Showing papers on "Bipolaron published in 2018"
TL;DR: It is found that bipolaron formation typically requires strong impurity interactions beyond the validity of more commonly used weak-coupling approaches that lead to local Yukawa-type interactions.
Abstract: Mobile impurities in a Bose-Einstein condensate form quasiparticles called polarons. Here, we show that two such polarons can bind to form a bound bipolaron state. Its emergence is caused by an induced nonlocal interaction mediated by density oscillations in the condensate, and we derive using field theory an effective Schr\"odinger equation describing this for an arbitrarily strong impurity-boson interaction. We furthermore compare with quantum Monte Carlo simulations finding remarkable agreement, which underlines the predictive power of the developed theory. It is found that bipolaron formation typically requires strong impurity interactions beyond the validity of more commonly used weak-coupling approaches that lead to local Yukawa-type interactions. We predict that the bipolarons are observable in present experiments, and we describe a procedure to probe their properties.
134 citations
TL;DR: Using numerical simulations and analytical arguments, it is shown that strongly bound yet very light bipolarons appear for strong Peierls coupling, and these properties result from the specific form of the phonon-mediated interaction, which is of "pair hopping" instead of regular density-density type.
Abstract: It is widely accepted that phonon-mediated high-temperature superconductivity is impossible at ambient pressure, because of the very large effective masses of polarons or bipolarons at strong electron-phonon coupling. Here we challenge this belief by showing that strongly bound yet very light bipolarons appear for strong Peierls coupling. These bipolarons also exhibit many other unconventional properties; e.g., at strong coupling there are two low-energy bipolaron bands that are stable against strong Coulomb repulsion. Using numerical simulations and analytical arguments, we show that these properties result from the specific form of the phonon-mediated interaction, which is of "pair hopping" instead of regular density-density type. This unusual effective interaction is bound to have nontrivial consequences for the superconducting state expected to arise at finite carrier concentrations and should favor a large critical temperature.
55 citations
TL;DR: Evidence is provided that the rare-earth nickelates RNiO3 is a polaronic liquid that freezes into the insulating state, suggesting that changes in carrier concentration drive the MIT through aPolaronic mechanism, where the (bi)polaron liquid freezes intoThe insulating phase across the MIT temperature.
Abstract: Many-body effects produce deviations from the predictions of conventional band theory in quantum materials, leading to strongly correlated phases with insulating or bad metallic behavior. One example is the rare-earth nickelates RNiO3, which undergo metal-to-insulator transitions (MITs) whose origin is debated. Here, we combine total neutron scattering and broadband dielectric spectroscopy experiments to study and compare carrier dynamics and local crystal structure in LaNiO3 and NdNiO3. We find that the local crystal structure of both materials is distorted in the metallic phase, with slow, thermally activated carrier dynamics at high temperature. We further observe a sharp change in conductivity across the MIT in NdNiO3, accompanied by slight differences in the carrier hopping time. These results suggest that changes in carrier concentration drive the MIT through a polaronic mechanism, where the (bi)polaron liquid freezes into the insulating phase across the MIT temperature.
47 citations
TL;DR: In this paper, the two-dimensional Holstein-Hubbard model is studied by means of continuous-time quantum Monte Carlo simulations and the critical temperature of the charge-density-wave transition is determined as a function of coupling strength, phonon frequency, and Hubbard repulsion.
Abstract: The two-dimensional Holstein-Hubbard model is studied by means of continuous-time quantum Monte Carlo simulations. Using renormalization-group-invariant correlation ratios and finite-size extrapolation, the critical temperature of the charge-density-wave transition is determined as a function of coupling strength, phonon frequency, and Hubbard repulsion. The phase transition is demonstrated to be in the universality class of the two-dimensional Ising model and detectable via the fidelity susceptibility. The structure of the ground-state phase diagram and the possibility of a bipolaronic metal with a single-particle gap above ${T}_{c}$ are explored.
41 citations
01 Jan 2018
TL;DR: In this article, it was shown that strongly bound yet very light bipolarons appear for strong Peierls coupling, and these bipolarons also exhibit many other unconventional properties; e.g., at strong coupling there are two low-energy bipolaron bands that are stable against strong Coulomb repulsion.
Abstract: It is widely accepted that phonon-mediated high-temperature superconductivity is impossible at ambient pressure, because of the very large effective masses of polarons or bipolarons at strong electron-phonon coupling. Here we challenge this belief by showing that strongly bound yet very light bipolarons appear for strong Peierls coupling. These bipolarons also exhibit many other unconventional properties; e.g., at strong coupling there are two low-energy bipolaron bands that are stable against strong Coulomb repulsion. Using numerical simulations and analytical arguments, we show that these properties result from the specific form of the phonon-mediated interaction, which is of "pair hopping" instead of regular density-density type. This unusual effective interaction is bound to have nontrivial consequences for the superconducting state expected to arise at finite carrier concentrations and should favor a large critical temperature.
31 citations
TL;DR: In this paper, the UV-Vis spectra of polyaniline (Pani) films were measured in the range 200nm-900nm at constant potential as well as sweeping the potential.
22 citations
TL;DR: In this paper, the critical temperature of transition, energy, heat capacity, and the transition heat of ideal translation-invariant bipolaron gas are calculated. And the results obtained are used to explain experiments on high-temperature superconductors.
Abstract: Consideration is given to thermodynamical properties of a three-dimensional Bose-condensate of translation-invariant bipolarons (TI-bipolarons). The critical temperature of transition, energy, heat capacity, and the transition heat of ideal TI-bipolaron gas are calculated. The results obtained are used to explain experiments on high-temperature superconductors.
18 citations
TL;DR: In this article, it was shown that the PEDOT chain adopts a neutral benzenoid conformation after the removal of oxidizers with solvent washing, leading to the characteristic polaron and bipolaron absorption in the 800 and 1200 nm range.
Abstract: Vapour phase polymerized (VPP) PEDOT obtained using triblock copolymer PEG–PPG–PEG:Fe(III) tosylate polymeric oxidative layers has shown record-high conductivity and unique thermoelectric properties. These properties are related to the molecular weight, morphology and doping of PEDOT. Here we show that in its unwashed condition, the PEDOT chain adopts a neutral benzenoid conformation. The polymer chain converts into the charged quinoid structure after the removal of oxidizers with solvent washing. X-ray diffraction results suggest that the dopant is also incorporated into the packed polymer after the washing process. The changes in the chain structure and doping lead to the characteristic polaron and bipolaron absorption in the 800 and 1200 nm range. We observed a large contraction of the film after washing that is likely due to these changes, along with the removal of excessive polymer:oxidizer trapped in the PEDOT matrix. The contraction of films can be completely suppressed by mechanical clamping. PEDOT films without contraction show both a higher conductivity and higher optical transparency.
16 citations
TL;DR: In this article, a metal free flexible p-type semiconductor in a hybrid structure of paper/graphite/polyaniline has been prepared in a facile technique of vapor phase oxidation of aniline on graphite incorporated paper.
15 citations
08 Mar 2018
TL;DR: In this paper, the exchange-correlation effects between two electrons of opposite spins occupying the same orbital from the average correlation among many electrons in a crystal were distinguished, and the electron-phonon interaction is essential to counterbalance the Coulomb repulsion and to stabilize the electron pairs.
Abstract: Starting from the shell structure in atoms and the significant correlation within electron pairs, we distinguish the exchange-correlation effects between two electrons of opposite spins occupying the same orbital from the average correlation among many electrons in a crystal. In the periodic potential of the crystal with lattice constant larger than the effective Bohr radius of the valence electrons, these correlated electron pairs can form a metastable energy band above the corresponding single-electron band separated by an energy gap. In order to determine if these metastable electron pairs can be stabilized, we calculate the many-electron exchange-correlation renormalization and the polaron correction to the two-band system with single electrons and electron pairs. We find that the electron-phonon interaction is essential to counterbalance the Coulomb repulsion and to stabilize the electron pairs. The interplay of the electron-electron and electron-phonon interactions, manifested in the exchange-correlation energies, polaron effects, and screening, is responsible for the formation of electron pairs (bipolarons) that are located on the Fermi surface of the single-electron band.
14 citations
TL;DR: In this paper, the exchange-correlation effects between two electrons of opposite spins occupying the same orbital from the average correlation among many electrons in a crystal were distinguished, and the electron-phonon interaction is essential to counterbalance the Coulomb repulsion and to stabilize the electron pairs.
Abstract: Starting from the shell structure in atoms and the significant correlation within electron pairs, we distinguish the exchange-correlation effects between two electrons of opposite spins occupying the same orbital from the average correlation among many electrons in a crystal. In the periodic potential of the crystal with lattice constant larger than the effective Bohr radius of the valence electrons, these correlated electron pairs can form a metastable energy band above the corresponding single-electron band separated by an energy gap. In order to determine if these metastable electron pairs can be stabilized, we calculate the many-electron exchange-correlation renormalization and the polaron correction to the two-band system with single electrons and electron pairs. We find that the electron-phonon interaction is essential to counterbalance the Coulomb repulsion and to stabilize the electron pairs. The interplay of the electron-electron and electron-phonon interactions, manifested in the exchange-correlation energies, polaron effects, and screening, is responsible for the formation of electron pairs (bipolarons) that are located on the Fermi surface of the single-electron band.
TL;DR: In this paper, the stability and coherence of magneto-bipolaron in asymmetric quantum dot (QD) under the laser field was investigated. And the authors showed that the bipolaron stability strongly depends on the electron-phonon coupling constant, magnetic field, laser frequency and high laser field strength.
TL;DR: In this paper, the free volume related fluorescence behavior in electron beam irradiated chalcone chromophore doped poly(methyl methacrylate) (PMMA) composite films have been studied using FTIR, UV-Visible, XRD and Positron Annihilation techniques.
TL;DR: In this paper, the authors derive kinetic equations for polaron hopping in organic materials that explicitly take into account the double occupation possibility and pair intersite correlations, and provide a self-consistent framework for describing the bipolaron mechanism of the organic magnetoresistance.
Abstract: We derive kinetic equations for polaron hopping in organic materials that explicitly take into account the double occupation possibility and pair intersite correlations. The equations include simplified phenomenological spin dynamics and provide a self-consistent framework for the description of the bipolaron mechanism of the organic magnetoresistance. At low applied voltages, the equations can be reduced to those for an effective resistor network that generalizes the Miller-Abrahams network and includes the effect of spin relaxation on the system resistivity. Our theory discloses the close relationship between the organic magnetoresistance and the intersite correlations. Moreover, in the absence of correlations, as in an ordered system with zero Hubbard energy, the magnetoresistance vanishes.
TL;DR: It is shown that it is possible for the bipolaron pair to merge into a state composed of a confined soliton-antisoliton pair, which is characterized by the appearance of states within less than 0.1 eV from the Fermi level.
Abstract: The dynamical scattering of two oppositely charged bipolarons in non-degenerate organic semiconducting lattices is numerically investigated in the framework of a one-dimensional tight-biding–Hubbard model that includes lattice relaxation. Our findings show that it is possible for the bipolaron pair to merge into a state composed of a confined soliton-antisoliton pair, which is characterized by the appearance of states within less than 0.1 eV from the Fermi level. This compound is in a narrow analogy to a meson confining a quark-antiquark pair. Interestingly, solitons are quasi-particles theoretically predicted to arise only in polymer lattices with degenerate ground state: in the general case of non-degenerate ground state polymers, isolated solitons are not allowed.
TL;DR: In this article, the diffusion coefficient and activation energies for the motion of both polarons and bipolarons were analyzed using a phenomenological approach and the results indicated that the presence of bipolarons may inhibit the efficiency of organic-based devices.
Abstract: Intrachain diffusion of charge carriers in organic conductors is analyzed. Using a tight-binding model Hamiltonian that includes strong electron–phonon coupling combined with a Langevin equation, we simulate both polaron and bipolaron dynamics under quantum-corrected thermal effects. Nonadiabatic molecular time evolution is used to determine how these quasiparticles diffuse through a nondegenerate conjugated polymer. By means of a phenomenological approach, we evaluate the diffusion coefficient and activation energies for the motion of both polarons and bipolarons. The analysis of activation energies, in agreement with available experimental data, suggests that the presence of bipolarons may inhibit the efficiency of organic-based devices. The results presented here point to the importance of taking a closer look at the effects of bipolaron dynamics in organic devices.
TL;DR: In this paper, the electronic properties of guest Cs atoms in a deformable lattice are investigated at various densities $n, showing optical absorptions of small bipolarons and the appearance of a Drude component superimposed on a MIR sideband suggesting a phase transition to a polaronic metal.
Abstract: The electronic properties of guest Cs atoms in a deformable lattice are investigated at various densities $n$. Low values of $n$ show optical absorptions of small bipolarons. At intermediate $n$ values, new bands appear in the midinfrared (MIR) and high-frequency regions, which coexist with the small bipolaron bands. With a further increase in $n$, the small bipolaron bands become less discernible and subsequently disappear, resulting in the appearance of a Drude component superimposed on a MIR sideband suggesting a phase transition to a polaronic metal. In this itinerant phase, an approximately twofold mass enhancement is observed. This continuous transition of a gas of small bipolarons to a polaronic metal characterized by a Fr\"ohlich polaron reveals an important part of the complex phase diagram of the metal-insulator transition in a deformable lattice.
TL;DR: In this paper, the high energy part of the angle-resolved photo-emission spectroscopy (ARPES) spectra of cuprate superconductors has been studied.
Abstract: An approach to considering systems with a high concentration of correlated carriers and strong long-range electron-phonon interaction and to calculating the high-energy part of the angle-resolved photoemission spectroscopy (ARPES) spectra of such systems is suggested. Joint relaxation of strongly coupled fields-a field of correlated electrons and phonon field-after photoemission is studied to clarify the nature of characteristic features observed in the high-energy part of the ARPES spectra of cuprate superconductors. Such relaxation occurs in systems with strong predominantly long-range electron-phonon interaction at sufficiently high carrier concentration due to the coexistence of autolocalized and delocalized carriers. A simple method to calculate analytically a high-energy part of the ARPES spectrum arising is proposed. It takes advantage of using the coherent states basis for the phonon field in the polaron and bipolaron states. The approach suggested yields all the high-energy spectral features like broad Gaussian band and regions of 'vertical dispersion' being in good quantitative agreement with the experiments on cuprates at any doping with both types of carriers. Demonstrated coexistence of autolocalized and delocalized carriers in superconducting cuprates changes the idea about their ground state above the superconducting transition temperature that is important for understanding transport and magnetic properties. High density of large-radius autolocalized carriers revealed may be a key to the explanation of charge ordering in doped cuprates.
TL;DR: In this article, a bisheterocyclic derivatives of alkyl carbazole with A-CZ-A architecture are investigated and their opto-electronic and electrochemical properties are presented.
Abstract: In this work novel bisheterocyclic derivatives of alkylcarbazole with A–CZ–A architecture are investigated (CZ stands for alkylcarbazole). The study presents their opto-electronic and electrochemical properties which influence on the possibility of their prospective application. Monomers undergo electropolymerisation with formation of conducting layer of polythiophene derivatives, while presence of chalcone moiety hampers the process. Two-step oxidation processes of polymers results in generation of polaron and bipolaron types of charge carriers on the macromoleculs’ chains. The charge is delocalized over center and side subunits (bithiophene or bithiazole one) in first stage of oxidation. It is possible to influence on the properties of the polymers and their composition by variation of synthesis condition like solvent polarity and applied potential boundaries. Obtained conducting polymers show high stability under ambient conditions. Their energy gap values are estimated with electrochemical and spectroscopic methods.
TL;DR: In this article, the authors investigated the hot carrier dynamics in Ti4O7 by ultrafast time-resolved optical reflectivity and found that photoexcitation can effectively reduce both T c1 and T c2 by increasing the pump fluence, allowing the light-control of the I-M transition.
Abstract: We report on the systematic investigation of hot carrier dynamics in Ti4O7 by ultrafast time-resolved optical reflectivity. We find the transient indication for its two-step insulator–metal (I–M) transition, i.e., from the long-range ordered bipolaron low-temperature insulating phase to the disordered bipolaron high-temperature insulating phase at T c1 and to the free-carrier metallic phase at T c2. Our results reveal that photoexcitation can effectively reduce both T c1 and T c2 by increasing the pump fluence, allowing the light-control of the I–M transition. We address a phase diagram that provides a framework for the photoinduced I–M transition and helps the potential use of Ti4O7 for photoelectric and thermoelectric devices.
Posted Content•
TL;DR: In this article, it is demonstrated that according to translation-invariant bipolaron theory of high temperature superconductors, the different types of experiments measure for the gap different values, thus tunneling experiments determine the bipolaron energy for a superconducting gap.
Abstract: The explanation of the nature of superconducting gap in high temperature superconductors (HTSC) is a fundamental task which solution can lead to the understanding of superconducting mechanism. However, it has not been fully solved yet. From the mid of the twentieth century when Bardeen, Cooper and Schrieffer constructed their theory it has been believed that a superconducting gap is a collective phenomenon of electron excitations. In this work it is demonstrated that according to translation-invariant bipolaron theory of HTSC the different types of experiments measure for the gap different values. Thus tunneling experiments determine the bipolaron energy for a superconducting gap. On the other hand, the angle - resolved photoemission spectroscopy method measures the phonon frequency for which the electron-phonon interaction is maximum. Such effects as kinks in spectral measurements of gap, its angular dependence, existence of pseudogap and others have got natural explanations.
TL;DR: In this article, the authors report on the high-temperature evolution of far and mid- infrared reflectivity and emissivity spectra of ambient orthorhombic ErMnO3 from 12 K to sample decomposition above 1800 K.
Abstract: We report on the high-temperature evolution of far- and mid- infrared reflectivity and emissivity spectra of ambient orthorhombic ErMnO3 from 12 K to sample decomposition above 1800 K. At low temperatures the number of phonons agrees with the predictions for orthorhombic space group D2h16-Pbnm (Z=4) and coexists with a paramagnon spin resonance and rare earth crystal field transitions. Increasing the temperature, a number of vibrational bands undergo profile broadening and softening approaching the orbital disordered phase where the orthorhombic O' lower temperature cooperative phase coexists with cubic-orthorhombic O. O-ErMnO3 undergoes a first order order-disorder transition into the perovskite cubic phase at Tcubic ~1329 K where the three triple degenerate phonons allowed by the space group Pm-3m(Z=1) are identified. At about 800 K, a quantitative small polaron analysis of the orthorhombic mid-infrared real part optical conductivity shows that antisymmetric and symmetric breathing modes sustain the strongest electron-phonon interactions. Above Tcubic the bipolaron fingerprint profile is the mid-infrared dominant and only feature. Its appearance correlates with the localized screening of the highest vibrational mode reststrahlen band. We propose that the longitudinal optical mode macroscopic field screening is consequence of dynamically sharing {\delta} disproportioned eg electrons hovering over the JT distorted octahedral dimer [Mn (QJT)3+{\delta} (Mn(QJT)3-{\delta}))O6/2]2. A thermal driven insulator-metal transition is detected with onset ~1600 K. We also address the occurrence of an inhomogeneity induced THz band result of heating the samples in dry air, triggering Mn3+-Mn4+ double exchange, under the presence of Mn4+ smaller ions stabilizing the orthorhombic lattice.
TL;DR: In this article, the critical temperature of the transition of a translation-invariant bipolaron Bose gas into the superconducting state, its energy, heat capacity and heat of transition were investigated.
Abstract: The properties of a Bose gas of translation-invariant (TI) bipolarons analogous to Cooper pairs are considered. As in the BCS theory, the description of a TI-bipolaron gas is based on the electron-phonon interaction and Froehlich Hamiltonian. As distinct from the BCS theory, when the correlation length greatly exceeds the mean distance between the pairs, here we deal with the opposite case when the correlation length is much less than the distance between the pairs. We calculate the critical temperature of the transition of a TI-bipolaron Bose-gas into the superconducting state, its energy, heat capacity and heat of the transition. The results obtained are used to explain the experiments on high-temperature superconductors. Possible ways of raising the critical temperature of high-temperature superconductors are discussed.
TL;DR: FAPESP under Grant 2016/02503-8, CNPq, as well as by the Basque Government through the grant IT641-13 as mentioned in this paper, were used to support the work of as mentioned in this paper.
Abstract: FAPESP under Grant 2016/02503-8, CNPq, as well as by the Basque Government through the grant IT641-13
Dissertation•
01 Jan 2018
TL;DR: In this paper, the properties of defects and intrinsic polaron trapping have been calculated using density functional theory (DFT) and other computational methods, using the embedded cluster method, and the peaks of the optical absorption spectra are predicted at 3.5 and 4.2 eV for cubic and rhombohedral LaAlO, respectively.
Abstract: Thin films of metal oxides, like Al₂O₃ and LaAlO₃, play a crucial role in emerging nanoelectronic devices. Using density functional theory (DFT) and other computational methods, the properties of defects and intrinsic polaron trapping have been calculated in LaAlO₃ and amorphous Al₂O₃. The spectroscopic properties of neutral (Vₒ⁰) and charged (Vₒ⁺) oxygen vacancies in cubic and rhombohedral LaAlO₃ have been investigated using Time Dependent DFT and the embedded cluster method. The peaks of the optical absorption spectra are predicted at 3.5 and 4.2 eV for Vₒ⁰ and 3.6 eV for Vₒ⁺ in rhombohedral LaAlO₃. The calculated electron paramagnetic resonance (EPR) parameters of Vₒ⁺ accurately predict the width (3 mT) and position of its EPR spectrum. Amorphous Al₂O₃ is then investigated, which has applications in non-volatile memory and a-IGZO (amorphous indium-gallium-zinc oxide) thin film transistors. Amorphous Al₂O₃ structures were generated using a molecular dynamics melt-quench approach and found to be in good agreement with experiment. DFT calculations, using a tuned hybrid functional, determined that the a-Al₂O₃ band gap decreases to 5.5 eV, compared to 8.6 eV in α-Al₂O₃, because of the reduction in Al coordination number in the amorphous phase. This causes a shift in the electrostatic potential that lowers the conduction band minimum, adding support to experimental measurements of band offsets. Then intrinsic polaron and bipolaron trapping in a-Al₂O₃ is modelled. The average trapping energy of hole polarons in a-Al₂O₃ was calculated to be 1.26 eV, much higher than the 0.38 eV calculated for α-Al₂O₃. Electrons were found not to trap in both crystalline and amorphous Al₂O₃. To explain the negative charging of Al₂O₃ films the properties of oxygen, hydrogen and aluminium defects were calculated. A mechanism is proposed to explain experimental trap spectroscopy measurements, whereby negatively charge defects are compensated by positively charged defects that have unoccupied states in the band gap. These predictions will facilitate experimental identification of defect states in LaAlO₃ and Al₂O₃ and their effect on nanodevices.
TL;DR: The findings point to the formation of a compound species formed from the coupling between a bipolaron and an exciton, which might enlighten the understanding of the electroluminescence processes in organic light-emitting devices.
Abstract: The recombination dynamics of two oppositely charged bipolarons within a single polymer chain is numerically studied in the scope of a one-dimensional tight-binding model that considers electron–el...
TL;DR: In this article, the thermodynamic properties of a three-dimensional Bose-condensate of translation-invariant bipolarons (TI-bipolarons) were investigated.
Abstract: Consideration is given to thermodynamical properties of a three-dimensional Bose-condensate of translation-invariant bipolarons (TI-bipolarons). The critical temperature of transition, energy, heat capacity and the transition heat of TI-bipolaron gas are calculated. The results obtained are used to explain experiments on high-temperature superconductors.
TL;DR: In this paper, the authors investigated the hot carrier dynamics in Ti4O7 by ultrafast time-resolved optical reflectivity and found that photoexcitation can effectively lower down both Tc1 and Tc2 with pump fluence increasing, allowing a light-control of I-M transition.
Abstract: We report on systematic investigation of hot carrier dynamics in Ti4O7 by ultrafast time-resolved optical reflectivity. We find the transient indication for its two-step insulator-metal (I-M) transition, in which two phase transitions occur from long-range order bipolaron low-temperature insulating (LI) phase to disordered bipolaron high-temperature insulating (HI) phase at Tc1 and to free carrier metallic (M) phase at Tc2. Our results reveal that photoexcitation can effectively lower down both Tc1 and Tc2 with pump fluence increasing, allowing a light-control of I-M transition. We address a phase diagram that provides a framework for the photoinduced I-M transition and helps the potential use of Ti4O7 for photoelectric and thermoelectric devices.
Dissertation•
21 Mar 2018
TL;DR: In this article, a model that shows the presence of symmetry d-wave in a class of superconductors of high Tc, as well as the condition for the existence of density waves in the states of equilibrium, is presented.
Abstract: High-temperature superconductors have different properties than conventional superconductors, one of these important properties is non-isotropic symmetry of the order parameter. In this work we present a model that shows the presence of symmetry d-wave in a class of superconductors of high Tc, as well as the condition for the existence of density waves in the states of equilibrium. We first analyze a three-body system, a bipolaron and two electrons, in order to study the effect of local and non-local Coulomb repulsion on the symmetry of the order parameter for the exact case and also the strong coupling limit. It is also shown the construction of an effective Hamiltonian that decouples the electron-bipolaron interaction in order to approach the collective problem of infinite bodies and we see how the proposed model predicts the formation of density waves for a specific region of the physical parameters of the studied Hamiltonian .