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Fusion: a General Framework for Hierarchical Tilings

100%
Frank N.
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vol. 126
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issue 2
461-466
EN
One well studied way to construct quasicrystalline tilings is via inflate-and-subdivide (a.k.a. substitution) rules. These produce self-similar tilings-the Penrose, octagonal, and pinwheel tilings are famous examples. We present a different model for generating hierarchical tilings we call "fusion rules". Inflate-and-subdivide rules are a special case of fusion rules, but general fusion rules are more flexible and allow for defects, changes in geometry, and even constrained randomness. A condition that produces homogeneous structures and a method for computing frequency for fusion tiling spaces are discussed.
2
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Conductance Fluctuations in PbSe: Manifestation of Ballistic Transport in Macroscale?

33%
Grabecki G., Takeyama S., Adachi S., Takagi Y., Dietl T., Kamińska E., Piotrowska A., Papis E., Frank N., Bauer G.
Acta Physica Polonica A
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1995
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vol. 88
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issue 4
727-730
EN
Precise magnetoresistance measurements on microstructures of photolithographically patterned PbSe epilayers have been performed in the mag­netic field range up to 17 Τ. Unusually large, reproducible magnetoconductance fluctuations have been observed. The fluctuation amplitude decreases exponentially with the magnetic field. A correlation magnetic field of the fluctuations corresponds to the Aharonov-Bohm effect which involves elec­tron trajectories much smaller than the electron mean free path. This points strongly to the ballistic, not diffusive, origin of the observed phenomenon.
3
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Mesoscopic Phenomena in Microstructures of IV-VI Epilayers

33%
Grabecki G., Dietl T., Plesiewicz W., Lenard A., Skośkiewicz T., Kamińska E., Piotrowska A., Papis E., Frank N., Bauer G.
Acta Physica Polonica A
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1995
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vol. 87
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issue 2
551-554
EN
Magnetoresistance measurements of photolithographically patterned PbSe and Pb-{1-y}Mn_{x}Se microstructures were performed. Reproducible mag­netoconductance fluctuations with the amplitude increasing with decreasing temperature were observed. Unexpectedly, these fluctuations contain a com­ponent periodic in the magnetic field, and their magnitude is greater than that expected from the current theory of the universal conductance fluctua­tions. Possible explanations are discussed.
4
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Conductance Anomalies in Strained Quantum Wires: the Case of PbSe and PbTe

27%
Grabecki G., Wróbel J., Dietl T., Sawicki M., Skośkiewicz T., Papis E., Kamińska E., Piotrowska A., Frank N., Ueta Y., Sprinholtz G., Bauer G.
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EN
We show that conducting edge channels are formed in free standing wires of PbSe/BaF_{2} and PbTe/BaF_{2} as temperature is lowered. The effect results from spatially inhomogeneous strain caused by a difference between the thermal expansion coefficients of the epilayer and the substrate. The presence of the edge channels can explain anomalous mesoscopic effects observed previously in these wires.
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