Bipolaron Energy Research Articles

Stability conditions for a large anharmonic bipolaron

A large polaron is a quasiparticle that consists of a nearly free electron interacting with the phonons of a material, whose lattice parameters are much smaller than the polaron scale. The electron-phonon interaction also leads to an attractive interaction between electrons, which can allow two polarons to pair up and form a bipolaron. It has been shown that large bipolarons can form in theory due to strong one-electron--one-phonon coupling, but they have not been seen in real materials because the critical value of the required electron-phonon interaction is too large. Here, we investigate the effect of one-electron--two-phonon coupling on the large bipolaron problem. Starting from a generalization of the Fr\"ohlich Hamiltonian that includes both the standard one-electron--one-phonon interaction as well as an anharmonic one-electron--two-phonon interaction, we use the path-integral method to find a semianalytical upper bound for the bipolaron energy that is valid at all values of the Fr\"ohlich coupling strength $\ensuremath{\alpha}$. We find the bipolaron phase diagram and conditions for the bipolaron stability by comparing the bipolaron energy to the energy of two free polarons. The critical value of the Fr\"ohlich coupling strength ${\ensuremath{\alpha}}_{\text{crit}}$ is calculated as a function of the strength of the one-electron--two-phonon interaction. The results suggest that large bipolaron formation is more likely in materials with significant one-electron--two-phonon interaction as well as strong one-electron--one-phonon interaction, such as strontium titanate.

Properties of optical bipolaron in symmetric quantum dot

Optical bipolaron properties in the symmetric quantum dot were investigated using the Lee-Low-Pines-Huybrechts method and the Tokuda linear combination operator method. Algebraic expressions are derived for the energies of the fundamental and first excited states, the effective mass, mobility, binding energy and oscillation period of the optical bipolaron. Results prove that the energies of fundamental and first excited states increase with the coupling constant. Another point is that the strong coupling method dominates the weak coupling and the intermediate one when the electron-phonon coupling enhances. We also observe that the binding energy becomes always positive when confinement strength is above 5. In other points, the binding energy of optical bipolaron is well studied in all coupling, especially in weak coupling. It is also noticed that energies are increasing the function of the dielectric ratio and the oscillation period is reducing with the dielectric ratio. This proves that the electron-electron interaction is strengthened in a quantum dot. The stronger the coupling, the higher mobility in the case of low temperature. • The ground and first excited energies, binding energy, Oscillation Period, Effective mass and mobility of bipolaron. • We have plotted Ground state energy and excited state energy of bipolaron versus the electron-phonon coupling constant in different couplings. • Ground state energy, excited state energy and oscillation period of bipolaron versus confinement strength at various values of the dielectric ratio are plotted. • We plotted Variation of binding energy of bipolaron versus confinement strength in all coupling. (a) Ω ≺ 4 ; (b) Ω ≻ 4 • We have plotted Variation of mobility versus confinement strength at different values of dielectric ratio. • We have plotted Variation of ground state effective mass (a) and excited effective mass (b) versus electron-phonon coupling constant.

Stability and decoherence of optical bipolaron in symmetric quantum dot

Optical bipolaron’s stability and decoherence confined in the symmetric quantum dot are investigated utilizing the modified Lee, Low, and Pines variational method. The binding energy of optical bipolaron in symmetrical quantum dot systems is obtained by computing the energy of the fundamental state, the energy of the ground state of the single polaron, and the prime state excited energy. The formation of the bipolaron in quantum dot structures is thus obtained. Optical bipolaron stability appears to be quite sensitive to the dimensionality of the quantum dot and the material, where α and η material parameters are considered. By investigating information processing, it is possible to compute Shannon’s entropy to study a qubit’s decoherence when in the superimposed state of the fundamental and the prime state excited. We see that decoherence time grows and shrinks with the dielectric constant and the dispersion coefficient. Thus, there exists a threshold dielectric constant and dispersion coefficient which maximizes decoherence time. This threshold dielectric constant and dispersion coefficient increases with the reduction in electron–phonon coupling. This study gives a guideline for the appropriate materials used in the construction of nanodevice.

Трансляционно-инвариантная биполяронная теория сверхпроводимости и спектроскопические эксперименты

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.

Программа трехмерного моделирования и визуализации конформационной динамики биомакромолекул Maya-K-PDB

The work is devoted to obtaining the bipolaron functional in anisotropic crystals by Buimistrov-Pekar method for an arbitrary electron-phonon coupling. The effect of electron correlations related to the direct dependence of the wave function from the distance between the electrons on bipolaron energy is studied. The single-center and two-center (coaxial configuration) bipolaron models in crystals with anisotropic effective mass for the limiting case of quasi-systems (the system “light axis”) were compared.

Застосування методів квантової теорії поля до розробки трансляційно-інваріантної теорії полярона та біполярона

The polaron and bipolaron energy functionals obtained in the framework of quantum field theory have been studied. Exact analytical expressions for the effective functionals are derived in terms of the two-parametrical trial function for a polaron and the three-parametrical one for a bipolaron. Variational solutions are found for the energies of the systems under study in the case of the intermediate values of Fr¨ohlich electron-phonon coupling constant, 4 ≤ a ≤20.

Pekar bipolaron and the virial theorem (arbitrary coupling)

The work is devoted to issues related with implementation of the virial theorem for one-center bipolaron. The virial theorem expressions have been obtained for an electron system with Coulomb interactions in the phonon field. It is shown that for the bipolaron functional (one-center configuration) virial theorem holds for arbitrary electron-phonon coupling. As a specific example of the virial theorem for one-center bipolaron configuration, the author adduces numerical calculations of the energy of the ground state and the various contributions (kinetic energy, electron-phonon interaction, electron energy, phonon energy) into the energy of bipolaron, performed within the framework of Buimistrov-Pekar method. It is shown that the virial theorem is fulfilled with high accuracy for the two-electron systems with Coulomb interactions for an arbitrary value electron-phonon coupling. The necessary condition for formation of a bipolaron stable state is accounting electron correlations associated with the direct dependence of the trial electron wave function of the system from the interelectron distance.

Influence of Magnetic Field and LO Phonon Effects on the Spin Polarization State Energy of Strong-Coupling Bipolaron in a Quantum Dot

On the basis of Lee–Low–Pines unitary transformation, the influence of magnetic field and LO phonon effects on the energy of spin polarization states of strong-coupling bipolarons in a quantum dot (QD) is studied by using the variational method of Pekar type. The variations of the ground state energy \(E_0\) and the first excited state the energy \(E_1\) of bipolarons in a two-dimensional QD with the confinement strength of QDs \(\omega _0\), dielectric constant ratio \(\eta \), electron–phonon coupling strength \(\alpha \) and cyclotron resonance frequency of the magnetic field \(\omega _{c}\) are derived when the influence of the spin and external magnetic field is taken into account. The results show that both energies of the ground and first excited states (\(E_0\) and \(E_1)\) consist of four parts: the single-particle energy of electrons \(E_\mathrm{e}\), Coulomb interaction energy between two electrons \(E_\mathrm{c}\), interaction energy between the electron spin and magnetic field \(E_\mathrm{S}\) and interaction energy between the electron and phonon \(E_{\mathrm{e-ph}}\); the energy level of the first excited state \(E_1\) splits into two lines as \(E_1^{(1+1)}\) and \(E_1^{(1-1)}\) due to the interaction between the single-particle “orbital” motion and magnetic field, and each energy level of the ground and first excited states splits into three “fine structures” caused by the interaction between the electron spin and magnetic field; the value of \(E_{\mathrm{e-ph}}\) is always less than zero and its absolute value increases with increasing \(\omega _0\), \(\alpha \) and \(\omega _c\); the effect of the interaction between the electron and phonon is favorable to forming the binding bipolaron, but the existence of the confinement potential and Coulomb repulsive energy between electrons goes against that; the bipolaron with energy \(E_1^{(1-1)}\) is easier and more stable in the binding state than that with \(E_1^{(1+1)}\).

Translation invariant theory of polaron (bipolaron) and the problem of quantizing near the classical solution

A physical interpretation of translation-invariant polarons and bipolarons is presented, some results of their existence are discussed. Consideration is given to the problem of quantization in the vicinity of the classical solution in the quantum field theory. The lowest variational estimate is obtained for the bipolaron energy E(η) with E(0) = -0.440636α2, where α is a constant of electron-phonon coupling, η is a parameter of ion binding.

Energy and critical ionic-bond parameter of a 3D large-radius bipolaron

A theory of a strong-coupling large-radius bipolaron has been developed. The possibility of the formation of 3D bipolarons in high-temperature superconductors is discussed. For the bipolaron energy, the lowest variational estimate has been obtained at α > 8, where α is the electron-phonon coupling constant. The critical ionic-bond parameter ηc = ɛ∞/ɛ0, where ɛ∞ and ɛ0 are the high-frequency and static dielectric constants, has been found to be ηc = 0.2496.

Transition of polaron to bipolaron structure in conjugated polymers

We describe the effects of removing one more electron from conjugated polymers with polarons. We use a Su-Schrieffer-Heeger model modified to include an external electric field and electron–electron interactions via a Parr-Pariser-Pople mean field Hamiltonian. Within the Unrestricted Hartree–Fock approximation, we study the dynamics performing numerical simulations. We have found that removing one electron from a conducting polymer bearing a single polaron leads to the creation of a structure that contains a bipolaron coupled to a breather. The bipolaron energy levels in the gap oscillate with higher amplitude due to the bipolaron–breather coupling. The bipolaron–breather pair can be decoupled through the action of an external electric field. Lattice oscillation modes are created due to the bipolaron motion and the energy levels associated to the bipolaron still oscillate, nevertheless, with smaller amplitude. The effects of the external electric field on the bipolaron–breather dynamics are studied by changing the electric field intensity.

Electron correlations and instability of a two-center bipolaron

The energy of a large bipolaron is calculated for various spacings between the centers of the polarization potential wells of the two polarons with allowance made for electron correlations (i.e., the explicit dependence of the wave function of the system on the distance between the electrons) and for permutation symmetry of the two-electron wave function. The lowest singlet and triplet 23S states of the bipolaron are considered. The singlet polaron is shown to be stable over the range of ionic-bond parameter values η≤ηm≈0.143 (η=ɛ∞/ɛ0, where ɛ∞ and ɛ0 are the high-frequency and static dielectric constants, respectively). There is a single energy minimum, corresponding to the single-center bipolaron configuration (similar to a helium atom). The binding energy of the bipolaron for η → 0 is Jbp=−0.136512e4m*/ℏ2ɛ∞2 (e and m* are the charge and effective mass of a band electron), or 25.8% of the double polaron energy. The triplet bipolaron state (similar to an orthohelium atom) is energetically unfavorable in the system at hand. The single-center configuration of the triplet bipolaron corresponds to a sharp maximum in the distance dependence of the total energy Jbp(R); therefore, a transition of the bipolaron to the orthostate (e.g., due to exchange scattering) will lead to decay of the bound two-particle state. The exchange interaction between polarons is antiferromagnetic (AFM) in character. If the conditions for the Wigner crystallization of a polaron gas are met, the AFM exchange interaction between polarons can lead to AFM ordering in the system of polarons.

Electron Correlations and Spatial Configuration of the Bipolaron

Bipolaron energy is calculated for various distances between the centers of polarization wells of two polarons with accounting the electron correlations. A singlet bipolaron is stable at a rather high energy of ion binding η < η m 0.143, η = e/e 0 (e x and e 0 are the high-frequency and static dielectric constants, respectively). The unique energy minimum corresponds to a one-center bipolaron (analog of a helium atom). The bipolaron binding energy constitutes up to 25.8 % of a double polaron energy at η → 0. A triplet bipolaron (analog of ortho-helium) is energetically disadvantageous. The one-center configuration of a triplet bipolaron corresponds to a maximum on the distance dependence of the total energy J Bp (R). The exchange interaction between polarons has antiferromagnetic character. A prediction is made about a possibility of Wigner crystallization of a polaron gas which occurs with antiferromagnetic ordering in the polaron svstem.

The stability of magnetobipolarons in low-dimensional systems

We investigate the stability condition of large bipolarons confined in a parabolic potential containing certain parameters and a uniform magnetic field. The variational wave function is constructed as a product form of electronic parts, consisting of center of mass and internal motion, and a part of coherent phonons generated by Lee-Low-Pines transformation from the vacuum. An analytical expression for the bipolaron energy is found, from which the ground and excited-state energies are obtained numerically by minimization procedure. The bipolaron stability region is determined by comparing the bipolaron energy with those of two separate polarons, which is already calculated within the same approximation. It is shown that the results obtained for the ground state energy of bipolarons reduce to the existing works in zero magnetic field. In the presence of a magnetic field, the stability of bipolarons is examined, for three types of low-dimensional system, as function of certain parameters, such as the magnetic-field, the electron-phonon coupling constant, Coulomb repulsion and the confinement strength. Numerical solutions for the energy levels of the ground and first excited states are examined as functions of the same parameters.

Tunnelling gaps and d-wave stripes in cuprates: A unified approach

Abstract The Frohlich electron-phonon interaction in cuprates and other charge-transfer oxides is shown to be much stronger than any magnetic interaction. The polaron shift due to the Frohlich interaction of about 1 eV suggests that carriers are smali (bi)polarons at all temperatures and dopings, in agreement with the oxygen isotope effect on the carrier mass, optical conductivity and other experimental observations. Two distinct energy scales, the d-wave superconducting order parameter and charge segregation in the form of stripes in cuprates, are unified in the framework of the bipolaron theory as a result of the formation of mobile bipolarons in the normal state and their Bose-Einstein condensation. Within the theory both the d-wave superconducting order parameter and the striped charge distribution result from the bipolaron (centre-of-mass) energy band dispersion rather than from any particular interaction.

Tunnelling gaps and d-wave stripes in cuprates: a unified approach

Abstract The Fröhlich electron-phonon interaction in cuprates and other charge-transfer oxides is shown to be much stronger than any magnetic interaction. The polaron shift due to the Fröhlich interaction of about 1 eV suggests that carriers are smali (bi)polarons at all temperatures and dopings, in agreement with the oxygen isotope effect on the carrier mass, optical conductivity and other experimental observations. Two distinct energy scales, the d-wave superconducting order parameter and charge segregation in the form of stripes in cuprates, are unified in the framework of the bipolaron theory as a result of the formation of mobile bipolarons in the normal state and their Bose-Einstein condensation. Within the theory both the d-wave superconducting order parameter and the striped charge distribution result from the bipolaron (centre-of-mass) energy band dispersion rather than from any particular interaction.

Ground state of an optical bipolaron with an intermediate strengthof coupling

The ground-singlet state of an optical bipolaron in theregion of intermediate coupling strengths is analysed.It is shownthat the spatial structure of a bipolaron with intermediatecoupling strength is that of an axially symmetric quasi-moleculardimer.The bipolaron energies of coupling are determined for different couplingconstants and dielectric parameters of a medium.The electronic terms of the ground-dimer state are represented as afunction of the distance between quasi-particles.The intermediateregion of coupling constants is shown to give rise to anadditional specific term in the total energy,which depends on the dielectric properties of a medium and makesthe bipolaron energy of coupling higher (atε*/ε∞>1.06) or lower (atε*/ε∞<1.06) than the value in thelimit of adiabatic and strong coupling.

D-WAVE BIPOLARONIC STRIPES IN CUPRATES

Two distinct energy scales, the d-wave superconducting order parameter, and the charge segregation in the form of stripes in cuprates are unified in the framework of the bipolaron theory as a result of the formation of mobile bipolarons in the normal state and their Bose-Einstein condensation. Within the theory both the d-wave superconducting order parameter and striped charge distribution result from the bipolaron (center-of-mass) energy band dispersion rather than from any particular interaction.

Influence of electron–electron correlations on bipolaron in strong electrolytes

We develop a microscopic theory of two spin-pairing electrons in ionic liquids. The bipolaron energy and electron density are calculated by variational estimates at various cation-core effects.

D-Wave Bose–Einstein condensation and the London penetration depth in superconducting cuprates

As has been recently established, bipolaron formation leads to a d-wave Bose–Einstein condensate in cuprates owing to the bipolaron (center-of-mass) energy dispersion rather than to a particular pairing interaction. We show that the unusual low-temperature-dependence of the magnetic field penetration depth λ( T) in cuprates can be explained within the bipolaron scenario as well. Both linear positive and negative slopes of λ( T) occur depending on the random field profile and amount of disorder.