arXiv subjects

Philip B. Allen

Publications and source records attributed to Philip B. Allen.

64 records · Page 4Linked to original sources

arXiv1999

Surface Phonons and Other Localized Excitations

The diatomic linear chain of masses coupled by harmonic springs is a textboook model for vibrational normal modes (phonons) in crystals. In addition to propagating acoustic and optic branches, this model is known to support a ``gap mode'' localized at the surface, provided the atom at the surface has light rather than heavy mass. An elementary argument is given which explains this mode and provides values for the frequency and localization length. By reinterpreting this mode in different ways, we obtain the frequency and localization lengths for three other interesting modes: (1) the surface vibrational mode of a light mass impurity at the surface of a monatomic chain; (2) the localized vibrational mode of a stacking fault in a diatomic chain; and (3) the localized vibrational mode of a light mass impurity in a monatomic chain.

cond-mat↗

arXiv1999

Diffusons, Locons, Propagons: Character of Atomic Vibrations in Amorphous Si

Numerical studies of amorphous silicon show that the lowest 4% of vibrational modes are plane-wave like ("propagons") and the highest 3% of modes are localized ("locons"). The rest are neither plane-wave like nor localized. We call them "diffusons." Since diffusons are by far the most numerous, we try to characterize them by calculating such properties as wavevector and polarization (which seem not to be useful), "phase quotient" (a measure of the change of vibrational phase on between first neighbor atoms), spatial polarization memory, and diffusivity. Localized states are characterized by finding decay lengths, inverse participation ratios, and coordination numbers of the atoms participating.

cond-mat.dis-nn↗

arXiv1999

Toward a Theory of Orbiton Dispersion in LaMnO_3

At 750K, LaMnO_3 has a cooperative Jahn-Teller (JT) distortion, with Mn atoms in distorted oxygen octahedra. This lifts the degeneracy of the singly-occupied $e_g$ orbitals of the Mn$^{3+}$ ions, which then become orbitally ordered. We use a minimal model to describe the ordered phase at T=0. The on-site Coulomb repulsion $U$ is set to infinity. There are two electronic orbitals and three oxygen vibrational coordinates per unit cell. In addition to spin excitations and phonons, the model has electronic excitations consisting of mis-orienting orbitals on Mn ions. Neglecting coupling to the oxygen displacements, the gap to such excitations is $2Δ=16g^2/K$ where $g$ is the electron-phonon coupling and $K$ is the oxygen spring constant. When static oxygen displacements are coupled, this excitation becomes a self-trapped exciton with energy $Δ$, half the JT gap. Adding dynamic oxygen displacements in one-phonon approximation introduces dispersion to both the (previously Einstein-like) phonons and the orbital excitons (``orbitons''). One of the phonon branches has zero frequency at $\vec{k}=(0,0,π)$. This is the Goldstone mode of the JT broken symmetry.

cond-mat.str-el↗

arXiv1999

The Anti-Jahn-Teller Polaron in LaMnO$_3$

Distortions of the oxygen sublattice couple to $e_g$ orbitals of Mn$^{3+}$ and drive a cooperative Jahn-Teller (orbital ordering) transition in LaMnO$_3$. A simple model for this transition is studied. Without further adjustment, the model predicts the shape and stability of small (anti-Jahn-Teller) polarons which form when holes are doped into the material. This leads to a new description of the lightly doped insulator, the anti-ferromagnetic to ferromagnetic transition, and the metal-insulator transition.

cond-mat.str-el↗

arXiv1999

Theory of sound attenuation in glasses: The role of thermal vibrations

Sound attenuation and internal friction coefficients are calculated for a realistic model of amorphous silicon. It is found that, contrary to previous views, thermal vibrations can induce sound attenuation at ultrasonic and hypersonic frequencies that is of the same order or even larger than in crystals. The reason is the internal-strain induced anomalously large Grüneisen parameters of the low-frequency resonant modes.

cond-mat↗

arXiv1998

Electron transport through a circular constriction

We calculate the conductance of a circular constriction of radius $a$ in an insulating diaphragm which separates two conducting half-spaces characterized by the mean free path $\ell$. Our exact result interpolates between the Maxwell conductance in diffusive ($\ell \ll a$) and the Sharvin conductance in ballistic ($\ell \gg a$) transport regime. Following the earlier approach of Wexler we find the explicit form of the Green's function for the linearized Boltzmann operator. The formula for the conductance deviates by less than 11% from the naive interpolation formula obtained by adding resistances in the diffusive and the ballistic regime.

cond-mat.dis-nn↗

arXiv1997

Thermal Expansion and Gruneisen Parameters of Amorphous Silicon: A Realistic Model Calculation

Using a realistic model, the mode Gruneisen parameters and the temperature dependent coefficient of linear thermal expansion are calculated for amorphous silicon. The resulting values of the Gruneisen parameters differ from the crystalline case in having all diversity suppressed, except for a minority of high-frequency localized and low-frequency resonance modes. The latter have very large, mostly negative Gruneisen parameters (up to -31), caused by volume driven internal strain. As a result, the values for thermal expansivity are lower than those of crystalline silicon and are sample dependent.

cond-mat.dis-nn↗

arXiv1996

Polaron and bipolaron formation in a cubic perovskite lattice

The Rice-Sneddon model for BaBiO$_3$ is a nice model Hamiltonian for considering the properties of polarons and bipolarons in a three-dimensional oxide crystal. We use exact diagonalization methods on finite samples to study the stability and properties of polarons and bipolarons. Because polarons, when they form, turn out to be very well-localized, we are able to converge accurately our calculations for two-electron bipolaron wavefunctions, accounting for the Coulomb interaction without approximation. Some of our results are compared with and interpreted by reference to the variational method of Landau and Pekar. We calculate both electronic and vibrational excitations of the small polaron solutions, finding a single vibrational state localized with the full symmetry of the polaron, which has its energy significantly increased. Both on-site (Hubbard) and long-range Coulomb repulsion are included in the bipolaron calculation, but due to the high degree of localization, the long-range part has only a small influence. For a reasonable on-site repulsion $U$ equal to 2 times the band width $W$, bipolaron formation is significantly suppressed; there is a large window of electron-phonon coupling where the polaron is stable but the bipolaron decays into two polarons.

cond-mat↗

arXiv1996

Anharmonic Decay of Vibrational States in Amorphous Silicon

Anharmonic decay rates are calculated for a realistic atomic model of amorphous silicon. The results show that the vibrational states decay on picosecond timescales and follow the two-mode density of states, similar to crystalline silicon, but somewhat faster. Surprisingly little change occurs for localized states. These results disagree with a recent experiment.

cond-mat↗

arXiv1995

Interactions for odd-omega gap singlet superconductors

A class of singlet superconductors with a gap function $Δ({\bf k}, ω_n)$ which is {\it odd} in both momentum and Matsubara frequency was proposed recently \cite{ba}. To show an instability in the {\it odd} gap channel, a model phonon propagator was used with the $p$-wave interaction strength larger than the $s$-wave. We argue that the positive scattering matrix element entering the Eliashberg equations leads to a constraint on the relative strength of $p$- and $s$-wave interactions which inhibits odd pairing. However, a general spin dependent electron-electron interaction can satisfy all constraints and produce the odd singlet gap. A possibility which may lead to an odd gap is a strongly antiferromagnetically correlated system, such as a high-$T_c$ material.

cond-mat↗