Flux Dependence of Persistent Current in a Mesoscopic Disordered  Tight Binding Ring

Heinrichs, J.

doi:10.1142/s0217979202010026

Cited by 4 publications

(42 citation statements)

References 29 publications

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“…Next we develop a perturbation theory to discuss the effect of a weak site-energy disorder on the eigenvalues of the two-channel ring threaded by a flux φ. This generalizes our earlier treatment [8] of the effect of disorder on persistent current in a one-dimensional ring. The latter [8] has also been applied recently for studying the effect of short-range correlated disorder on persistent current in one dimension [18].…”

Section: Uessupporting

confidence: 85%

“…4 of [9]) for the effect of weak disorder on persistent current in a ten-channel (cylindrical) ring, in terms of single-and two-channel contributions obtained in Ref. [8] and in the present paper, Eqs (46, 46a).…”

Section: A Calculation Of the Persistent Currentmentioning

confidence: 79%

“…and the matrix product N n=1 P n is expanded to quadratic order in the quantities ∆E − 1 2 (ε 1n + ε 2n ) . This yields [8]…”

Section: Uesmentioning

confidence: 94%

“…. N of spacing a per chain [7,8]. Here ϕ i n denotes the amplitude of an eigenstate wavefunction at site n on chain i (i = 1, 2), ε in and E denote the atomic energy of site n on chain i and energy eigenvalues in units of minus a constant nearest-neighbour hopping parameter.…”

Section: Two-chain Cylindrical Ring Model and Eigenvalue Equa-tionmentioning

confidence: 99%

“…On the other hand, the periodicity φ 0 /2 is also obtained exactly for the effect of the disorder in a one-dimensional ring. Since, however, the φ 0 /2 periodicity of the averaged free particle persistent current was not explicitely mentioned in [8], we briefly discuss it here, along with the influence of the disorder in one dimension. These results are important for our qualitative interpretation below of salient features of numerical simulation results of Bouchiat and Montambaux ( fig.…”

Section: A Calculation Of the Persistent Currentmentioning

confidence: 99%

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Analytic study of persistent current in a two-channel disordered mesoscopic ring

Heinrichs¹

2011

Phys. Rev. B

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We present an extensive analytical study of persistent current in a weakly disordered two-chain cylindrical ring threaded by an Aharonov-Bohm flux 0 < φ < φ 0 /2 (with φ 0 the flux quantum) and described by the Anderson model. The effect of the disorder reveals a strong reduction of the persistent current for flux values near φ 0 /4.In conjunction with the pure system (zeroth order) current profile averaged over numbers of electrons and earlier results for the effect of disorder in one-dimensional rings, our two-channel results provide a simple interpretation of salient features of numerical results of Bouchiat and Montambaux (BM) for persistent current in an assembly of many-channel disordered rings. Singlechannel (one-dimensional) effects are responsible for the dip in the persistent obtained by BM near φ = 0 and the corresponding peak near φ 0 /2, while the effect of disorder in independent channel pairs accounts for abrupt decreases of current superimposed to a continuous linear decay as the flux value φ 0 /4 is approached from above and from below, respectively. The persistent current in the two-channel ring involves a free particle current averaged over electron numbers of periodicity φ 0 /2, and a dominant disorder effect which has periodicity φ 0 .

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Section: Uessupporting

confidence: 85%

Section: A Calculation Of the Persistent Currentmentioning

confidence: 79%

“…and the matrix product N n=1 P n is expanded to quadratic order in the quantities ∆E − 1 2 (ε 1n + ε 2n ) . This yields [8]…”

Section: Uesmentioning

confidence: 94%

Section: Two-chain Cylindrical Ring Model and Eigenvalue Equa-tionmentioning

confidence: 99%

Section: A Calculation Of the Persistent Currentmentioning

confidence: 99%

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Analytic study of persistent current in a two-channel disordered mesoscopic ring

Heinrichs¹

2011

Phys. Rev. B

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Electronic transport in an anisotropic Sierpinski gasket

Jana¹,

Chakrabarti²,

Chattopadhyay³

2010

Physica B: Condensed Matter

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We present exact results on certain electronic properties of an anisotropic Sierpinski gasket fractal. We use a tight binding Hamiltonian and work within the formalism of a real space renormalization group (RSRG) method. The anisotropy is introduced in the values of the nearest neighbor hopping integrals. An extensive numerical examination of the two terminal transmission spectrum and the flow of the hopping integrals under the RSRG iterations strongly suggest that an anisotropic gasket is more conducting than its isotropic counter part and that, even a minimal anisotropy in the hopping integrals generate continuous bands of eigenstates in the spectrum for finite Sierpinski gaskets of arbitrarily large size. We also discuss the effect of a magnetic field threading the planar gasket on its transport properties and calculate the persistent current in the system. The sensitivity of the persistent current on the anisotropy and on the band filling is also discussed.

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Enhancement of persistent current in metal rings by correlated disorder

Heinrichs

2008

J. Phys.: Condens. Matter

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We study analytically the effect of a correlated random potential on the persistent current in a one-dimensional ring threaded by a magnetic flux φ, using an Anderson tight-binding model. In our model, the system of N = 2M atomic sites of the ring is assumed to be partitioned into M pairs of nearest-neighbour sites (dimers). While the individual atomic site energies are assumed to be identically distributed gaussian variables with autocorrelation parameter ε 2 0 , the dimer site energies are chosen to be correlated with a gaussian strength α 2 < ε 2 0 . For this system we obtain the exact flux-dependent energy levels to second order in the random site energies, using an earlier exact transfer matrix perturbation theory. These results are used to study the mean persistent current generated by N e ≤ N spinless electrons occupying the N e lowest levels of the flux-dependent energy band at zero temperature. Detailed analyzes are carried out in the case of low filling of the energy band (1 ≪ N e ≪ N ) and for a half-filled band (N e = N/2), for magnetic fluxes −1/2 < φ/φ 0 < 1/2.In the half-filled band case, the uncorrelated part of the disorder reduces the persistent current while the correlated part enhances it, in such a way that for α 2 < ε 2 0 /2 the current decreases with the disorder, while for α 2 > ε 2 0 /2 it increases with it. Also, while showing a specific dependence on the flux, the disorder effect has the same dependence on the parity of N e as the pure system free electron current. In contrast, at low filling of the energy-band, the disorder induced effect in the persistent current depends critically on the parity: due to a peculiar dependence on the flux, it yields a reduction of the current for odd N e and an enhancement of it for even N e . The observability of the effects of weak correlated disorder on persistent current in the half-filled band case is restricted to ring sizes in the nanoscale range, for which no measurements presently exist.

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Flux Dependence of Persistent Current in a Mesoscopic Disordered Tight Binding Ring

Cited by 4 publications

References 29 publications

Analytic study of persistent current in a two-channel disordered mesoscopic ring

Analytic study of persistent current in a two-channel disordered mesoscopic ring

Electronic transport in an anisotropic Sierpinski gasket

Enhancement of persistent current in metal rings by correlated disorder

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