Possible solution of the conductivity exponent puzzle for the metal-insulator transition in heavily doped uncompensated semiconductors

Stupp, H.; Hornung, M.; Lakner, Mitja; Madel, O.; Löhneysen, H. v.

doi:10.1103/physrevlett.71.2634

Cited by 151 publications

(183 citation statements)

References 33 publications

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“…Refs. [13][14][15][16][17][18]. However, several studies have pointed to inconsistencies of the zero-temperature extrapolations inherent in the critical-exponent determination [8,12,[18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Metal-insulator transition in amorphousSi1−xNix:Evidence for Mott’s minimum metallic conductivity

et al. 1999

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We study the metal-insulator transition in two sets of amorphous Si 1−x Ni x films. The sets were prepared by different, electron-beam-evaporation-based technologies: evaporation of the alloy, and gradient deposition from separate Ni and Si crucibles. The characterization included electron and scanning tunneling microscopy, glow discharge optical emission spectroscopy, energy dispersive X-ray analysis, and Rutherford back scattering. Investigating the logarithmic temperature derivative of the conductivity, w = d ln σ/d ln T , we observe that, for insulating samples, w(T ) shows a minimum, increasing at both low and high T . Both the minimum value of w and the corresponding temperature seem to tend to zero as the transition is approached. The analysis of this feature of w(T, x) leads to the conclusion that the transition in Si 1−x Ni x is very likely discontinuous at zero temperature in agreement with Mott's original views. 71.30.+h,71.23.Cq, Typeset using REVT E X

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Section: Introductionmentioning

confidence: 99%

Metal-insulator transition in amorphousSi1−xNix:Evidence for Mott’s minimum metallic conductivity

et al. 1999

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“…5 at the T 0 metal-insulator transition in Si:P has remained a puzzle for over a decade [1]. Stupp et al [2] recently have proposed a reanalysis of the Hence, the 6% smaller n, required by Stupp et al to raise p would not permit a self-consistent treatment of the observed critical behavior on both sides of the metal-insulator transition. …”

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confidence: 99%

“…5 at the T 0 metal-insulator transition in Si:P has remained a puzzle for over a decade [1]. Stupp et al [2] recently have proposed a reanalysis of the data which gives p = 1 [2] is dominated by a nonrandom impurity distribution and should not be compared with the usual theories of critical phenomena.…”

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confidence: 99%

Critical behavior of Si:P at the metal-insulator transition

1994

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TransitionThe apparent value of the conductivity exponent p =0. 5 at the T 0 metal-insulator transition in Si:P has remained a puzzle for over a decade [1]. Stupp et al. [2] recently have proposed a reanalysis of the Hence, the 6% smaller n, required by Stupp et al. to raise p would not permit a self-consistent treatment of the observed critical behavior on both sides of the metal-insulator transition.

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“…[7], reasons for the earlier experiments not agreeing with one another have been traced to difficulties in having a system allowing sufficient access into the critical region and possessing a well defined critical point. In contrast, the current work is done on a system where the critical point can be clearly identified, and the critical region is experimentally accessible.…”

mentioning

confidence: 99%

“…Therefore, the emphasis has been to obtain the conductivity as a function of T , as close to T = 0 as possible. In spite of intense efforts over several decades [7] it turned out to be rather difficult to access the critical regime in a reliable way. While so far all such experiments confirm the continuous nature of the transition, the values of the critical exponents remain controversial.…”

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Asymmetric Metal-Insulator Transition in Disordered Ferromagnetic Films

Misra

et al. 2011

Phys. Rev. Lett.

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We present experimental data and a theoretical interpretation on the conductance near the metalinsulator transition in thin ferromagnetic Gd films of thickness b ≈ 2 − 10nm. A large phase relaxation rate caused by scattering of quasiparticles off spin wave excitations renders the dephasing length L φ b in the range of sheet resistances considered, so that the effective dimension is d = 3. The observed approximate fractional temperature power law of the conductivity is ascribed to the scaling regime near the transition. The conductivity data as a function of temperature and disorder strength collapse on to two scaling curves for the metallic and insulating regimes. The best fit is obtained for a dynamical exponent z ≈ 2.5 and a correlation length critical exponent ν ′ ≈ 1.4 on the metallic side and a localization length exponent ν ≈ 0.8 on the insulating side.PACS numbers: 75.45.+j, 75.50.Cc, 75.70.Ak Since the scaling theory of Anderson localization has been proposed in 1979 [1], the metal-insulator transition in disordered conductors [2] has been one of the most extensively studied cases of quantum phase transition, both experimentally and theoretically. In its simplest form it describes non-interacting electrons in a disordered potential, where the disorder can be controlled experimentally in a variety of ways, e.g by systematic doping. One of the most dramatic predictions of the scaling theory is the absence of extended states, and therefore true metallic behavior, in systems in dimensions d ≤ 2. This has been verified in numerous experiments [3]. The other prediction is the existence of a critical point in d > 2 where the conductivity in the metallic phase goes to zero continuously with increasing disorder, in contrast to having a minimum metallic conductivity [4]. Electron-electron interactions are known to modify the behavior near a metal-insulator transition in a significant way [5]. For example, indications of a metallic state in two-dimensional systems have been found in experiment, and a number of theoretical scenarios explaining such a state have been developed [6].Near the transition, the behavior is characterized by power laws with critical exponents. For example, the dc conductivity σ(λ), with λ being a measure of disorder, follows a power law σ ∼ t s , where t = (1 − λ/λ c ) denotes the distance to the critical point at the critical disorder λ c and s is the conductivity exponent. The dynamical conductivity at the critical point, on the other hand, is characterized by the dynamical exponent z as σ(ω; λ c ) ∼ ω 1/z . The correlation length on the metallic side (λ < λ c ) diverges at the critical point as ξ ∼ t −ν ′ and the localization length (λ > λ c ) diverges as ξ ∼ |t| −ν . The critical exponents ν and ν ′ may be different. In d = 3 dimensions the relation s = ν ′ holds. The exponents in d = 3 have not been calculated in a reliable way up to now.As for any quantum phase transition, the critical exponents can not be measured experimentally at the true T = 0 critical point, but must be inferre...

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Possible solution of the conductivity exponent puzzle for the metal-insulator transition in heavily doped uncompensated semiconductors

Cited by 151 publications

References 33 publications

Metal-insulator transition in amorphousSi1−xNix:Evidence for Mott’s minimum metallic conductivity

Metal-insulator transition in amorphousSi1−xNix:Evidence for Mott’s minimum metallic conductivity

Critical behavior of Si:P at the metal-insulator transition

Asymmetric Metal-Insulator Transition in Disordered Ferromagnetic Films

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