David Emin

Studies of small-polaron motion IV. Adiabatic theory of the Hall effect

Abstract The two-dimensional molecular crystal model of Friedman and Holstein describing the motion of a small polaron in the presence of a magnetic field is studied in the adiabatic approximation. Upon averaging over the electronic coordinates, according to the standard prescription, one finds that the vibrational Hamiltonian contains (in addition to the usual terms, namely the carrier-free vibrational Hamiltonian supplemented by the energy of the excess electron expressed as a function of vibrational coordinates) a term which is linearly dependent on the lattice momentum and proportional to the magnetic field. In the adiabatic theory the effect of the magnetic field on the motion of the small polaron is found by studying the influence of the magnetic term of the vibrational Hamiltonian on the particular vibrational motions which correspond to the passage of the excess carrier from one site to a particular neighbor. In the present work, concerned only with the high temperature regime (in practice, temperatures above 1 2 θ Debye ) within which the small polaron moves through the lattice by a succession of incoherent jumps between neighboring sites, the vibrational motion is treated classically, as is appropriate at sufficiently high temperatures. It is found that although the temperature dependence of the drift mobility that is herein calculated differs little from that derived in the Friedman-Holstein perturbation calculation, the Hall mobility temperature dependence (for reasonable choices of the physical parameters) differs markedly from the perturbation result. In particular, for appropriate choices of the physical parameters, the adiabatic Hall mobility can be a decreasing function of temperature. Thus the absence of an activated Hall mobility is not in itself evidence against small polaron motion.

High mobility n‐type charge carriers in large single crystals of anatase (TiO2)

Resistivity, thermopower, and Hall‐effect measurements on large single crystals of the anatase form of TiO2 all indicate high mobility n‐type carriers that are produced by thermal excitation from a density of ∼1018 cm−3 putatively present shallow donor states. The decrease of the mobility with increasing temperature is consistent with the scattering of carriers by the optical phonons of TiO2.

Phonon-assisted transition rates I. Optical-phonon-assisted hopping in solids

Abstract An extensive calculation of the optical-phonon-assisted transition rates for non-adiabatic electronic hopping motion in a solid is presented. Holsteins Molecular Crystal Model is used as a basis for study and the computation involves no restrictions on either the magnitude of the electron-lattice coupling strength, the temperature, or the difference between the electronic energies of the initial and final sites. In the strong-coupling small-polaron regime, the jump rates, associated d.c. conductivity, a.c. conductivity, and electric-field dependence of the d.c. conductivity, for a crystal are all calculated. These transport properties manifest qualitatively distinct behaviours corresponding to whether the temperature is above or well below the optical-phonon temperature. In the low-temperature regime the energy-conserving processes which involve the absorption of the minimum amount of vibrational energy provide the dominant contribution to the thermally activated jump rates. At sufficiently high...

Icosahedral boron-rich solids

Boron‐rich molecules and solids hold a special place within chemistry. They do not follow the general bonding rules we are taught in chemistry classes. For example, some boron‐rich solids are composed of 12‐atom clusters of boron atoms in which each boron atom resides on a vertex of an icosahedron. These solids are very stable refractory materials with melting temperatures up to 2400 °C—a thousand degrees greater than silicons. Beyond this, they possess numerous novel structural, electronic and thermal properties that are not only interesting but useful.

On the existence of free and self-trapped carriers in insulators: an abrupt temperature-dependent conductivity transition

Abstract A variational calculation of the eigenstates of the three-dimensional analogue of Holsteins Molecular Crystal Model is utilized as a basis for determining the conditions under which carrier self-trapping does or does not occur in this system. It is found that below a temperature-dependent critical value of the electron-lattice coupling strength self-trapping does not occur; the eigenstates then correspond to an excess electron being only weakly coupled to the vibratory motion. Above a larger temperature-dependent critical value of the electron-lattice coupling strength only self-trapped (small-polaron) eigenstates exist. Between these two (temperature-dependent) critical values of the electron-lattice coupling strength both types of solutions are found. The condition for the existence of the weakly coupled situation, as well as that for the self-trapped circumstance, is shown to be derivable from arguments which are independent of the detailed variational calculation. These ancillary derivations...

The sign of the Hall effect in hopping conduction

Abstract The absolute sign of the Hall effect is determined for several situations charac teristic of hopping in covalent materials. In particular, it is shown that the hopping of an excess electron between the antibonding orbitals of an odd-membered (three-site) ring will yield an ‘anomalously’ signed Hall effect, namely, p-type. In addition, the Hall effect for holes moving between bonding orbitals in a similar odd-membered structure will yield an n-type Hall effect. However, electron hopping between the antibonding orbitals and hole hopping between the bonding orbitals of an even-membered (four-site) ring yields the conventional result : n-type and p-type Hall effects, respectively. Other physically relevant situations are also discussed. These examples all serve to illustrate that the sign of the Hall effect for both electrons and holes depends not only on the local geometry but on the nature and relative orientations of the local orbitals between which the carrier moves. Furthermore, these results pr...

HALL-EFFECT SIGN ANOMALY AND SMALL-POLARON CONDUCTION IN (LA1-XGDX)0.67CA0.33MNO3

The Hall coefficient of Gd-doped La{sub 2/3}Ca{sub 1/3}MnO{sub 3} exhibits Arrhenius behavior over a temperature range from 2T{sub c} to 4T{sub c}, with an activation energy very close to (2)/(3) that of the electrical conductivity. Although both the doping level and thermoelectric coefficient indicate holelike conduction, the Hall coefficient is electronlike. This unusual result provides strong evidence in favor of small-polaronic conduction in the paramagnetic regime of the manganites. {copyright} {ital 1997} {ital The American Physical Society}

A proposed boron-carbide-based solid-state neutron detector

Its large cross section for absorption of thermal neutrons has made B10 a frequent candidate for use in neutron detectors. Here a boron-carbide-based thermoelectric device for the detection of a thermal-neutron flux is proposed. The very high melting temperatures and the radiation tolerance of boron carbides make them suitable for use within hostile environments (e.g., within nuclear reactors). The large anomalous Seebeck coefficients of boron carbides are exploited in proposing a relatively sensitive detector of the local heating that follows the absorption of a neutron by a B10 nucleus in a boron carbide.

Unravelling Small-Polaron Transport in Metal Oxide Photoelectrodes

Transition-metal oxides are a promising class of semiconductors for the oxidation of water, a process that underpins both photoelectrochemical water splitting and carbon dioxide reduction. However, these materials are limited by very slow charge transport. This is because, unlike conventional semiconductors, material aspects of metal oxides favor the formation of slow-moving, self-trapped charge carriers: small polarons. In this Perspective, we seek to highlight the salient features of small-polaron transport in metal oxides, offer guidelines for their experimental characterization, and examine recent transport studies of two prototypical oxide photoanodes: tungsten-doped monoclinic bismuth vanadate (W:BiVO4) and titanium-doped hematite (Ti:α-Fe2O3). Analysis shows that conduction in both materials is well-described by the adiabatic small-polaron model, with electron drift mobility (distinct from the Hall mobility) values on the order of 10(-4) and 10(-2) cm(2) V(-1) s(-1), respectively. Future directions to build a full picture of charge transport in this family of materials are discussed.

Rhombohedral crystal structure of compounds containing boron‐rich icosahedra

The crystal structures of several icosahedral boron containing compounds have been refined using Mo Kα intensity data. Though these compounds, α‐boron, boron carbide, boron phosphide and boron arsenide, differ chemically, all have the same basic rhombohedral structure. The structures consist of icosahedral units bonded together with direct B‐B bonds as well as other linkage units. Similarities in electron distributions are found with respect to the icosahedra in all the compounds; differences are associated with the linkage units. The icosahedral bond distances show trends as one progresses along the series with increasing linkage units.