Numerical studies of inverse localisation length in one dimension

Andereck, Barbara S.; Abrahams, Elihu

doi:10.1088/0022-3719/13/15/003

Cited by 89 publications

(27 citation statements)

References 6 publications

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“…Numerically [39] and analytically [42], it was found that the variance is proportional to the inverse square root of system size. The first leading contribution for the variance comes from the m = 1 term, Eq.…”

Section: Localization Length: Log(t )mentioning

confidence: 99%

“…On the other hand, it is found that the logarithm of the transmission is statistically well behaved [33,[39][40][41][42]. In the weak-disorder limit, the explicit expression of the inverse localization length was found using a perturbation approach to the first order in disorder strength [37,42,43].…”

Section: Localization Length: Log(t )mentioning

confidence: 99%

“…(47), and the computation is directly following: where a/ l loc = W 2 /3v 2 F up to the order of W 2 . Therefore, we obtain the previously known relation [39,42]:…”

Section: Localization Length: Log(t )mentioning

confidence: 99%

“…Like the transmission, which was discussed earlier, the resistance is not a statistically well behaved quantity since its fluctuations increase faster than its average with system size. Nevertheless, various approaches have been used to compute the moments of the resistance [34,35,40,44], and the scaling behavior of resistance with system size attracted a great deal of attention [33,35,39]. Our formalism does not offer significant advantages for computing the disorder average of the resistance; nonetheless, we carry out the calculation for the sake of completeness of the formulation developed in this paper.…”

Section: Resistance: R = 1/ Tmentioning

confidence: 99%

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Nonperturbative expression for the transmission through a leaky chiral edge mode

2014

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Chiral edge modes of topological insulators and Hall states exhibit nontrivial behavior of conductance in the presence of impurities or additional channels. We present a simple formula for the conductance through a chiral edge mode coupled to a disordered bulk. For a given coupling matrix between the chiral mode and bulk modes, and a Green's function matrix of bulk modes in real space, the renormalized Green's function of the chiral mode is expressed in closed form as a ratio of determinants. We demonstrate the usage of the formula in two systems: (i) a 1d wire with random on-site impurity potentials for which we found that the disorder averaging is made simpler with the formula, and (ii) a quantum Hall fluid with impurities in the bulk for which the phase picked up by the chiral mode due to the scattering with the impurities can be conveniently estimated.

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Section: Localization Length: Log(t )mentioning

confidence: 99%

Section: Localization Length: Log(t )mentioning

confidence: 99%

“…(47), and the computation is directly following: where a/ l loc = W 2 /3v 2 F up to the order of W 2 . Therefore, we obtain the previously known relation [39,42]:…”

Section: Localization Length: Log(t )mentioning

confidence: 99%

Section: Resistance: R = 1/ Tmentioning

confidence: 99%

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Nonperturbative expression for the transmission through a leaky chiral edge mode

2014

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“…In each particular case, we can obtain such a relation with the help of the transfer matrix. 12,30 It is well known 12,14 that at a temperature Tϭ0, the value of G depends significantly on the product k F L. In or- der to study the effect of potential barriers, we also consider the conductance G T of the ring at a nonzero temperature: 1…”

Section: ͑7͒mentioning

confidence: 99%

Interference phenomena and ballistic transport in a one-dimensional ring

Moskalets¹

1997

Low Temperature Physics

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Dipole moments of polyenic oligomeric systems. Part I. A one-dimensional molecular wire model

Morales¹,

González-Rojas²

1998

J. Phys. Org. Chem.

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Ground-state dipolar moments of oligomeric compounds, containing electron-donor (D) and electronacceptor (A) groups as two terminal units of the polyenic bridge (D-wire-A), can well be described by means of a onedimensional molecular wire model, which considers a scattering process of electrons through the charge-transfer conduction channel. The dipole moment of the oligomers (m n ) follows a non-linear dependence of the polyenic bridge length (L) according to m n m H m I I À e Àv where m H is the dipole moment of the first compound of the series, without a polyenic unit (n = 0), m I is a limit value for L → ? and g is the one-dimensional conduction constant of the p-molecular orbital channel of the molecular wire. This model can be extended to all those conjugated oligomers of the D-wire-A type where the electronic charge of the donor group can induce a soliton wave as far as through the polyenic bridge towards the acceptor group.

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Numerical studies of inverse localisation length in one dimension

Cited by 89 publications

References 6 publications

Nonperturbative expression for the transmission through a leaky chiral edge mode

Nonperturbative expression for the transmission through a leaky chiral edge mode

Interference phenomena and ballistic transport in a one-dimensional ring

Dipole moments of polyenic oligomeric systems. Part I. A one-dimensional molecular wire model

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