Large Bipolarons Research Articles

Large-bipolaron liquids in cuprate superconductors.

Uniquely, large-bipolarons' self-trapped holes occupy superoxygens, each comprising four oxygens circumscribed by four coppers in a CuO2 plane, formed as oxygens relax inward and coppers relax outward. Critically, concomitant oxygen-to-copper electron transfer eliminates copper spins. The d-symmetry of superoxygens' ground state molecular orbital tracks the superoxygens' predominant zero-point radial vibrations. These large bipolarons' distinctive charge transport, absorption, magnetism, local atomic vibrations, condensation into a liquid, and subsequent superconductivity are consistent with cuprate superconductors' long-established unusual properties.

Free energy of a two-liquid system of charge carriers in strongly coupled electron and phonon fields and common nature of three phases in hole-doped cuprates

Hole-doped cuprates exhibit partially coexisting pseudogap (PG), charge ordering (CO) and superconductivity; we show that there exists a class of systems in which they have a single nature as it has recently been supposed. Since the charge-ordered phase exhibits large frozen deformation of the lattice, we develop a method for calculating the phase diagram of a system with strong long-range (Fröhlich) electron–phonon interaction. Using a variational approach, we calculate the free energy of a two-liquid system of carriers with cuprate-like dispersion comprising a liquid of autolocalized carriers (large polarons and bipolarons) and Fermi liquid of delocalized carriers. Comparing it with the free energy of pure Fermi liquid and calculating (with standard methods of Bose liquid theory) a temperature of the superfluid transition in the large-bipolaron liquid we identify regions in the phase diagram with the presence of PG (caused by the impact of the (bi)polarons potential on delocalized quasiparticles), CO and superconductivity. They are located in the same places in the diagram as in hole-doped cuprates, and, as in the latter, the shape of the calculated phase diagram is resistant to wide-range changes in the characteristics of the system. As in cuprates, the calculated temperature of the superconducting transition increases with the number of conducting planes in the unit cell, the superfluid density decreases with doping at overdoping, the bipolaron density (and bipolaronic plasmon energy) saturates at optimal doping. Thus, the similarity of the considered system with hole-doped cuprates is not limited to the phase diagram. The results obtained allow us to discuss ways of increasing the temperature of the superfluid transition in the large-bipolaron liquid and open up the possibility of studying the current-carrying state and properties of the bipolaron condensate.

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.

Formation of strong-coupling (bi)polarons and related in-gap states in lightly-doped cuprate superconductors

The formation of large polarons and bipolarons and related in-gap states in lightly-doped cuprates is studied in the strong electron–phonon coupling regime. The ground-state energies, binding energies and binding radius of strong-coupling large (bi)polarons are calculated using the continuum model and adiabatic approximation taking into account both the short- and long-range electron–phonon interactions. The obtained results show that the binding energies of such large (bi)polarons in the cuprates are progressively increased with decrease in the high frequency dielectric constant [Formula: see text] and ratio [Formula: see text] (where [Formula: see text] is the static dielectric constant). As a result, large (bi)polarons become nearly small (bi)polarons. It is shown that hole carriers strongly interact with acoustic and optical phonons and their self-trapping leads to the formation of (bi)polaronic states in the charge-transfer (CT) gap of the cuprates. As the cuprate system is doped, the CT gap of the parent compound is filled in with low-energy (bi)polaronic states. The calculated energies of such (bi)polaronic states are in good agreement with the experimentally observed energies of new states appearing in the CT gap of the parent cuprates. The calculated values of the binding radius of large polarons are also well consistent with the existing experimental data.

Mobile inter-site bipolarons in presence of long-range interactions

We report an exact diagonalization study of strongly correlated electron–phonon (EP) systems like doped polar insulators within the framework of the polaronic t−Jp model considering realistic long-range Coulomb and EP (Fröhlich) interactions on linear and square clusters. For a small ratio of polaronic hopping amplitude (t) and exchange interaction (Jp), polarons predominantly occupy the nearest-neighbor (NN) position with NN spin–singlet pairing (d-wave type). With the increase in the t∕Jp ratio, bipolaron size increases and finally becomes large and constant depending on the lattice size. The crossover from small to large bipolaron is nearly independent of system size but depends on the cluster geometry. Bipolaron effective mass and kinetic energy calculation show that at t∕Jp∼0.3, light and small bipolarons are perfectly mobile. In linear chain, bipolaron composite is formed within a region of 0<t∕Jp<0.5. Results suggest the existence of the superconducting phase at the vicinity of t∕Jp∼ 0.3.

Large (bi)Polarons for Novel Energy Conversion and Superconductivity

Materials containing high densities of exceptionally displaceable ions (e.g. perovskites) have extremely large ratios of their static to high-frequency dielectric constants, > 2. Large polarons form in such materials as their electronic charge carriers self-trap by displacing surrounding ions. Large polarons are very heavy-massed slow-moving quasi-particles that are very weakly scattered by ambient phonons. Large-polaron mobilities, e.g. 1 cm2/V-sec at 300 K, are much smaller than the minimum possible for conventional electronic charge carriers. The minimum mobility for an itinerant charge carrier of effective mass m, eh/mkT, occurs when its mean-free-path falls to its de Broglie wavelength, e.g. 300 cm2/V-sec at room temperature for m equaling the free-electron mass. Distinctively, large-polarons frequency-dependent conductivities consist of two contributions that separate as the temperature is reduced. Large polarons Drude-like contributions are relegated to frequencies below those of characteristic phonons. Contributions from excitations of large polarons self-trapped electronic carriers occur above those of characteristic phonons. Oppositely charged large polarons repel one another at short range. The resulting suppressed recombination facilitates exceptionally efficient solar cells. Large polarons of the same charge attract one another at short range to enable their real-space pairing into singlet bipolarons. Additional attractions between large bipolarons facilitates their condensation into liquids that can exhibit superconductivity.

Strong long-range electron–phonon interaction as possible driving force for charge ordering in cuprates

A model resulting in charge ordering (CO) similar to that observed in cuprate superconductors is under study. It includes strong long-range electron–phonon interaction (EPI) and high density of correlated carriers. Coexistence of large bipolarons and delocalized carriers is a feature of such system. We develop generalized variation method to calculate the bipolaron size (CO period) in the ground normal state of such system at various doping. The approach allows the revealing of a possible physical reason of strongly different doping behavior of the CO wave vector in different cuprates. Obtained doping dependences of the CO period and temperature of the CO decay demonstrate quantitative agreement with those observed in cuprates. Predicted in the suggested approach ratio of the CO wave vector to the wave vector of the high-energy anomaly (HEA) in ARPES spectrum is in consent with that in cuprates. Calculated resonant x-rays scattering on the CO emerging in the model is in good agreement with experiments on cuprates including the asymmetry of the CO peaks’ cross-section. A gap arises in the spectrum of delocalized carriers near antinodal direction due to their scattering on the periodic potential created by autolocalized carriers, analogously to photon crystal effect.

Formation of intermediate coupling optical polarons and bipolarons in two-dimensional systems

The formation of the optical polaron and bipolaron in two-dimensional (2D) systems is studied in the intermediate electron–phonon coupling regime. The total energies of the 2D polaron and bipolaron are calculated by using the Buimistrov–Pekar method of canonical transformations. The obtained results are compared with other existing results obtained by using the Feynman path integral method and the modified Lee–Low–Pines unitary transformation method. It is shown that the electron–phonon correlation significantly reduces the total energy of the 2D polaron in comparison with the energy of the strong coupling (adiabatic) polaron. It is found that the polaron formation in 2D systems is possible when the electron–phonon coupling constant α is greater than the critical value αc≃2.94, which is much lower than a critical value of the electron–phonon coupling constant α in three-dimensional (3D) systems. The critical values of the Fröhlich coupling constant α and the ratio η=ε∞/ε0 (where ε∞ and ε0 are the high frequency and static dielectric constants, respectively), which determine the bipolaron stability region in 2D systems, are calculated numerically. It is interesting for application to the layered cuprate superconductors that the (bi)polarons are formed more easily in quasi-2D regions than in the bulk. It is argued that the high-Tc cuprate superconductivity can exist above the bulk superconducting transition temperature Tc as the persisting superfluidity of polaronic (bosonic) Cooper pairs and large bipolarons at quasi-2D grain boundaries or in the CuO2 layers above Tc.

Large bipolaron density at organic semiconductor/electrode interfaces

Bipolaron states, in which two electrons or two holes occupy a single molecule or conjugated polymer segment, are typically considered to be negligible in organic semiconductor devices due to Coulomb repulsion between the two charges. Here we use charge modulation spectroscopy to reveal a bipolaron sheet density >1010 cm−2 at the interface between an indium tin oxide anode and the common small molecule organic semiconductor N,N′-Bis(3-methylphenyl)-N,N′-diphenylbenzidine. We find that the magnetocurrent response of hole-only devices correlates closely with changes in the bipolaron concentration, supporting the bipolaron model of unipolar organic magnetoresistance and suggesting that it may be more of an interface than a bulk phenomenon. These results are understood on the basis of a quantitative interface energy level alignment model, which indicates that bipolarons are generally expected to be significant near contacts in the Fermi level pinning regime and thus may be more prevalent in organic electronic devices than previously thought.

Application of Z-scan technique for the study of nonlinear absorption in chemically reduced LiNbO3 crystals

The nonlinear absorption (NLA) was studied by open-aperture Z-scan experiments in the chemically reduced nominally pure LiNbO3 crystals at cw-illumination with the red (644 nm) and green (514.5 nm) laser beams. The magnitude of the measured NLA is considerably different from the reported Z-scan results obtained in as-grown LiNbO3. The positive sign of NLA obtained with the red light has been related to the generation of the small bound polarons absorbing in red and near-IR ranges. Application of green light results in the light-induced transparency, i.e. the Z-scan traces show negative sign of NLA. Intensity dependence of Z-scan traces allows for conclusion that the photo-induced dissociation of small NbLi4+:NbNb4+ bipolarons and sequent generation of small polarons gives the dominating contribution to the nonlinear optical absorption in reduced crystals with a large bipolarons concentration.

Electron-Phonon Interaction in the Presence of Strong Coulomb Repulsion

We consider the Hubbard-Holstein model on a 2D tilted eight-site square lattice at quarter fillings having on-site (λ 1) and inter-site (λ 2) electron-phonon (EP) interactions and inter-site Coulomb repulsion (V ). Mobility of electrons decreases, and hence, localization of electrons is favored by λ 1 as well as inter-site Coulomb repulsion in the non-interacting limit (U/t = 0.0). In the interacting case (U/t = 8.0), an initial delocalization effect observed due to the competition between on-site Coulomb repulsion and EP interaction λ 1 though V favors localization. For smaller λ 1, the competition between λ 2 and V increases the delocalization effect. As λ 2 increases further, localization occurs. In the interacting case, localization occurs at much higher values of λ 2 due to the additional delocalization effect of U. On-site (S0) and/or large bipolarons are formed with λ 1 in the presence of V, and inter-site Coulomb repulsion effectively increases λ 1. Thus, V favors the formation of S0 bipolarons. However, the formation of S1 bipolarons is suppressed by inter-site Coulomb repulsion. An existence of critical λ 2 = λ 2c is observed for the formation of on-site (S0) and neighboring-site (S1) bipolarons.

Nature of extrinsic and intrinsic self-trapping of charge carriers in underdoped cuprate high-Tc superconductors

Nature of extrinsic and intrinsic self-trapping (ST) of charge carriers in cuprates have been studied theoretically. The binding energies and radii of the extrinsic and intrinsic large polarons and bipolarons in cuprates are calculated variationally using the continuum model and adiabatic approximation. We have shown that the extrinsic and intrinsic three-dimensional (3D) large bipolarons exist in underdoped cuprates at $\eta=\varepsilon_{\infty}/\varepsilon_0<0.127$ and $\eta<0.138$, respectively [where $\varepsilon_{\infty}$ ($\varepsilon_0$) is the optic (static) dielectric constant].

Carrier localization, Anderson transitions and stripe formation in hole-doped cuprates

Three distinctly different scenarios are proposed for the carrier localization in three- dimentional (3D) lightly doped cuprates in which the self-trapping and pairing of hole carriers (i) near the small-radius dopants and (ii) in a defect-free deformable lattice lead to the formation of the extrinsic and intrinsic (bi)polaronic states in the charge-transfer gap of the cuprates, and (iii) the self-trapping of hole carriers away from the large-radius dopants results in the formation of the in-gap hydrogenic impurity states. We have shown that the extrinsic and intrinsic 3D large bipolarons exist in La-based lightly doped cuprates at η = ɛ∞/ɛ0 < 0:127 and η < 0:138, respectively, where ɛ∞/ɛ0 is the optic (static) dielectric constant. We use the uncertainty relation to obtain the specificc conditions for the Anderson and new MITs in cuprates. The applicability limits of these MITs in La-based cuprates are clarified. Our results are in good agreement with the existing experiments on La-based cuprates.

Landau-Pekar Bipolaron in Singlet and Triplet States

We give an overview of studies a bipolaron stability by variational method. For bipolaron formations, a relation is established between the variational principle and the virial theorem optimizing the electronic wave functions. We present a large number of qualitative and quantitative arguments, which indicate that the Landau-Pekar bipolaron is an axially-symmetrical formation. Much attention is paid to the analysis of the influence of the Coulomb electron-electron correlations on the stability of a large bipolaron. In detail we analyzed the criteria for determining the optimal wave functions. It is established that a step-by-step increase in the flexibility of the electronic wave function due to the electron correlations does not stabilize a one-center bipolaron. We show after into account of electron-electron correlations a singlet bipolaron retains spatial axially-symmetrical. At the same time, the electron-excited triplet states of Landau-Pekar bipolaron have spherical symmetry. The results of Kasirina and Lakhno are based on the one-center bipolaron model are incorrect. Presented evidence that the correct application of the variational method and correct account of electron-electron correlations only increase the binding energy of the bipolaron but symmetry of Hartree-Fock approximation can not change. We adduce proofs which point to methodological errors of one-center bipolaron model as well as arising from their calculations incorrect physical consequences. As illustrated in this review the axially symmetric Landau-Pekar bipolaron can correctly interpret the experimentally detected spectroscopic data.

Z-scan study of nonlinear absorption in reduced LiNbO3 crystals

The nonlinear absorption (NLA) was studied by open-aperture Z-scan experiments in the chemically reduced nominally pure LiNbO3 crystals at cw-illumination with the red (644 nm) and green (514.5 nm) laser beams. The magnitude of the measured NLA is considerably different from the reported Z-scan results obtained in as-grown LiNbO3. The positive sign of NLA obtained with the red light has been related to the generation of the small bound polarons absorbing in red and near-IR ranges. Application of green light results in the light-induced transparency, i.e., the Z-scan traces show negative sign of NLA. Intensity dependence of Z-scan traces allows for conclusion that the photo-induced dissociation of small NbLi4+:NbNb4+ bipolarons and sequent generation of small polarons gives the dominating contribution to the nonlinear optical absorption in reduced crystals with a large bipolarons concentration.

Bipolarons and polarons in the Holstein-Hubbard model: analogies and differences

The single bipolaron problem is examined in the context of the 1D Holstein-Hubbard model, emphasizing analogies and differences with respect to the complementary single polaron physics. The bipolaron band structure below the phonon threshold is revealed, showing a complex relationship between numerous excited bands as the adiabatic limit is approached. Light bipolarons with significant binding energy, the stability of large bipolarons, the small to large bipolaron crossover as a function of the Hubbard repulsion, as well as the bipolaron dissociation, are investigated in detail, disentangling adiabatic, nonadiabatic and lattice coarsening effects. It is emphasized that condensation of bipolarons occurs in the dilute limit only at very low temperatures.

Possible mechanisms of carrier localization, metal–insulator transitions and stripe formation in inhomogeneous hole-doped cuprates

Possible mechanisms of carrier localization, metal–insulator transitions (MITs) and stripe formation in inhomogeneous hole-doped cuprates have been studied theoretically. Three distinctly different scenarios are proposed for the carrier localization in three-dimensional (3D) lightly doped cuprates in which the self-trapping and pairing of hole carriers (i) near the small-radius dopants and (ii) in a defect-free deformable lattice lead to the formation of the extrinsic and intrinsic (bi)polaronic states in the charge-transfer gap of the cuprates, and (iii) the self-trapping of carriers away from the large-radius dopants results in the formation of the in-gap hydrogenic impurity states. The binding energies and radii of the extrinsic and intrinsic large (bi)polarons in cuprates are calculated variationally using the continuum model and adiabatic approximation. We have shown that the extrinsic and intrinsic 3D large bipolarons exist in lightly doped cuprates at η = ε ∞ / ε 0 < 0.127 and η < 0.138 , respectively, where ε ∞ ( ε 0 ) is the optic (static) dielectric constant. While the optical bipolarons can exist if η < 0.134 and the Fröhlich coupling constants α are greater than 5.8. The dopant- and carrier-driven inhomogeneities favor the specific charge ordering in the form of a 3D network of carrier-rich and carrier-poor stripes and the formation of different superlattices and in-gap bands of dopants and large polarons. The localized in-gap states develop into metallic states at some critical doping levels. We use the uncertainty relation to obtain the specific conditions for the Mott, Anderson and new MITs in cuprates. The applicability limits of these MITs in cuprates are clarified. We argue that the new MITs in the cuprates caused by the strong carrier–defect–phonon and carrier–phonon interactions are accompanied by the formation of a 3D self-organized network of carrier-poor (insulating) and carrier-rich (metallic) stripes, which coexist in a wide range of doping x ≃ 0.02 − 0.20 , and the suppression of superconductivity observed in underdoped region near the x=1/8 is caused by the formation of insulating stripes on a global scale and by the preponderance of insulating phase compared with the metallic one. Our results are in good agreement with the existing experiments on La-based and other cuprates.

Fermi Glass Versus High-Temperature Superconductivity Behavior

Very recently BaSrNiO4 was reported to be a Fermi glass (Schilling et al. in J. Phys., Condens. Matter 21:015701, 2009). Its structure is essentially the one of K2NiF4 as is that of La2CuO4, in which the occurrence of high-temperature superconductivity (HTS) upon hole doping was first reported (Bednorz and Muller in Z. Phys. B 64:189, 1986; Adv. Chem. 100:757, 1988). The carriers in both have mainly eg character, and move in a stochastic potential as documented by a number of experiments. The difference of the two behaviors is mainly ascribed to the formation of intersite bipolarons (Kabanov and Mihailovic in J. Supercond. 13:950, 2000) , which is estimated to be up to two orders of magnitude larger in La2CuO4 than in BaSrNiO4. From this it follows that for HTS to occur, a large bipolaron formation energy in layered structures is required.

Ground and Excited States of Bipolarons in Two and ThreeDimensions

The properties of large bipolarons in two and three dimensions areinvestigated by averaging over the relative wavefunction of the twoelectrons and using the Lee-Low-Pines-Huybrechts variational method.The ground-state (GS) and excited-state energies of the Fröhlichbipolaron for the whole range of electron-phonon coupling constantscan be obtained. The energies of the first relaxed excited state(RES) and Franck–Condon (FC) excited state of the bipolaron are alsocalculated. It is found that the first RES energy is lower than theFC state energy. The comparison of our GS and RES energies withthose in literature is also given.

Precursor non-superconducting pairing and novel superconductivity in underdoped and optimally doped cuprates

The precursor non-superconducting pairing of carriers and the novel superconductivity in high- T c cuprates are studied within the large (bi)polaron model and the new BCS-like fermion and boson mean-field approximations by treating a two-component charge carrier picture. It is argued that pre-formed pairs (large bipolarons) reside in underdoped cuprates between the CuO 2 planes and remain localized in the z-direction. With lowering temperature, these large bipolarons condense into a superfluid quasi-one-dimensional Bose-liquid state. In the intermediate electron–phonon coupling regime, the Cooper-pair formation and condensation in the CuO 2 layers occur also at different temperatures. Large bipolarons and polaron Cooper pairs in optimally doped cuprates condense into a superfluid Bose-liquid state almost at the same temperature due to the doping-induced dimensional crossover.