Anomalous hopping exponents of ultrathin metal films

Marković, Nina; Christiansen, C.; Grupp, D. E.; Mack, A. M.; Martinez-Arizala, G.; Goldman, A. M.

doi:10.1103/physrevb.62.2195

Cited by 34 publications

(19 citation statements)

References 26 publications

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“…δ = 0.75 is higher than the Mott value of δ = 0.25 associated with a flat density of states and the value of δ = 0.5 derived by Efros and Shklovskii [21] for the zero temperature Coulomb gap. However, experiments on materials such as ultrathin metal films find values for δ = 0.75 ± 0.05 [13,14,15,16,17] in agreement with our value of δ for large E g . The mechanism behind this exponent has been a puzzle [13,36].…”

Section: Density Of Statessupporting

confidence: 91%

“…However, experiments on materials such as ultrathin metal films find values for δ = 0.75 ± 0.05 [13,14,15,16,17] in agreement with our value of δ for large E g . The mechanism behind this exponent has been a puzzle [13,36]. Here we see that a possible simple explanation for the experimental observation of an anomalous hopping exponent is that the Coulomb gap in the single particle density of states is filling in with increasing temperature.…”

Section: Density Of Statessupporting

confidence: 91%

“…However, for large values of E g , δ ≈ 0.75. Both values have been seen experimentally [11,13,14,15,16,17]. In section III, we present our results.…”

Section: Introductionsupporting

confidence: 67%

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1/fnoise in electron glasses

Shtengel

2003

Phys. Rev. B

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We show that 1/ f noise is produced in a 3D electron glass by charge fluctuations due to electrons hopping between isolated sites and a percolating network at low temperatures. The low frequency noise spectrum goes as ω −α with α slightly larger than 1. This result together with the temperature dependence of α and the noise amplitude are in good agreement with the recent experiments. These results hold true both with a flat, noninteracting density of states and with a density of states that includes Coulomb interactions. In the latter case, the density of states has a Coulomb gap that fills in with increasing temperature. For a large Coulomb gap width, this density of states gives a dc conductivity with a hopping exponent of ≈ 0.75 which has been observed in recent experiments. For a small Coulomb gap width, the hopping exponent ≈ 0.5.

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Section: Density Of Statessupporting

confidence: 91%

Section: Density Of Statessupporting

confidence: 91%

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1/fnoise in electron glasses

Shtengel

2003

Phys. Rev. B

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“…On the insulating side of the superconductor-insulator transition in ultrathin quench-condensed Ag, Bi, Pb and Pd films [7] VRH data agree with Eq. (11) with = 2 / 3 p .…”

Section: Variable Range Hopping In Thin Film With Large Dielectric Cosupporting

confidence: 74%

Variable range hopping in thin film with large dielectric constant

Shklovskiǐ

2017

Low Temperature Physics

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In a film with large dielectric constant κ the electric field of an electron spreads inside the film before exiting the film at large distances of order of κd (d is the film width). This leads to the logarithmic Coulomb repulsion between electrons and modifies the shape of the Coulomb gap in the density of localized states in a doped film. As a result the variable range hopping conductivity in such a film has a peculiar temperature dependence, where the domain of the ln σ(T) ∝ (T 0 /T) p dependence, with the index p  0. where κ is the dielectric constant of the solid, the density of localized states ( ) g E has the soft Coulomb gap. As a result the VRH conductivity σ obeys the Efros-Shklovskii (ES) law [1,2]

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“…All of this implies that the nonlinearities are intrinsic. In addition, much higher resistances were measured in the same apparatus at lower temperatures for other films not exhibiting either superconductivity or flattening [15]. Finally, the temperatures at which R(T ) became temperature-independent were well above 1K, making a scenario of not cooling the electrons unlikely [16].…”

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confidence: 91%

Evidence of Collective Charge Behavior in the Insulating State of Ultrathin Films of Superconducting Metals

2002

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Nonlinear I-V characteristics have been observed in insulating quench-condensed films which are locally superconducting. We suggest an interpretation in terms of the enhancement of conduction by the depinning of a Cooper pair charge density wave, Cooper pair crystal, or Cooper pair glass that may characterize the insulating regime of locally superconducting films. We propose that this is a more likely description than the Coulomb blockade or charge-anticharge unbinding phenomena.In the context of the Bose-Hubbard model, which is equivalent to the model of a Josephson junction array with charging, zero-temperature superconductorinsulator(SI) transitions in two dimensions (2D), tuned by disorder or magnetic field, are believed to be direct, with metallic behavior only at the quantum critical point [1]. Recent experiments have suggested the existence of a significant metallic phase between the superconductor and insulator. The Stanford group reported this for nominally superconducting MoGe films in moderate magnetic fields at low temperatures, and conjectured that it was due to dissipation [2]. They later found "true" superconductivity in low fields [3]. Long ago, metallic behavior was reported in quench-condensed granular films over a range of thicknesses intermediate between those for which films were insulating and superconducting [4], and it was found more recently in Josephson junction arrays [5]. Re-examination of the theory has involved the inclusion of aspects of percolation [6], elaboration of the Bose-Hubbard model [7,8], and consideration of dissipative Bose systems [9]. Das and Doniach [7] explained aspects of Ref. 4 by extending the Bose-Hubbard model to high filling and including nearest-neighbor as well as on-site Coulomb interactions. Their phase diagram contains the possibility of an intervening Bose metal phase, or a direct transition, depending upon the relative magnitudes of the various Coulomb and Josephson coupling energies. The Bose metal contains free vortices and antivortices, prevented from Bose condensing by dissipation. The insulator is a condensate of vortices, or in other language, a Cooper pair charge density wave (CDW). Phillips and Dalidovich [8], using the original form of the Bose-Hubbard model, also demonstrated that there was a Bose metallic phase. This followed from a subtle cancellation in the expression for the conductivity between an exponentially small population of bosonic quasiparticles and their associated exponentially long scattering time. The Bose insulator in this picture results from dissipative processes such as coupling to a heat bath, or from a high enough level of disorder. Ng and Lee [9], using a different approach to theory of dissipative Bose systems, suggest that a Bose metal does not exist at zero temperature, but note a crossover regime at finite temperature that could be identified as a metallic phase.In this letter we shift the focus to the study of the insulating regime of granular quench-condensed films. In the past the insulator has not been carefully...

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Anomalous hopping exponents of ultrathin metal films

Cited by 34 publications

References 26 publications

1/fnoise in electron glasses

1/fnoise in electron glasses

Variable range hopping in thin film with large dielectric constant

Evidence of Collective Charge Behavior in the Insulating State of Ultrathin Films of Superconducting Metals

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