Numerical studies on the anderson localization problem

Stein, J.; Krey, U.

doi:10.1007/bf01325498

Cited by 68 publications

(29 citation statements)

References 25 publications

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“…I n the paper of Anderson [14] it has been shown that for numerical reasons the transition to localized states takes place at sufficiently strong disorder and corresponds to M z = 0.05. (This fact is confirmed by the results of numerical calculations [15].) Therefore, a transition from the band mechanism to a hopping one takes place a t T > wo.…”

Section: Resultssupporting

confidence: 82%

Mobility of a Small Polaron at Low Temperatures

Gogolin

1981

Physica Status Solidi (b)

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Section: Resultssupporting

confidence: 82%

Mobility of a Small Polaron at Low Temperatures

Gogolin

1981

Physica Status Solidi (b)

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“…17,24 Reference 24 obtained universal values for cЈϭ0.07Ϯ0.01 and cЉϭ0.11Ϯ0.02. From a 3D point of view, using cЈϭ0.07 and a typical sp 2 C-C bond length a 0 ϭ1.4 Å, min 3D ϳ1.3ϫ10 3 S/cm is obtained, which is much larger than the observed zero-temperature conductivity.…”

Section: Mott's Minimum Metallic Conductivitymentioning

confidence: 99%

Unusual semimetallic behavior of carbonized ion-implanted polymers

Prigodin

Burns

et al. 1998

Phys. Rev. B

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We report a comprehensive charge transport study of ion-implanted rigid rod and ladder polymers p-phenylenebenzobisoxazole, p-phenylenebenzobisthiazole, and benzimidazobenzophenanthroline. The three pristine materials are strong and stable polymers with a room temperature conductivity RT ϳ10 Ϫ12 S/cm. After high dosage ion implantation using Kr ϩ , a carbonized and conducting layer forms on the surface of the film samples with RT Ͼ10 2 S/cm. The experimental results suggest that this carbonized layer is semimetallic with unusual properties. The observed dc conductivity follows (T)ϭ 0 ϩ⌬(T), where ⌬(T) is weakly temperature dependent and interpreted within the model of weak localization and electron-electron interaction effects. The model reveals that the interaction effect is three dimensional for the experimental temperature range ͑3-300 K͒, whereas the weak localization effect undergoes a dimensional crossover at ϳ60 K from three to two-dimensions with decreasing temperature. The magnetoconductance, thermoelectric power, and microwave dielectric constant results are all in agreement with this semimetallic model. In addition, all these results consistently point to an enhanced interaction effect at low temperatures due to the reduced dimensionality of the localization effect. It is concluded that a sp 2 rich and three-dimensional interconnected carbon network reformed upon ion implantation of the densely packed pristine polymers is responsible for the semimetallic behavior.

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“…18,19 Once the semiinfinite clean leads are attached to the finite sample (at planes 1 and N along x-axis for a two-probe geometry, Fig. 3), the "self-energy"Σ r,a =Σ r,a L +Σ r,a R , arising from the "interaction" with the leads (L-left, R-right), provides a well-defined imaginary part in the definition of the Green operators…”

Section: 13mentioning

confidence: 99%

“…Such mesoscopic formulas provide means to compute the quantum conductance-a sample specific quantity which takes into account the finite system size, measuring geometry, arrangement of impurities, non-local features of quantum transport, and can describe ballistic transport (where local relation j = σE does not hold). Attempts to use the original Kubo formulas on finite samples, throughout premesoscopic history 18,19 of the Anderson localization theory, were thwarted with ambiguities, which can be traced back to the general questions on the origin of dissipation. 23 This stems from the fact that stationary regime cannot be reached unless the system is infinite or coupled to a 000 000 000 111 111 111 000 000 000 111 111 111 000 000 000 111 111 111 000 000 000 000 111 111 111 111 000 000 000 000 111 111 111 111 000 000 000 000 111 111 111 111 000 000 000 000 111 111 111 111 000 000 000 000 111 111 111 111 000 000 000 000 111 111 111 111…”

Section: 13mentioning

confidence: 99%

Deconstructing Kubo formula usage: Exact conductance of a mesoscopic system from weak to strong disorder limit

Nikolić

2001

Phys. Rev. B

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In both research and textbook literature one often finds two "different" Kubo formulas for the zerotemperature conductance of a non-interacting Fermi system. They contain a trace of the product of velocity operators and single-particle (retarded and advanced) Green operators: Tr(vxĜ rv xĜ a ) or Tr(vx ImĜvxImĜ). The study investigates the relationship between these expressions, as well as the requirements of current conservation, through exact evaluation of such quantum-mechanical traces for a nanoscale (containing 1000 atoms) mesoscopic disordered conductor. The traces are computed in the semiclassical regime (where disorder is weak) and, more importantly, in the nonperturbative transport regime (including the region around localization-delocalization transition) where concept of mean free path ceases to exist. Since quantum interference effects for such strong disorder are not amenable to diagrammatic or nonlinear σ-model techniques, the evolution of different Green function terms with disorder strength provides novel insight into the development of an Anderson localized phase.PACS numbers: 72.10. Bg, 72.15.Rn, 05.60.Gg At first sight, the title of this paper might sound perplexing. What else can be said about Kubo formula 1 after almost a half of a (last) century of explorations in practice, as well as through numerous re-derivations in both research 2 and textbook 3,4 literature? Kubo linear response theory (KLRT) represents the first full quantum-mechanical transport formalism. It connects irreversible processes in nonequilibrium to the thermal fluctuations in equilibrium [fluctuation-dissipation theorem (FDT)]. Therefore, the study of transport is limited to the nonequilibrium states close to equilibrium. Nevertheless, the computation of linear kinetic coefficients is greatly facilitated since final expressions deal with equilibrium expectation values of relevant physical quantities (which are much simpler than the corresponding nonequilibrium ones 5 ). It originated 6 from the Einstein relation for the diffusion constant and mobility of a particle performing a random walk.Until the scaling theory of localization, 7 and ensuing computation of the lowest order quantum correction, weak localization 8 (WL), to the Drude conductivity, it almost appeared that microscopic and complicated Kubo formulation of quantum transport merely served to justify the intuitive Bloch-Boltzmann semiclassical approach 3 to transport in weakly disordered (k F ℓ ≫ 1, k F is the Fermi wave vector and ℓ is the mean free path) conductors. Furthermore, the advent of mesoscopic physics 9 has led to reexamination of major transport ideas-in particular, we learned how to apply properly KLRT to finite-size systems. Thus, the equivalence was established 2 between the rigorous Kubo formalism and heuristically founded Landauer-Büttiker 10 scattering approach to linear response transport of non-interacting quasiparticles.11 This has emerged as an important tool in for studying mesoscopic transport phenomena, where system size and interface...

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Numerical studies on the anderson localization problem

Cited by 68 publications

References 25 publications

Mobility of a Small Polaron at Low Temperatures

Mobility of a Small Polaron at Low Temperatures

Unusual semimetallic behavior of carbonized ion-implanted polymers

Deconstructing Kubo formula usage: Exact conductance of a mesoscopic system from weak to strong disorder limit

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