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Observation of double percolation transitions in Ag-SnO$_2$ nanogranular films

Two percolation transitions are observed in Ag$_x$(SnO$_2)_{1-x}$ nanogranular films with Ag volume fraction $x$ ranging from $\sim$0.2 to $\sim$0.9. In the vicinity of each percolation threshold $x_{ci}$ ($i$$=$1, 2), the variation in $σ$ with $x$ obeys a power law for $x$$>$$x_{ci}$. The origin of the first percolation transition at $x_{c1}$ ($x_{c1}$$>$$x_{c2}$) is similar to that of the classical one, while the second transition is explained as originating from the tunneling to the second-nearest neighboring Ag particles. These observations provide strong experimental support for the validity of current theories concerning tunneling effect in conductor-insulator nanogranular composites.