of states of a EHM polaron were studied in Ref. [7] and Ref.[8], respectively. Fehske, Loos and Wellein [4] investigated the electron-lattice correlations, singleparticle spectral function and optical conductivity of a polaron within the EHM in the strong and weak coupling regimes by means of an exact Lancroz diagonalization method. Other properties of EHM, such as the ground state spectral weight, the average kinetic energy and the mean number of phonons were studied in [14-16] by means of the variational and Quantum Monte Carlo simulation approaches. The work [17] extended the EHM to the adiabatic limit. The effect of the different type polarized vibrations of ions and the arrangement of the ions on mass of a po-

Two-dimensional Yukawa interactions from nonlocal Proca quantum electrodynamics

“…First, let us write the Feynman rules of Eq. (26) in Euclidean space. The free electronpropagator reads…”

“…(16), would imply a renormalized mass parameter in the reduced model, given by Eq. (26). Within the Landau gauge λ ¼ ∞, the corrected gauge-field propagator with the insertion of polarization tensor reads…”

“…Then, after dimensional reduction, the corresponding 3D theory is still the same as in Eq. (26) and that it is gauge invariant.…”

“…If we now couple the PQED model, to a Higgs field in the broken phase, such that a massive term is generated to the gauge field, this changes the propagator from 1=ð2 ffiffiffiffiffi p 2 p Þ to 1=ð2 ffiffiffiffiffi p 2 p þ mÞ, which clearly shows that we shall obtain a different model from the one associated to Eq. (26). The potential is now given by a combination of Coulomb and Keldysh [34] The corrected electron propagator S F is…”

“…Motivated by this well-known result, we shall use the paradigm of including a mass term, for the intermediate particle, in order to generate a short-range interaction, i.e., the Yukawa potential in the plane. This potential has been applied to describe bound states [24,25], electron-ion interactions in a crystal [26], and interactions between dark energy and dark matter [27] among others. Nevertheless, a planar quantum-field theory accounting for this interaction, for both static and dynamical regime, has not been derived yet.…”