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Original Paper
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Theoretical study of persistent current in a nanoring made of a band insulator
Article first published online: 10 SEP 2012
DOI: 10.1002/pssb.201248066
Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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How to Cite
Mošková, A., Moško, M. and Tóbik, J. (2013), Theoretical study of persistent current in a nanoring made of a band insulator. Phys. Status Solidi B, 250: 147–159. doi: 10.1002/pssb.201248066
Publication History
- Issue published online: 8 JAN 2013
- Article first published online: 10 SEP 2012
- Manuscript Accepted: 6 AUG 2012
- Manuscript Revised: 1 AUG 2012
- Manuscript Received: 13 FEB 2012
- 1, Introduction to Mesoscopic Physics ( Oxford University Press, Oxford, UK, 2002).
- 2
- 3
- 4
- 5, Phys. Rev. 137, A787 (1965); Phys. Rev. 166, 415 (1968).
- 6
- 7
- 8
- 9, , , and , Phys. Rev. Lett. 86, 1594 (2001).
- 10, , , , and , Phys. Rev. Lett. 102, 136802 (2009).
- 11
- 12, arXiv:1112.3395v1.
- 13
- 14, , , , , and , Phys. Rev. Lett. 86, 3124 (2001).
- 15
- 16, , and , in: Encyclopedia of Nanoscience and Nanotechnology, Vol. 3 ( American Scientific Publishers, CA, 2004), p. 267.
- 17
- 18
- 19, , , and , Phys. Rev. Lett. 84, 2223 (2000).
- 20
- 21
- 22
- 23, , and , Physica E 40, 1991 (2008). A rather heuristic derivation in that work relies on the on-site atomic orbitals instead of the on-site crystal Wannier functions, and only the rings with odd number of electrons are considered. The persistent current found in that paper can be obtained from our present result (Eq. (48)), if the factor γ1(−α1)(N−1) is replaced by γN. This causes a much faster decay of the current and the effect of the alternating sign is lost.
- 24and , Physica E 40, 1498 (2008). In that work also the asymptotic expressions for persistent current at full filling were given for a perioidic array of strong δ barriers, but without any derivation.
- 25, , , arXiv:1001.0496v2. The version 1 of this arXiv text resembles the work [23] in the sense that it still does not rely on the concept of the Wannier functions. It also contains a few mistakes. The version 2 contains all derivations of our present paper in a lengthy form.
- 26
- 27
- 28
- 29, Introduction to Fourier Analysis and Wavelets ( American Mathematical Society, Providence, USA, 2002).
- 30In fact, the details of the Γn dependence of the lowest band are not essential for the resulting persistent current since the main contribution to the current is due to the light-hole band (see the text). We note for completeness that in the GaAs and InAs the ΓN dependence of the lowest band exhibits the same sign for all N except for a few isolated values of N where the sign is opposite. We plot the whole ΓN curve of the lowest band with a fixed sign for simplicity. Due to this simplification the ΓN curve exhibits a few local minima: the ΓN values at these minima in fact do not have the same sign as the rest of the curve.
- 31and , Phys. Status Solidi B 68, 405 (1975).
- 32
- 33
- 34
- 35
- 36, , , and , J. Phys.: Condens. Matter 23, 225801 (2011).
- 37and , Solid State Physics ( Sounders College Publishing, Cornell University, London, 1976).
- 38
- 39
- 40, , and , Phys. Rev. B 45, 3499 (1992). In that paper the persistent current in the conducting 1D ring was analyzed in presence of the Peierls instability. At very low temperatures, the instability opens a small energy gap at the Fermi level and the ring becomes insulating. The paper shows that in such case the current decays with the ring length at least like 1/N2, admitting also the possibility of the exponential decay.
- 41In case of the Peierls insulator the gap is small and the current is expected to decay with raising temperature exponentially [40].
- 42Precisely, Eq. (50) shows the decay |n|−1/2|α1||n|. A purely exponential decay was predicted by , Phys. Rev. 115, 809 (1959). Very sophisticated estimates by and , Phys. Rev. Lett. 86, 5341 (2001) and by and , Phys. Rev. B 75, 115428 (2007) predict (in our notations) the decay |n|−3/4|α1||n|. For our purposes, the exact nature of the power law prefactor is of minor importance.
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