Anderson localization in 1D systems with correlated disorder

Cain, Philipp; Schreiber, Michael

doi:10.1140/epjb/e2011-20212-1

Cited by 53 publications

(53 citation statements)

References 29 publications

(59 reference statements)

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“…5. Notice that this phenomenon is essentially different from the more customary case of the Anderson model with correlated disorder, where correlations are introduced directly on the disordered potential [60][61][62][63][64], and is more similar to the case of periodic-on-average systems [65].…”

Section: B Differences From a Disordered Quantum Wirementioning

confidence: 77%

Effects of disorder on electron tunneling through helical edge states

Sternativo

Dolcini

2014

Phys. Rev. B

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A tunnel junction between helical edge states, realized via a constriction in a Quantum Spin Hall system, can be exploited to steer both charge and spin current into various terminals. We investigate the effects of disorder on the transmission coefficient $T_p$ of the junction, by modelling disorder with a randomly varying (complex) tunneling amplitude $\Gamma_p=|\Gamma_p| \exp[i \phi_p]$. We show that, while for a clean junction $T_p$ is only determined by the absolute value $|\Gamma_p|$ and is independent of the phase $\phi_p$, the situation can be quite different in the presence of disorder: phase fluctuations may dramatically affect the energy dependence of $T_p$ of any single sample. Furthermore, analysing three different models for phase disorder (including correlated ones), we show that not only the amount but also the way the phase $\phi_p$ fluctuates determines the localisation length $\xi_{loc}$ and the sample-averaged transmission. Finally, we discuss the physical conditions in which these three models suitably apply to realistic cases.Comment: 14 pages, 7 figure

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Section: B Differences From a Disordered Quantum Wirementioning

confidence: 77%

Effects of disorder on electron tunneling through helical edge states

Sternativo

Dolcini

2014

Phys. Rev. B

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“…Using relation (21), in Fig. 1 we show a ¼ 1 the degree of asymmetry of the dichotomous noise and is the correlation time of the dichotomous noise.…”

Section: The Asymmetric Dichotomous Disordered Tlsmentioning

confidence: 99%

“…Figure 1(b) shows the behavior of a as a function of the asymmetry parameter in the neighborhood of the symmetric value ¼ 1. In this case, for each¯xed ; a and b depend on in the form given by (21), namely, a ¼ 1…”

Section: The Asymmetric Dichotomous Disordered Tlsmentioning

confidence: 99%

“…On the other hand, the in°uence of the short-range and long-range correlation in disordered low-dimensional system has been extensively studied in the last time. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] As a result, we can say that when the system presents long-range correlation, it is possible to¯nd extended states, or even, extended state bands, but for short-range correlation, only a¯nite number of extended states or resonances can appear.…”

Section: Introductionmentioning

confidence: 99%

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Disorder–order transitions in diluted and nondiluted direct transmission lines with asymmetric dichotomous noise

Lazo

Humire

Saavedra

2014

Int. J. Mod. Phys. C

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In this work we study the localization properties of diluted and nondiluted disordered direct transmission lines (TLs), when we distribute two values of inductances, L A and L B , according to an asymmetric dichotomous sequence. Using the scaling properties of the participation number D we study the localization properties in the thermodynamic limit. For certain and parameter speci¯c values, which characterize the dichotomous noise, we have found the following limit conditions: lim !1 mð!; ; Þ ! 1:0 or lim !1 mð!; ; Þ ! 1:0, for the appearing of the disorder-order transitions. Here mð!; ; Þ are the slopes of the linear relationships between lnðDÞ and lnðNÞ. In addition, in each ! c resonance frequency generated by the dilution process we demonstrate the existence of extended intermediate states in the thermodynamic limit.

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“…This is indeed the case for the Anderson transition [24]. Moreover, the low energy properties of the Dirac phase in graphene are known to be sensitive to disorder correlations [25] .…”

Section: Introductionmentioning

confidence: 70%

New quantum transition in Weyl semimetals with correlated disorder

2017

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A Weyl semimetal denotes an electronic phase of solids in which two bands cross linearly. In this paper we study the effect of a spatially correlated disorder on such a phase. Using a renormalization group analysis, we show that in three dimensions, three scenarios are possible depending on the disorder correlations. A standard transition is recovered for short range correlations. For disorder decaying slower than 1/r 2 , the Weyl semimetal is unstable to any weak disorder and no transition persists. In between, a new phase transition occurs. This transition still separates a disordered metal from a semi-metal, but with a new critical behavior that we analyze to two-loop order.

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Anderson localization in 1D systems with correlated disorder

Cited by 53 publications

References 29 publications

Effects of disorder on electron tunneling through helical edge states

Effects of disorder on electron tunneling through helical edge states

Disorder–order transitions in diluted and nondiluted direct transmission lines with asymmetric dichotomous noise

New quantum transition in Weyl semimetals with correlated disorder

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