Orientational order of hut clusters grown coherently on the substrate

Abstract

Within the Tersoff approximation we obtain the analytic expressions for the elastic hut-hut and pyramidpyramid interaction energies. Numerous experimental results show that the orientation of a Ge hut ridge is either parallel or perpendicular to the ͓010͔ direction of Si, and we treat these two possible hut orientations as spin variables in the two-dimensional ͑2D͒ Ising model. To study the thermal-equilibrium configuration of hut orientations, we map the Hamiltonians of the square-lattice and rectangular-lattice hut systems ͑SLHS and RLHS͒ onto that of the isotropic and anisotropic 2D Ising models with antiferromagnetic couplings, respectively, where the latter is accompanied by a magnetic field. We predict that a hut-orientation order-disorder phase transition takes place in the SLHS, and obtain the dependences of the transition temperature on the hut size, the aspect ratio of the hut base, and the hut-lattice spacing. For the case of the RLHS, the relations of critical temperatures to the hut-lattice constant, hut base aspect ratio, and size are also found by performing intensive Monte Carlo simulations.

Origin of matching effect in anti-dot array of superconducting NbN thin films

“…All transport measurements were performed using the standard four probe technique. The measurements were performed either in a conventional 4 He flow cryostat fitted with an 8 T superconducting magnet down to 2 K or in a 3 He cryostat fitted with a 6 T superconducting magnet down to 300 mK.…”

A two-coil mutual inductance technique to study matching effect in disordered NbN thin films

“…In recent years, the matching effect observed in superconducting films with periodic array of holes, has been a subject of considerable theoretical [1,2,3,4] and experimental attention [5,6,7,8,9,10,11,12,13,14,15,16]. In magnetic fields, matching effect manifests as a periodic variation of superconducting transition temperature (T c ) and critical current (I c ) with a period commensurate with integer number of flux quantum (Φ 0 ) passing through each unit cell.…”

“…A film with periodic array of holes can be visualized as a periodic network of side sharing loops, provided the width of the superconducting region is smaller than the Ginzburg-Landau coherence length (ξ). It has been theoretically shown that in such networks quantum interference (QI) effects would also give rise to T c oscillations similar to single-loop Little Parks [3], though additional weaker structures could appear at non-integral rational fractions of flux filling [4]. The second mechanism is related to vortex pinning.…”

“…The real and imaginary part of the mutual inductance (M' and M'') corresponding to the inductive and dissipative part, is given by M' ( '' ) =V' ( '' ) /(2Iπν), where ν is the frequency of the excitation current. The measurements are performed either in a conventional 4 He flow cryostat fitted with an 8 T superconducting magnet down to 2 K or in a 3 He cryostat fitted with a 6 T superconducting magnet down to 300 mK. The 3 He cryostat is designed to have the sample and coil assembly immersed in 3 He inside the pot to avoid temperature gradients.…”

“…The measurements are performed either in a conventional 4 He flow cryostat fitted with an 8 T superconducting magnet down to 2 K or in a 3 He cryostat fitted with a 6 T superconducting magnet down to 300 mK. The 3 He cryostat is designed to have the sample and coil assembly immersed in 3 He inside the pot to avoid temperature gradients. determined from the intersection of two tangents drawn above and below the transition.…”