Exotic spectra, wavefunctions and transport in incommensurate lattices |
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Authors: | A Lahiri T K Roy A Bhowal |
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Institution: | (1) Vidyasagar Evening College, 700 006 Calcutta, India;(2) Saha Institute of Nuclear Physics, 700 064 Calcutta, India |
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Abstract: | We present numerical results on a range of related issues for a number of incommensurate TMB’s, each of which shows a metal-insulator
type transition as a binding-to-hopping ratio is made to increase through some limiting value. These supplement a series of
similar results on a couple of 1D lattices in a number of recent works (see below). A brief review pertaining to spectral
properties and wavefunctions in incommensurate lattices is followed by results on the above TBM’s relating to an interesting
correlation between the gross features of wavefunctions and the energies arranged in a particular sequence termed thelattice-ordered sequence, and also between the lattice-ordered energies and the on-site potentials. We present a qualitative explanation
of these correlations on the basis of perturbation theory. Basic results on dynamics of wavepackets in relation to spectral
characteristics of incommensurate TBM’s are also reviewed. Features of lattice-ordered energies and wavefunctions for the
TBM’s under study are used in the framework of the so-called Maryland construction, leading to a qualitative prediction of
criteria for recurrent and non-recurrent wavepacket dynamics in these lattices, and these predictions are checked against
numerical iterations of the relevant ‘quantum maps’. Closely related to the dynamics of wavepackets are the transport properties
of these lattices. Results are available to indicate that the unusual spectral characteristics of pseudorandom lattices lead
to novel features in transport properties of these systems. In this context, low temperature a.c conductivity in these lattices
is a good probe for the spectral characteristics and wavefunctions. However, not much is known about the a.c conductivity,
excepting a set of early results pertaining to the low frequency regime, principally because of the fact that the a.c conductivity
depends on global characteristics of the spectrum and the entire set of wavefunctions. We present a simple model whereby the
gross structure of variation of the a.c conductivity with frequency can be obtained from a knowledge of the spectrum alone
for the set of TMB’s under consideration. Numerical computations show that despite its simplicity, the model leads to results
in good agreement with those from the Kubo-Greenwood formula for a.c conductivity. |
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Keywords: | Tight binding model aperiodic lattice localization m-i transition lattice ordered sequence transport properties ac conductivity wave packet dynamics |
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