Numerical simulations of shot noise in degenerate disordered conductors in reduced dimensions

Kolek, Andrzej; Stadler, A. W.; Hałdaś, G.

doi:10.1103/physrevb.64.075202

Cited by 10 publications

(16 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Under simple assumptions on the distribution function of Lyapunov exponents, one gets the limiting values for M C both in diffusive and critical (3D) regimes. We will also confirm the validity of Nazarov's theory [15] in diffusive case for higher moments and in 4 d = ; for 2 M = and 1 2 3 d Q D = , , it was already shown in [13] and [14], though less precisely because of smaller system sizes and thus larger disturbing ballistic effects.…”

Section: Introductionsupporting

confidence: 82%

“…It is usefull to plot them as a function of conductivity G, rather than of L. Figure 4 left shows, that in 2D the 2 R only roughly approaches the predicted value, at larger G (smaller W ) the ballistic regime disturbs the conver- Table 2. gence. 2 ( ) R G was shown already in [13]. In order to judge the influence of ballistic, we plot the data also for lower W and L in Fig.5 2 R and 3 R , resp.…”

Section: Diffusive M R Combinations Of M Tmentioning

confidence: 98%

“…The first two of these equations were derived and the second one compared to numerical simulations in [13] and [14]. The values on rhs are summarized in …”

Section: Original Papermentioning

confidence: 99%

See 2 more Smart Citations

Shot noise and higher current moments in dimensions 2, 3 and 4

Travěnec

2005

Physica Status Solidi (b)

View full text Add to dashboard Cite

T G = / , and we show indications that all of them are as good order parameters as the conductance itself. In the limit of infinite system size, two limiting values of F and M C are found; the stable one in the metallic regime, and the unstable one, characterizing the critical point for 2 d > . We present analytical expressions for both limiting values, together with a compact formula for current cumulants at 3D criticality. Our data confirm also Nazarov's microscopic theory [Phys. Rev. B 52, 4720 (1995)], as we show numerically for special linear combinations of M T .

show abstract

Section: Introductionsupporting

confidence: 82%

Section: Diffusive M R Combinations Of M Tmentioning

confidence: 98%

See 1 more Smart Citation

Shot noise and higher current moments in dimensions 2, 3 and 4

Travěnec

2005

Physica Status Solidi (b)

View full text Add to dashboard Cite

show abstract

“…Here by the theory only the inequality 1 d f z l holds [2,3] whereas numerical simulations give incompatible results [4]. Our recent finite size scaling calculations of quantum mechanical conductance show that superlocalization takes place also for the states inside the band [5]. We have found that for 2D percolation cluster the geometrical average of g $ |w| 2 scales like in Eq.…”

mentioning

confidence: 84%

“…The simulations were performed on 2D percolation cluster at critical sites concentration p = p c = 0.593 by the finite size scaling technique. The conductance g was calculated with the help of Landauer-Bü ttiker formalism and Green's function technique for increasing size L of square lattice (see [5] for more details of the computation technique). The population of the samples was very large (50000) so the evaluation of conductance distribution was possible (see Fig.…”

mentioning

confidence: 99%

Conductance Distribution in Superlocalization Regime

Kolek

Hałdaś

Stadler

2002

phys. stat. sol. (b)

View full text Add to dashboard Cite

Subject classification: 73.23.AnThe phenomenon of superlocalization has been studied by means of numerical simulations performed on two-dimensional percolation cluster at the threshold site concentration p = p c = 0.593. It is shown that superlocalization takes place also for the states inside the band. In this case the averaged logarithm of conductance scales with the size of percolation cluster L as hln gi $ ÀL df with localization exponent d f ffi 1.14. The distribution of ln g arises from the multiplication of two random variables, namely the chemical length l and inverse localization length g. The distribution of g is Gaussian with size independent average and variance which scales like var g $ hli --1 . The distribution of l has a long tail towards large l. Its average and variance scale like hli $ L df and var l $ hl 2 i. There is a small correlation between l and g, which decreases as L df=2 as the size of the percolation cluster increases.It is well known that in fractal geometry electronic wave functions are superlocalized. Namely, their mean amplitudes behave like [1, 2]where r is the distance from the center of the wave function w, xr is the localization length measured in r-space and d f is the localization exponent. This was rigorously proven for deep states below the band for which the relation d f = z l , where z l is the exponent which describes scaling of the average chemical length (the shortest part) of the percolation cluster is expected [2]. Namely, hli $ L z l . Less knowledge concerns the states within the band. Here by the theory only the inequality 1 d f z l holds [2, 3] whereas numerical simulations give incompatible results [4]. Our recent finite size scaling calculations of quantum mechanical conductance show that superlocalization takes place also for the states inside the band [5]. We have found that for 2D percolation cluster the geometrical average of g $ |w| 2 scales like in Eq. (1) and exponent d f ffi 1.14 was found for energies E = --3.5t and 0.5t, where t is the hopping matrix element (see Fig. 1). In this paper we focus on the distribution of conductance in the superlocalization regime. As in the previous work [5] our main tool is the use of numerical simulations. The simulations were performed on 2D percolation cluster at critical sites concentration p = p c = 0.593 by the finite size scaling technique. The conductance g was calculated with the help of Landauer-Bü ttiker formalism and Green's function technique for increasing size L of square lattice (see [5] for more details of the computation technique). The population of the samples was very large (50000) so the evaluation of conductance distribution was possible (see Fig. 2a). Unlike for Euclidean geometries the histogram of z --ln (g/g 0 )/2 is not Gaussian: a long tail grows up for small g's (large z's).

show abstract

Fractal-to-Euclidean Crossover in Quantum Percolation

Hałdaś¹,

Kolek²,

Stadler³

2002

phys. stat. sol. (b)

View full text Add to dashboard Cite

Extensive numerical studies of quantum percolation in 2D show no indications of localizationdelocalization transition. At the percolation threshold, i.e. for p = p c , the scaling curve b @ ln g/@ ln L exhibits a fractal-like behavior. For ln g ( 0 it senses superlocalization: it has the slope d f ffi 1.14. For ln g ) 0 it saturates at --t/n + d --2 ffi --1, where t and n are percolation critical exponents. For small size L ($10) of percolation cluster the distribution of variable l 1 = arccosh (1/ ffiffiffiffiffi ffi T 1 p ), where T 1 is the first transmission eigenvalue, has the exponential tail P(l 1 ) $ exp (--l 1 ), which is characteristic for chaotic cavities with one-moded leads. For intermediate sizes P(l 1 ) changes to Wigner surmise typical for metallic states. For large sizes the shape of P(l 1 ) results from the "convolution" of the first Lyapunov exponent g 1 (which is Gaussian) and chemical length l (which has a tail for large l). For p > p c we observe a crossover from fractal-like behavior for L ( x p , x p is the percolation correlation length, to Euclidean-like behavior, characteristic for homogeneous disorder, for L ) x p .Recent series expansion studies (see e.g.[1]) suggest that there is a localization-delocalization transition in 2D quantum percolation, which is in contradiction to some numerical results (see e.g. [2]). Apart from this controversy another question arises: On one hand, quantum percolation can be considered as a kind of random potential and its conductance g is expected to follow the universal scaling curve b @ ln g/@ ln L with the limits b E / d --2 = 0 for lng ) 0 and b E / ln g for ln g ( 0. On the other hand, at the threshold concentration of sites p = p c the percolation cluster (p.c.) has a fractal geometry for which the b-curve is quite different [3], b F / --t/n + d --2 ffi --1 for ln g ) 0 and b F / d f ln g for ln g ( 0.Here either d f = 1 [3] or d f = z l ffi 1.15 [4] and t, n and z l are percolation critical exponents for conductivity, correlation length, and chemical distance, respectively. In this paper, the results of extensive numerical simulation of quantum percolation on a square lattice are presented. Tight binding Hamiltonian with hopping restricted to nearest neighbors and on-site disorder are used. The conductance exp (hln gi) averaged in the ensemble of 50000 configurations of L Â L square lattice inserted into infinite, disorder-free L-wide strip is calculated for increasing size up to L = 100. The results presented in Fig. 1 reveal the following behavior: (i) For p = p c the conductance shows superlocalization [4,5]. The exponent d f ffi 1.14 is found in good agreement with the conjecture d f = z l . This result is not so obvious if we note that our calculations are performed in the middle of the band, i.e. for E = 0.5, where by the theory only the relation 1 d f z l holds [4]. (ii) For p > p c and in the limit L ! 1 data follow b E -the scaling function for 2D (Euclidean) space. This means that no indications of localization-delocalization transition...

show abstract

Numerical simulations of shot noise in degenerate disordered conductors in reduced dimensions

Cited by 10 publications

References 16 publications

Shot noise and higher current moments in dimensions 2, 3 and 4

Shot noise and higher current moments in dimensions 2, 3 and 4

Conductance Distribution in Superlocalization Regime

Fractal-to-Euclidean Crossover in Quantum Percolation

Contact Info

Product

Resources

About