Temperature dependence of the longitudinal resistivity at several constant magnetic fields. (a) Phase fluctuation zone in between and . Pair arrow-indicated characteristic temperatures: the offset temperature , the onset temperature , the critical temperature , and the temperature at the resistivity maximum . Inset: the granular morphology characterized by SEM. (b) Plots of the resistivity vs for and . The dotted-dashed red lines are the expected logarithmic behavior. (c) The low temperature segment (4–1 K) of the curve characterized by the FHM. The reverse resistivity is plotted vs on a semilogarithmic scale. The dotted-dashed red line is the expected Mott’s law in three dimensions.
Magnetic field-driven SITs. (a) Moving of the hopping threshold by magnetic fields to the resistivity maxima as indicated by the vertical bars (, ). Inset: the magnetic field of plotted as a function of its temperature. (b) Magnetic field dependence of the longitudinal resistivity near and at the temperatures of . The intersections are chained by a quadratic fitting (dashed-dotted line).
Scaling analysis of the intersections [see Fig. 2(b)] by Fisher’s finite-size scaling law, which gives various values of the scaling exponent product . (a) Scaling analysis carried out by the so-called optimal collapse. (b) Magnetic field dependence of the value. (c) Temperature dependence of the value.
(a) Banana-shaped phase fluctuation zone highlighted in yellow. The states of are indicated by filled circles from red to violet. Area in between the curve of and the curve of is taken as a manifestation of the number of the unbound precursor Cooper pairs in the phase fluctuation zone. Inset: magnetic field dependence of the unbinding of the precursor Cooper pairs. (b) Precursor scenario in the phase fluctuation zone: Cooper pair-filled grains embedded in a matrix of normal state.
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