Localized Electrons on a Lattice with Incommensurate Magnetic Flux

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dc.creatorFishmen, Shmuel
dc.creatorShapir, Yonathan
dc.creatorWang, Xiang-Rong
dc.date1992-08-29
dc.date.accessioned2026-07-07T03:06:43Z
dc.date.available2026-07-07T03:06:43Z
dc.descriptionThe magnetic field effects on lattice wavefunctions of Hofstadter electrons strongly localized at boundaries are studied analytically and numerically. The exponential decay of the wavefunction is modulated by a field dependent amplitude J(t) which depends sensitively on the value of alpha (the magnetic flux per plaquette in units of a flux quantum, t is the distance from the boundary). While for rational values p/q, the envelope of J(t) increases as 2**t/q, the behavior for irrational alpha is erratic with an aperiodic structure which changes drastically with alpha. For algebraic alpha it is found that J(t) increases as a power law t**b(alpha) while it grows faster for transcendental alpha. This is very different from the growth rate exp{sqrt(t)} typical for random phases. The theoretical analysis is extended to lattices in which the distances between adjacent layers increase as r**n with n>0. Different behavior of J(t;n) is found in various regimes of n. It changes from periodic for small n to random like for large n.
dc.description30 pages, 14 fig. (not included, available from ysha@uordbv upon request)
dc.identifierhttps://arxiv.org/abs/cond-mat/9208024
dc.identifierhttp://arxiv.org/abs/cond-mat/9208024
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/26910
dc.subjectCondensed Matter
dc.subjectHigh Energy Physics - Theory
dc.titleLocalized Electrons on a Lattice with Incommensurate Magnetic Flux
dc.typetext

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