Small Polaron Theory Research Articles

Characterization of electron transport in naphthyl-oxadiazole doped polycarbonate film

Electron-transport behavior in 2.5-bis(4-naphthyl)-1,3,4-oxadiazole (BND) doped polycarbonate (PC) film was characterized through the analysis of the dependences of electron mobility on electric field, temperature, and dopant concentration according to Schein's procedure. In BND doped PC film, the zero-field activation energy (E 0) was found to depend on the distance between hopping site (p). Further, the zero-field electron-mobility u(F=0) was represented by the equation μ(F=0) = a 0ρ 2exp(−F 0(ρ)/kT), where a 0= 3.6 × 10 14 V −1s −1. These results demonstrate that electron transport in BND doped PC is described as adiabatic hopping on the basis of the small polaron theory.

Transport in α-sexithiophene films

The field-effect mobility of hole polarons in α-sexithiophene, measured in thin film transistors, was shown to be well fitted by Holstein's small polaron theory. Unfortunately, Holstein's formulation is based on an integral that does not converge. We show that the data are well fitted by a theory of polaron transport that was successful in accounting for mobility in molecular crystals of naphthalene.

Optical absorption spectra and the nature of conduction carriers of hole-doped Sr 1+ xLa 1− xFeO 4

The optical absorption as calculated from the diffuse reflectivity in the range of 0.5–5 eV and the temperature dependence of d.c. electrical conductivity of Sr 1+ x La 1− x FeO 4 (0 ≦ x ≦ 0.3) with a K 2NiF 4 structure, were measured. The results obtained were analyzed based on the small polaron model, and discussed with reference to the changes in the physical properties and the electronic structure previously reported. The Mott type and charge-transfer type excitations were observed at ∼2.2 and ∼2.7 eV, respectively, in the optical absorption spectrum of the undoped SrLaFeO 4. An additional broad absorption band below 1 eV was observed, and its intensity was directly proportional to the d.c. electrical conductivity at room temperature. Thus the absorption band below 1 eV was assigned to the optically induced polaron hopping. Based on the small polaron theory, the hopping energies of small polarons from 0.14 to 0.24 eV were obtained. These values were close to the activation energies of d.c. electrical conductivity obtained from the σT 3 2 vs 1 T plots. The results, in which the Fermi-level was fixed in the middle of the energy band gap of the photoemission spectroscopy previously reported could not be explained by the rigid-band model, but were consistent with the small polaron model.

Electrical properties of CuO doped sodium borate glasses

Electrical conduction in transition metal oxide (TMO) glasses is generally explained on the basis of the small polaron theory. Present results on CuO doped sodium borate glasses seem to be inexplicable on the basis of the above model. Experimental data on dc and ac conductivities of CuO doped sodium borate glasses at different frequencies are presented. It is found that these results can be explained in terms of the concept of small ionic polarons developed for superionic conductors.

Low temperature regime of diffusion of muon impurities in copper

We extend the usual small-polaron theory of diffusion to take into account states with finite energy width. The possibility of incoherent hopping down to T = 0 follows as a direct consequence. Assuming that positive muons in copper are in tunneling states involving just two sites and resonating with the crystal modes we calculate the temperature dependent diffusion coefficient. The results explain quantitatively the experimental data, including the anomalous regime occurring at temperatures below T = 80 K and the flat region close to T = 0. The calculation considers the real vibrational modes of copper, which leads to a remarkable agreement between theory and experiment.

Electronic conductivity of LiMn2O4B2O3 and LiMn2O4B2O3P2O5 glasses

A series of glasses in the pseudobinary system LiMn2O4-B2O3 and the pseudoternary system LiMn2O4-B2O3-P2O5 are prepared, and their electronic conductivity is measured. According to small polaron theory, the experimental results can be interpreted in terms of polaron-assisted hopping of small polarons. The glasses in the LiMn2O5-B2O3 system conduct in the non-adiabatic regime, and the substitution of P2O5 for B2O3 in the LiMn2O4-B2O3-P2O5 system does not change the conduction mechanism.

Effect of a deformation potential coupling on the ground-state energy of a tight-binding Fröhlich polaron

An upper bound to the ground-state energy of a tight-binding polaron (a polaron in a narrow band material) in a polar crystal is obtained, in the nonadiabatic limit, from a Hamiltonian that includes two contributions to the electron–phonon coupling: a short-range deformation potential interaction and a long-range dipolar interaction. A Debye cutoff on the phonon wave vectors is also assumed. A variational ground-state energy is deduced, using a modification of a tight-binding type Ansatz used in small-polaron theory, in the nonadiabatic limit. In the weak-coupling limit the ground state corresponds to that of a large polaron, while the strong-coupling limit gives a small-polaron state. The bandwidth greatly influences the state of the system and phase diagrams are presented that show the regions where the small and the large polarons are energetically favored. We find, in this variational context, that for a narrow band, the transition between the self-trapped state and the band state is continuous and that an intermediate-polaron state is involved. For a larger but moderate bandwidth, the system is found to switch abruptly from one state to the other, with a coexistence of both states around the transition region. Each of the two types of coupling is found to have an equivalent role in increasing the trapping energy of the electron and in reducing the bandwidth exponentially. Furthermore, their effect is cumulative.

Analytic Quantum Theory of Electron Transfer with a Reaction Mode Strongly Coupled to the Electron and Weakly Coupled to the Bath

We develop an effective analytic framework built around our own extension of standard small polaron theory. We assume a Hamiltonian in which the electron operators are strongly coupled to a single linear oscillator, the reaction mode, which is in turn weakly coupled to the heat bath. The Hamiltonian is transformed so that the previously bare electron is dressed in the quanta of the reaction mode but not in the quanta of the rest of the bath modes. The dressed electron, or [open quotes]reaction[close quotes], has no residual interaction with the transformed reaction mode; its remaining interactions with the bath can be treated perturbatively. Although our formalism describes the full kinetics, we present in detail here only the results of a Golden Rule calculation of the electron-transfer rate constant. We find that in the strict high-temperature limit the rate constant is of the Marcus form but with a reorganization energy that is simply the product of the reaction mode quantum energy and the dimensionless (strong) coupling constant squared, independent of the details of the phonon spectrum. This contrasts with earlier findings based on the standard polaron model that the reorganization energy is a weighted sum over the bath mode frequencies. 13more » refs., 1 fig.« less

Small-polaron hopping in Mott-insulating UO2

The DC electrical conductivity in the extrinsic regime of a slightly hyperstoichiometric sample of polycrystalline UO2+x is re-analysed using the general framework of small-polaron theory, taking into account the Mott-insulating nature of the ground state of the stoichiometric material. It is established that above about 150 K the holes move by non-adiabatic hopping, with a mobility activation energy of 0.28+or-0.02 eV. There is no conflict between electrical and thermodynamic data, contrary to some earlier theories. The implications for existing empirical determinations of the Mott-Hubbard gap, U, and the associated entropy of formation of altered-valency cations in the intrinsic regime is investigated, and new (preferred) values presented. The relatively large carrier densities predicted near melting necessitate some further consideration of the Coulomb interaction and of its influence both on the magnitude of U and on the mobility activation energy. Finally, attention is drawn to some outstanding discrepancies between the semi-empirical values of the small-polaron self-energy and mobility activation energy determined in this work, using Lang-Firsov theory, and those yielded by fully microscopic HADES calculations.

Polaron Effects in the Protonic Conductor Hydrogen Uranyl Phosphate

AbstractThe isotope effects on the conductivity of hydrogen uranyl phosphate reveal ionic polaron effects in this solid protonic conductor, in agreement with the small polaron theory. An absorption band is observed at 0.67 eV, which can be correlated with the conduction mechanism consisting in both tunnelling and over‐barrier hopping processes.

Observation of a transition from over-barrier hopping to activated tunneling diffusion: H and D on Ni(100).

Using a linear optical diffraction technique, we measured the surface diffusion coefficients for hydrogen (H) and deuterium (D) on Ni(100) at coverage \ensuremath{\theta}=0.7. From 200 K down to 120 K, the diffusion for both H and D evolves from a high-temperature activated behavior to a low-temperature activated behavior. For hydrogen, ${\mathit{D}}_{0}$=1.1\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}6}$ ${\mathrm{cm}}^{2}$/sec, ${\mathit{E}}_{\mathrm{diff}}$=3.5 kcal/mol from 200 to 160 K and ${\mathit{D}}_{0}$=1.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}9}$ ${\mathrm{cm}}^{2}$/sec, ${\mathit{E}}_{\mathrm{diff}}$=1.2 kcal/mol from 160 to 120 K. For deuterium, ${\mathit{D}}_{0}$=5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$ ${\mathrm{cm}}^{2}$/sec, ${\mathit{E}}_{\mathrm{diff}}$=5.0 kcal/mol from 200 to 170 K and ${\mathit{D}}_{0}$=9\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$ ${\mathrm{cm}}^{2}$/sec, ${\mathit{E}}_{\mathrm{diff}}$=1.05 kcal/mol from 170 to 120 K. Our preliminary analysis based upon small-polaron theories and available surface-phonon data suggests that the observed transition is most likely to be from an over-barrier hopping to an activated tunneling diffusion.

A Green functions approach to the orientational behaviour of pairs of coupled two-level tunnelling units

The equation of motion method for the Green's functions is applied to study the behaviour of pairs of interacting two-level tunnelling units, coupled with a phonon field to calculate, within the framework of the small-polaron theory, the dynamic susceptibilities and relaxation rates of the system. Explicit expressions for these quantities are obtained in the Debye approximation.

Conductivity, chemical equilibria and small polaron in oxide superconductor: YBa 2Cu 3O 7− δ

An investigation of the structures of the thermal variations of the conductivities, σ( T,δ)'s, and an examination of the chemical equilibria in YBa 2Cu 3O 7− δ indicate the existence of a small polaron in the normal state. The overall structures of σ ( T),δ)'s can be analyzed in terms of delocalized and localized (thermally activated) carriers with narrow band tunneling (Fermi energy of order of 10 −4 eV) and hopping (activation energy of the order of 10 −2eV), respectively. The rapidly increasing σ( T) observed in some cases at low decreasing temperatures corresponds to the heretofore unrecognized narrow band tunneling in the small polaron theory: as a consequence of the chemical equilibria which must be recognized in any mechanism of conductivity in the normal state, thermodynamic equilibria can be associated with small polarons in which charge is transported through the time rate of change in the dipole moments. A precondition for the onset of the superconducting state is the co-existence of the two mechanisms and some relation between their two parameters such as the one derived by Allender, Bray and Bardeen (Phys. Rev. B 7 (1973) 1020). The superconducting state appears to be a bipolaronic state.

Phonon-assisted diffusion and electromigration of light interstitials in metals.

We present a microscopic description of phonon-assisted diffusion of light interstitial impurities in metals including migration in the presence of an electron current (electromigration). The approach is self-consistent without separation into two parts (atom diffusion and electron scattering) and is appropriate for the regime of incoherent nonadiabatic atom hopping between polaron-type states at adjacent interstices. A general expression is obtained in the linear-response approximation for both the diffusion and the electron conduction contributions to atomic current. The atom current is shown to be related to an effective driving force through a Nernst-Einstein expression, and this driving force is shown to be the sum of a direct force and a wind force from the electron flow. The wind force in the general case is not determined by the Fiks-Huntington ballistic-model expression but decreases rapidly with the quantity ${\mathit{k}}_{\mathit{F}}$d, where ${\mathit{k}}_{\mathit{F}}$ is the electron Fermi momentum and d is the hopping distance. This decrease is due to strong recoil effects associated with momentum transfer to the lattice. Our results do not require the validity of the Condon approximation of small-polaron theory.

Small-polaron theory of doped antiferromagnets.

The spin-hole coherent-state path integral is used to generate a systematic large-spin expansion of the t-J model on the square lattice. The single hole's classical energy is minimized by small polarons with short-ranged interactions. Intersublattice hopping of polarons is forbidden by a tunneling selection rule. We derive the low-energy Lagrangian which reduces to the model of Wiegmann, Wen, Shankar, and Lee of N\'eel-gauge-field induced superconductivity.

Semiconducting properties of barium vanadate glasses doped with barium chloride

Semiconducting barium vanadate glasses doped with BaCl2 from 0 to 15 mol% were studied. Electrical d.c. conductivity σ measurements and an electron spin resonance investigation in the X-band were made. The concentration dependence of d.c. conductivity exhibits a minimum at 7 mol% BaCl2. The activation energy increases with increasing BaCl2 content up to 7% and decreases at higher concentrations of BaCl2. The temperature dependence of the d.c. conductivity shows the effect of BaCl2 as an oxidizing agent which controls the electrical conductivity, as a result of modification of the reduced vanadium valence ratio and a change in concentration of the paramagnetic ions. The plots of log σ versus 1 000/T are linear for all the BaCl2-doped glasses. The data of the d.c. investigations were analyzed in terms of small polaron theory, and this confirms the applicability of the polaronic hopping model of electrical transport. The influence of BaCl2 content on density indicates that in this ternary system the additivity role is not obeyed. The minimum occurs at the same concentration of 7 mol% BaCl2 as noted for the electrical conductivity.

Electronic conductivity in glasses of the TeO 2-V 2O 5-MoO 3 system

Conductivity and redox potential on glasses of the TeO 2-V 2O 5-MoO 3 system have been measured. For temperatures between 20 to 200°C, the electronic conductivity proceed by an activated mechanism. Variations of the pre-exponential factor interpreted by the small polaron theory indicate that only the vanadium ions are involved in the conduction mechanism. Cyclic voltamperometry measurements performed on TeO 2-V 2O 5-MoO 3 glasses as working electrode show that a 1 V difference between the V +V V +IV and Mo +VI Mo +V redox potentials exists in the glassy material. This correspond to an energy gap which may be to large to allow the electron transition from vanadium to molybdenum ions.

Systematic studies on Bi-Sr-Ca-Cu-O glasses and glass ceramics

Bi-Sr-Ca-Cu-O glasses and glass ceramics of various compositions have been synthesised. The glass transition temperature varies from 396 to 422 degrees C depending on the glass composition. DC electrical conductivity, measurements on these glasses show a sharp change in slope of the plot of logarithm of conductivity against reciprocal of temperature at a characteristic temperature that depends on the glass composition. The conductivity data divide into two distinct temperature regions: the conductivity mechanism at low temperatures has a much lower activation energy than that at higher temperatures. The results are discussed in terms of the small polaron theory. Electrical conductivity measurements on the bulk glass ceramics show that the samples of Bi4Sr3Ca3Cu4Ox, Bi4Sr3Ca3Cu6Ox, Bi2Sr2Ca2Cu3Ox and Bi4Sr2Ca4Cu6Ox compositions show superconductivity with Tc(onset) above liquid nitrogen temperature when heat treated at 820 degrees C for 3, 9, 12 and 24 h respectively. The Bi4Sr3Ca3Cu4Ox bulk superconducting glass ceramic is an almost single-phase material with preferred orientation such as the c axis is perpendicular to the sample surface. The Bi2Sr2Ca2Cu3Ox glass ceramic has higher Tc(onset) and thus shows the possibility of obtaining a superconducting material with Tc(zero) of 110 K. The possible reasons for the low Tc(zero) observed in these glass ceramics and the methods for its enhancement are discussed.

An In-Depth Study of the Effects of the Electric Field on Charge Carrier Mobilities in Molecularly Doped Polymers

Abstract It is well known that charge carrier mobilities μ in molecularly doped polymers (MDP) determined by transient photoconductivity experiments depend on three variables, the temperature T, the mean distance between dopant molecules ρ, and the electric field E. Recently introduced deconvolution procedures have made possible the first systematic determination of the dependence of μ on T, ρ, and E. This determination led to the suggestion that the T and ρ dependencies are consistent with small polaron theory. However, the electric field dependence of μ remains unexplained. In this paper we present an in-depth study of the electric field dependence of charge carrier mobilities in MDP.

Soliton excitations of a small-polaron band.

We present a generalization of small-polaron band theory based on methods used in the study of Davydov solitons. The eigenstates of the small-polaron band are found to be stationary solutions of our equations of motion; however, among the nonstationary solutions can be found a family of soliton states. The soliton solutions we obtain differ from Davydov solitons in fundamental ways, but are fully consistent with the theory of small polarons.