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Dennis P. Clougherty

Publications and source records attributed to Dennis P. Clougherty.

31 records · Page 2Linked to original sources
arXiv2007

Theory of electric polarization induced by inhomogeneity in crystals

We develop a general theory of electric polarization induced by inhomogeneity in crystals. We show that contributions to polarization can be classified in powers of the gradient of the order parameter. The zeroth order contribution reduces to the well-known result obtained by King-Smith and Vanderbilt for uniform systems. The first order contribution, when expressed in a two-point formula, takes the Chern-Simons 3-form of the vector potentials derived from the Bloch wave functions. Using the relation between polarization and charge density, we demonstrate our formula by studying charge fractionalization in a two-dimensional dimer model recently proposed.

cond-mat.mes-hall↗
arXiv2006

Polarons and Solitons in Jahn-Teller Systems

Using a semiclassical continuum model of an electron in a deformable molecular crystal, some properties of multicomponent generalizations of the polaron--``vector polarons''-- are elucidated. Analytical solutions for the case of two electronic bands coupled to two vibrational modes are given in detail. Within the model considered, the vector polaron can be classified by its wavefunction into several types and can have features that include: (1) a spatial variation in the electronic and vibrational character, and (2) low-energy internal degrees of freedom. For the case of electronic and vibrational degeneracy, local Jahn-Teller interactions can also lead to a novel spatiotemporal soliton, a long-lived excited state of the many-electron system stabilized by the conservation law resulting from degeneracy.

cond-mat.mtrl-sci↗
arXiv2006

Theory and Application of Dissociative Electron Capture in Molecular Identification

The coupling of an electron monochromator (EM) to a mass spectrometer (MS) has created a new analytical technique, EM-MS, for the investigation of electrophilic compounds. This method provides a powerful tool for molecular identification of compounds contained in complex matrices, such as environmental samples. EM-MS expands the application and selectivity of traditional MS through the inclusion of a new dimension in the space of molecular characteristics--the electron resonance energy spectrum. However, before this tool can realize its full potential, it will be necessary to create a library of resonance energy scans from standards of the molecules for which EM-MS offers a practical means of detection. Here, an approach supplementing direct measurement with chemical inference and quantum scattering theory is presented to demonstrate the feasibility of directly calculating resonance energy spectra. This approach makes use of the symmetry of the transition-matrix element of the captured electron to discriminate between the spectra of isomers. As a way of validating this approach, the resonance values for twenty-five nitrated aromatic compounds were measured along with their relative abundance. Subsequently, the spectra for the isomers of nitrotoluene were shown to be consistent with the symmetry-based model. The initial success of this treatment suggests that it might be possible to predict negative ion resonances and thus create a library of EM-MS standards.

physics.chem-ph↗
arXiv2006

Jahn-Teller Solitons, Structural Phase Transitions and Phase Separation

It is demonstrated that under common conditions a molecular solid subject to Jahn-Teller interactions supports stable Q-ball-like non-topological solitons. Such solitons represent a localized lump of excess electric charge in periodic motion accompanied by a time-dependent shape distortion of a set of adjacent molecules. The motion of the distortion can correspond to a true rotation or to a pseudo-rotation about the symmetric shape configuration. These solitons are stable for Jahn-Teller coupling strengths below a critical value; however, as the Jahn-Teller coupling approaches this critical value, the size of the soliton diverges signaling an incipient structural phase transition. The soliton phase mimics features commonly attributed to phase separation in complex solids.

cond-mat.mtrl-sci↗
arXiv2004

Vector Polarons in a Degenerate Electron System

We consider a one dimensional model of an electron in a doubly (or nearly) degenerate band that interacts with elastic distortions. We show that the electron equations of motion reduce to a set of coupled non-linear Schrodinger equations. For the case of interband electron-phonon coupling stemming from local Jahn-Teller interactions, new multicomponent self-localized polaron solutions --vector polarons-- are described and classified. The phase diagram for the different types of vector polarons in this model is presented. By interpreting the components of the orbital doublet as those of spin-1/2, our results can also be used to describe bound magnetic polarons.

cond-mat.mtrl-sci↗
arXiv2003

Anomalous Threshold Laws in Quantum Sticking

It has been stated that for a short-ranged surface interaction, the probability of a low-energy particle sticking to a surface always vanishes as $s\sim k$ with $k\to 0$ where $k=\sqrt{E}$. Deviations from this so-called universal threshold law are derived using a linear model of particle-surface scattering. The Fredholm theory of integral equations is used to find the global conditions necessary for a convergent solution. The exceptional case of a zero-energy resonance is considered in detail. Anomalous threshold laws, where $s\sim k^{1+α}, α> 0$ as $k\to 0$, are shown to arise from a soft gap in the weighted density of states of excitations; $α$ is determined by the behavior of the weighted density of states near the binding energy.

cond-mat↗
arXiv2002

Ferroelectricity in (K@C$_{60}$)$_n$

A theoretical analysis of the ground state of long-chain (K@C$_{60}$)$_n$ is presented. Within mean field theory, a ferroelectric ground state is found to be stable because of the pseudo-Jahn-Teller mixing of the b$_{1u}$ and the b$_{2g}$ band with a zone-center optical phonon involving the displacement of the endohedral K^+ ions. A phase diagram for this model is derived in the narrow bandwidth regime.

cond-mat.mtrl-sci↗
arXiv2002

Endohedral Impurities in Carbon Nanotubes

A generalization of the Anderson model that includes pseudo-Jahn-Teller impurity coupling is proposed to describe distortions of an endohedral impurity in a carbon nanotube. Treating the distortion within mean-field theory, spontaneous axial symmetry breaking is found when the vibronic coupling strength g exceeds a critical value g$_c$. The effective potential in the symmetry-broken state is found to have O(2) symmetry, in agreement with numerical calculations. For metallic zigzag nanotubes endohedrally-doped with transition metals in the dilute limit, the low-energy properties of the system may display two-channel Kondo behavior; however, strong vibronic coupling is seen to exponentially suppress the Kondo energy scale.

cond-mat.mtrl-sci↗
arXiv1998

Theory of Spontaneous Polarization of Endohedral Fullerenes

A pseudo-Jahn-Teller model describing central atom distortions is proposed for endohedral fullerenes of the form A@C$_{60}$ where A is either a rare gas or a metal atom. A critical (dimensionless) coupling $g_c$ is found, below which the symmetric configuration is stable and above which inversion symmetry is broken. Vibronic parameters are given for selected endohedral fullerenes.

cond-mat↗
arXiv1996

Stability and Teller's Theorem: A Thomas-Fermi Theory of Fullerenes

We study {{\rm C}$_{60}$} with the use of Thomas-Fermi theory. A spherical shell model is invoked to treat the nuclear potential, where the nuclear and core charges are smeared out into a shell of constant surface charge density. The valence electron distribution and the electrostatic potential are efficiently computed by integration of the Thomas-Fermi equation, subject to the shell boundary conditions. Total energy is numerically calculated over a range of shell radii, and the mechanical stability of the model is explored, with attention to the constraints of Teller's theorem. The calculated equilibrium radius of the shell is in good agreement with experiment.

chem-ph↗
arXiv1996

On the Stability of Endohedral Rare Gas Fullerenes

The stability of Ne@C$_{60}$ and He@C$_{60}$ is discussed in the context of a spherical model where the carbon atoms are smeared out into a uniform shell. The electronic properties of the sixty $π$ electrons together with those of the central atom are treated in the Thomas-Fermi approximation. Simple electrostatic reasoning elucidates the nature of the radial stability of the complex. A method to include non-spherical corrections is outlined. Possible bonding topologies of the central atom and the C$_{60}$ cage are discussed, as well as the relevance of these topologies to incipient central atom distortions.

chem-ph↗
arXiv1996

On The Low-Frequency Vibrational Modes of C$_{60}$

The vibrational spectrum of C$_{60}$ is compared to the spectrum of a classical isotropic elastic spherical shell. We show correlations between the low frequency modes of C$_{60}$ and those of the spherical shell. We find the spherical model gives the approximate frequency ordering for the low frequency modes. We estimate a Poisson ratio of $σ\approx 0.30$ and a transverse speed of sound of $v_s\approx 1800$ m/s for the equivalent elastic shell. We also find that $ω({\rm M_1})/ω({\rm M_0})=\sqrt{3\over 2}$ for the shell modes ${\rm M_0}$ and ${\rm M_1}$, independent of elastic constants. We find that this ratio compares favorably with an experimental value of 1.17.

mtrl-th↗