arXiv subjects

David A. Rabson

Publications and source records attributed to David A. Rabson.

6 recordsLinked to original sources

arXiv2016

Atomistic Simulation of frictional anisotropy on quasicrystal approximant surfaces

Park {\it et al.} have reported eight times greater atomic-scale friction in the periodic than in the quasiperiodic direction on the two-fold face of a decagonal Al-Ni-Co quasicrystal. We present results of molecular-dynamics simulations intended to elucidate mechanisms behind this giant frictional anisotropy. Simulations of a bare atomic-force-microscope tip on several model substrates and under a variety of conditions failed to reproduce experimental results. On the other hand, including the experimental passivation of the tip with chains of hexadecane thiol, we reproduce qualitatively the experimental anisotropy in friction, finding evidence for entrainment of the organic chains in surface furrows parallel to the periodic direction.

cond-mat.mtrl-sci↗

arXiv2003

Thermoelectric Modeling of the Non-Ohmic Differential Conductance in a Tunnel Junction containing a Pinhole

To test the quality of a tunnel junction, one sometimes fits the bias-dependent differential conductance to a theoretical model, such as Simmons's formula. Recent experimental work by Åkerman and collaborators, however, has demonstrated that a good fit does not necessarily imply a good junction. Modeling the electrical and thermal properties of a tunnel junction containing a pinhole, we extract an effective barrier height and effective barrier width even when as much as 88% of the current flows through the pinhole short rather than tunneling. A good fit of differential conductance to a tunneling form therefore cannot rule out pinhole defects in normal-metal or magnetic tunnel junctions.

cond-mat↗

arXiv2003

Diagnosis and Location of Pinhole Defects in Tunnel Junctions using only Electrical Measurements

In the development of the first generation of sensors and memory chips based on spin-dependent tunneling through a thin trilayer, it has become clear that pinhole defects can have a deleterious effect on magnetoresistance. However, current diagnostic protocols based on Andreev reflection and the temperature dependence of junction resistance may not be suitable for production quality control. We show that the current density in a tunnel junction in the cross-strip geometry becomes very inhomogeneous in the presence of a single pinhole, yielding a four-terminal resistance that depends on the location of the pinhole in the junction. Taking advantage of this position dependence, we propose a simple protocol of four four-terminal measurements. Solving an inverse problem, we can diagnose the presence of a pinhole and estimate its position and resistance.

cond-mat↗

arXiv2003

Applications of Group Cohomology to the Classification of Fourier-Space Quasicrystals

In 1962, Bienenstock and Ewald described the classification of crystalline space groups algebraically in the dual, or Fourier, space. Recently, the method has been applied to quasicrystals and modulated crystals. This paper phrases Bienenstock and Ewald's definitions in terms of group cohomology. A \textit{Fourier quasicrystal} is defined, along with its space group, without requiring that it come from a quasicrystal in real (direct) space. A certain cohomology group classifies the space groups associated to a given point group and quasilattice, and the dual homology group gives all gauge invariants. This duality is exploited to prove several results that were previously known only in special cases, including the classification of space groups for quasilattices of arbitrary rank in two dimensions. Extinctions in X-ray diffraction patterns and degeneracy of electronic levels are interpreted as physical manifestations of non-zero homology classes.

math-ph↗

arXiv2003

Cohomology for Anyone

Crystallography has proven a rich source of ideas over several centuries. Among the many ways of looking at space groups, N. David Mermin has pioneered the Fourier-space approach. Recently, we have supplemented this approach with methods borrowed from algebraic topology. We now show what topology, which studies global properties of manifolds, has to do with crystallography. No mathematics is assumed beyond what the typical physics or crystallography student will have seen of group theory; in particular, the reader need not have any prior exposure to topology or to cohomology of groups.

cond-mat↗

arXiv2001

Fourier-Space Crystallography as Group Cohomology

We reformulate Fourier-space crystallography in the language of cohomology of groups. Once the problem is understood as a classification of linear functions on the lattice, restricted by a particular group relation, and identified by gauge transformation, the cohomological description becomes natural. We review Fourier-space crystallography and group cohomology, quote the fact that cohomology is dual to homology, and exhibit several results, previously established for special cases or by intricate calculation, that fall immediately out of the formalism. In particular, we prove that {\it two phase functions are gauge equivalent if and only if they agree on all their gauge-invariant integral linear combinations} and show how to find all these linear combinations systematically.

cond-mat↗