Strong Commensurability Research Articles

Vortex core near planar defects in a clean layered superconductor

We investigate the structure of quasiparticle states localized in a core of an Abrikosov vortex in a clean layered superconductor in the presence of planar defects. It is shown that even a highly transparent defect opens a minigap at the Fermi energy. Its magnitude, $E_g\sim\Delta\sqrt{R}$, exceeds the mean level spacing for the chiral branch, $\omega_0\sim\Delta^2/E_F$, already for very small values of the reflection coefficient off the defect, $R\ll1$ ($\Delta$ is the bulk gap). For $R\gtrsim\sqrt{\Delta/E_F}$, formation of the minigap is accompanied by the appearance of subgap states localized along the defect, in accordance with [A. V. Samokhvalov \emph{et al.}, Phys.\ Rev.\ B \textbf{102}, 174501 (2020)]. The minigap takes its maximal value for the vortex located right at the defect, decreases with increasing the distance $b$ from the defect, and closes when $k_Fb\sim (\Delta/\omega_0)\sqrt{R}$. We also study various configurations of several planar defects (few crossing planes, stars, periodic structures). Although the minigap remains, a strong commensurability effect is observed. For two crossing planar defects, the magnitude of the minigap strongly depends on how close the intersection angle is to a rational fraction of $\pi$.

Generalised commensurability properties of efficiency measures: Implications for productivity indicators

We analyse the role of new weak and strong commensurability conditions on efficiency measures and especially on productivity measurement. If strong commensurability fails, then a productivity index (indicator) may exhibit a homogeneity bias yielding inconsistent and contradictory results. In particular, we show that the Luenberger productivity indicator is sensitive to proportional changes in the input-output quantities, while the Malmquist productivity index is not affected by such changes. This is due to the homogeneity degree of the directional distance function under constant returns to scale. In particular, the directional distance function only satisfies the weak commensurability axiom in general. However, if the directional distance function is a diagonally homogeneous function of the technology, then the directional distance function satisfies strong commensurability. This explains why the direction of an arithmetic mean of the observed data works well. Numerical examples and an empirical illustration are proposed. Under a translation homothetic technology, the Luenberger productivity indicator is not affected by any additive directional transformation of the observations.

Effect of Strong Orbital Magnetic Field on the Exciton Condensation in an Extended Falicov Kimball Model

A spinless, extended Falicov-Kimball model in the presence of a perpendicular magnetic field is investigated employing a self-consistent mean-field theory in two dimensions. In the presence of the field the excitonic average Δ =< di†fi > is modified: the exciton responds in subtle different ways for different values of the magnetic flux. We examine the effects of Coulomb interaction and hybridization between the localized and itinerant electrons on the excitonic average, for rational values of the applied magnetic field. The excitonic average is found to get enhanced exponentially with the Coulomb interaction while it saturates at large hybridization. The orbital magnetic field suppresses the excitonic average in general, though a strong commensurability effect of the magnetic flux on the behaviour of the excitonic order parameter is observed.

The interaction dynamics of a vehicle traveling along a simply supported beam under variable velocity condition

This paper studies the interaction dynamics of a vehicle traveling on a simply supported beam. A simple quarter-car planar model of the vehicle is taken into account. The system of the quarter-car model is treated as a moving mass with a massless harmonic force rolling on a simply supported beam. The objective of this paper is to present analytical and numerical methodologies to evaluate the vehicle–beam coupling effects when the vehicle moves under variable speed condition. Due to the presence of friction and convective acceleration, the vehicle can be accelerated by a forward force. Meanwhile, the vehicle is capable of reducing speed by applying a retard force to the vehicle and/or increasing the friction between the vehicle and beam. This results in variable velocity, acceleration, and deceleration, as well as unknown location of the vehicle along the beam. Result shows that as the spring stiffness of the suspension is close to the resonant value, strong commensurability between the oscillating frequency of the vehicle and the vibrant frequency of beam occurs when the instantaneous speed of the vehicle becomes a small quantity. In other words, a commensurable condition between the vehicle and beam is weakened when the vehicle is accelerated by a positive driving force; it becomes strong if the vehicle is decelerated by a negative reverse force and friction. If the vehicle reduces its traveling speed sharply, large amplitude and high oscillating frequency of the vehicle were generated. This significantly reduces the riding comfort for passengers in the vehicle. The applied force and coefficient of friction can be treated as tuning parameters to determine the resonant region of the interaction dynamics of a vehicle–beam system.

Commensurability Effects for Fermionic Atoms Trapped in 1D Optical Lattices

Fermionic atoms in two different hyperfine states confined in optical lattices show strong commensurability effects due to the interplay between the atomic density wave ordering and the lattice potential. We show that spatially separated regions of commensurable and incommensurable phases can coexist. The commensurability between the harmonic trap and the lattice sites can be used to control the amplitude of the atomic density waves in the central region of the trap.

Thermal fluctuations of vortex clusters in quasi-two-dimensional Bose-Einstein condensates

We study the thermal fluctuations of vortex positions in small vortex clusters in a harmonically trapped rotating Bose-Einstein condensate. It is shown that the order-disorder transition of two-shells clusters occurs via the decoupling of shells with respect to each other. The corresponding "melting" temperature depends stronly on the commensurability between numbers of vortices in shells. We show that "melting" can be achieved at experimentally attainable parameters and very low temperatures. Also studied is the effect of thermal fluctuations on vortices in an anisotropic trap with small quadrupole deformation. We show that thermal fluctuations lead to the decoupling of a vortex cluster from the pinning potential produced by this deformation. The decoupling temperatures are estimated and strong commensurability effects are revealed.

Thermodynamic and structural study of methanol thin films adsorbed on MgO(100)

Thermodynamic and structural properties of methanol monolayer and multilayer films adsorbed on MgO(1 0 0) surface have been investigated by neutron diffraction and volumetric adsorption isotherms techniques. The form of the measured adsorption isotherms varies with the temperature range. At higher temperature isotherms are composed of two steps with equal height indicating the condensation of two layers with identical density. At lower temperature the formation of the previous two layers undergoes a succession of transitions. The neutron diffraction spectra, measured at θ=2 monolayers, show a strong commensurability of the CH3OH monolayer and bilayer films with the MgO(1 0 0) surface.

Structure of the neopentane monolayer adsorbed on MgO(0 0 1): experiments and calculations

The monolayer of C(CH 3) 4 molecules adsorbed upon a highly homogeneous MgO powder surface has been studied by means of neutron diffraction techniques at the temperature 210 K. The structure of the monolayer presents a strong commensurability c(2 × 4) with the MgO(0 0 1) surface. The results of potential calculations support the proposed structure.

Strong commensurability effect on metal-insulator transition in (DCNQI) 2 Cu

Stability of three-fold lattice distortion in the insulating state of (DCNQI) 2 Cu isstudied by exactly diagonalizing a two-band Peierls Hubbard model on the 6×2 lattice. Self-doping is essentially important and caused by strong commensurability pinning, which are a consequence of moderate coupling of DCNQI π electrons with lattice and strong correlation of Cu d electrons.

Mixed Lamellar Films: Evolution, Commensurability Effects, and Preferential Defect Formation

The structure of lamellar poly(styrene-block-methyl methacrylate), denoted as P(S-b-MMA), diblock copolymer films on neutral poly(styrene-random-methyl methacrylate), denoted as P(S-r-MMA), brush surfaces was examined as a function of annealing time and film thickness using neutron reflectivity and small-angle neutron scattering. Upon annealing, microphase separation occurs quickly with perpendicular and parallel lamellae emanating from the neutral and air surfaces, respectively. This initial growth is followed by a slow increase in the amount of parallel lamellae with a concurrent decrease in the amount of perpendicular lamellae as the samples are annealed further. After long annealing times, the amounts of perpendicular and parallel lamellae do not change significantly. The mixed lamellar structures show a strong commensurability trend with film thickness having a period equal to that of the natural lamellar period. This is explained through the preferential formation of s1/2 disclinations having PS cores which dictate the observed commensurability trend. The preferential formation of these defects was observed by field emission scanning electron microscopy on films predominantly comprised of perpendicular lamellae.

Transition Temperature of Josephson Junction Arrays with Long-Range Interaction

We report measurements of the dependence on magnetic field and array size of the resistive transition of Josephson junction arrays with long-range interaction. Because every wire in these arrays has a large number of nearest-neighbors (9 or 18 in our case), a mean-field theory should provide an excellent description of this system. Our data agree well with this mean-field calculation, which predicts that Tc (the temperature below which the array exhibits macroscopic phase coherence) shows very strong commensurability effects and scales with array size.

Magnetotransport in lateral periodic potentials formed by surface-layer-induced modulation in InAs-AlSb quantum wells

We report the realization of strong lateral superlattice potentials in not-intentionally doped InAs-AlSb quantum wells. By spatially alternating the surface layer between thin layers of InAs and GaSb, which shift the pinning position of the Fermi level at the surface, we induce a lateral density modulation of 4×1011 cm−2, equivalent to a potential modulation of 30 meV inside quantum wells 20 nm away from the surface. Both one- and two-dimensional lateral potentials were fabricated and studied by magnetotransport measurements. Strong commensurability oscillations are observed.