Multiphonon Tunneling Conduction of LocalizedπElectrons in Amorphous Carbon Films

The temperature dependence of the dc conductivity has been measured on sputtered amorphous carbon films. The conductivity is proportional to $T^n$ with $n=15\mathrm{}-17$ over a wide temperature range, suggesting for the first time that the multiphonon tunneling transition with weak electron-lattice coupling of localized $\pi$ electrons is a probable mechanism for charge transport. This may be attributed to the delocalized nature of the $\pi$ defect in amorphous carbon.