Theory of the Room-Temperature QHE in Graphene

The unusual quantum Hall effect (QHE) in graphene is often discussed in terms of Dirac fermions moving with a linear dispersion relation. The same phenomenon will be explained in terms of the more traditional composite bosons, which move with a linear dispersion relation. The "electron" (wave packet) moves easier in the direction [1,1,0,c-axis] = [1,1,0] of the honeycomb lattice than perpendicular to it, while the "hole" moves easier in [0,0,1]. Since "electrons" and "holes" move in different channels, the number densities can be high especially when the Fermi surface has "necks". The strong QHE arises from the phonon exchange attraction in the neighborhood of the "neck" Fermi surfaces. The plateau observed for the Hall conductivity and the accompanied resistivity drop is due to the Bose-Einstein condensation of the c-bosons, each forming from a pair of one-electron--two-fluxons c-fermions by phonon-exchange attraction.Comment: 12 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1304.763

Quantum Theory of the Seebeck Coefficient in YBCO

The measured in-plane thermoelectric power (Seebeck coefficient) S ab in YBCO below the superconducting temperature T c ( ∼ 94 K) S ab is negative and T -independent. This is shown to arise from the fact that the “electrons” (minority carriers) having heavier mass contribute more to the thermoelectric power. The measured out-of-plane thermoelectric power S c rises linearly with the temperature T . This arises from moving bosonic pairons (Cooper pairs), the Bose-Einstein condensation (BEC) of which generates a supercurrent below T c . The center of mass of pairons moves as bosons. The resistivity ρ ab above T c has T -linear and T -quadratic components, the latter arising from the Cooper pairs being scattered by phonons

Fe-Mg heteorogeneity in the low-Ca pyroxenes during metamorphism of the ordinary chondrites

Pyroxenes in nine ordinary chondrites, ALH-764 (LL3), ALH-77214 (L3.4), ALH-77015 (L3.5), Yamato-74191 (L3.6), Hedjaz (L3.7), ALH-77304 (LL3.8), ALH-78084 (H3.9), Yamato-75097 (L4) and ALH-77230 (L4), were examined by an optical microscope, a scanning electron microscope with a back-scattered electron image technique, and an X-ray microprobe analyzer. Characteristic textures due to alternating lamellae of Fe-rich and Fe-poor compositions have been found in the low-Ca pyroxenes in the chondrites irrespective of their chemical groups, H, L and LL. As far as the author knows, this is the first observation of such lamellae textures in the pyroxenes. These textures are common and remarkable in the higher subtypes of type 3 chondrites (L3.6,L3.7,LL3.8 and H3.9), while they are rare in lower subtypes (<3.5) and type 4 chondrites. These textures are considered to have been formed in the Fe-Mg homogenization process of the ordinary chondrites during metamorphism

Enhancement of quantum gravity signal in an optomechanical experiment

No experimental evidence of the quantum nature of gravity has been observed yet and a realistic setup with improved sensitivity is eagerly awaited. We find two effects, which can substantially enhance the signal of gravity-induced quantum entanglement, by examining an optomechanical system in which two oscillators gravitationally couple and one composes an optical cavity. The first effect comes from a higher-order term of the optomechanical interaction and generates the signal at the first order of the gravitational coupling in contrast to the second order results in previous works. The second effect is the resonance between the two oscillators. If their frequencies are close enough, the weak gravitational coupling effectively strengthens. Combining these two effects, the signal in the interference visibility could be amplified by a factor of $10^{24}$ for our optimistic parameters. The two effects would be useful in seeking feasible experimental setups to probe quantum gravity signals.Comment: 18 pages, 7 figures, accepted version in PR

Edge-dominating cycles in graphs

AbstractA set S of vertices in a graph G is said to be an edge-dominating set if every edge in G is incident with a vertex in S. A cycle in G is said to be a dominating cycle if its vertex set is an edge-dominating set. Nash-Williams [Edge-disjoint hamiltonian circuits in graphs with vertices of large valency, Studies in Pure Mathematics, Academic Press, London, 1971, pp. 157–183] has proved that every longest cycle in a 2-connected graph of order n and minimum degree at least 13(n+2) is a dominating cycle. In this paper, we prove that for a prescribed positive integer k, under the same minimum degree condition, if n is sufficiently large and if we take k disjoint cycles so that they contain as many vertices as possible, then these cycles form an edge-dominating set. Nash-Williams’ Theorem corresponds to the case of k=1 of this result

On the metal-insulator-transition in vanadium dioxide

Vanadium dioxide (VO$_2$) undergoes a metal-insulator transition (MIT) at 340 K with the structural change between tetragonal and monoclinic crystals as the temperature is lowered. The conductivity $\sigma$ drops at MIT by four orders of magnitude. The low-temperature monoclinic phase is known to have a lower ground-state energy. The existence of a $k$-vector ${\boldsymbol k}$ is prerequisite for the conduction since the ${\boldsymbol k}$ appears in the semiclassical equation of motion for the conduction electron (wave packet). Each wave packet is, by assumption, composed of the plane waves proceeding in the ${\boldsymbol k}$ direction perpendicular to the plane. The tetragonal (VO$_2$)$_3$ unit cells are periodic along the crystal's $x$-, $y$-, and z-axes, and hence there are three-dimensional $k$-vectors. The periodicity using the non-orthogonal bases does not legitimize the electron dynamics in solids. There are one-dimensional ${\boldsymbol k}$ along the c-axis for a monoclinic crystal. We believe this decrease in the dimensionality of the $k$-vectors is the cause of the conductivity drop. Triclinic and trigonal (rhombohedral) crystals have no $k$-vectors, and hence they must be insulators. The majority carriers in graphite are "electrons", which is shown by using an orthogonal unit cell for the hexagonal lattice.Comment: 8 pages, 1 figur