Nonmetallic Conduction in Thin Metal Films at Low Temperatures

Resistance measurements were made on high-resistivity thin-film metal strips at temperatures as low as 10 mK. Unexpected logarithmic variations of the resistance with temperature and applied electric field were observed for strips with sheet resistance below ${R}_{\ensuremath{\square}}\ensuremath{\sim}10$ k\ensuremath{\Omega}/\ensuremath{\square} and widths \ensuremath{\gtrsim} 1 \ensuremath{\mu}m. Exponential increases in resistance were observed for similar films when the film width was decreased to about 0.1 \ensuremath{\mu}m or when ${R}_{\ensuremath{\square}}$ was increased to \ensuremath{\sim} 10 k\ensuremath{\Omega}/\ensuremath{\square}.