Field effect and magnetoresistance in small bismuth wires

Abstract

The change in the electrical resistance as a function of applied electrostatic charge, known as the field effect, has been measured in Bi wires ranging in size from 2.6 to 29 μm. These measurements were made at 4.2 K in the presence of applied magnetic fields of varying strengths and directions. The changes in resistance of the samples as a function of applied parallel magnetic field, in fields up to 7 × ${10}^5$ A/m, have been analyzed as a combination of the bulk longitudinal magnetoresistance and a decrease in the amount of surface scattering. Simultaneous measurements of the field effect in these magnetic fields show, in general, a decrease in the field effect as the surface scattering decreases. When the applied magnetic fields are not parallel to the sample axis the magnetoresistance data indicate increased surface scattering, and an increase in the size of the field effect is also seen. These results are interpreted as suggesting that a major contribution to the field effect in our samples is due to changes in the surface scattering of the intrinsic carriers caused by the added charge. The magnetoresistance data allow us to estimate the specularity coefficient $p$ for two samples to be 0.33 and 0.41, and the change in $p$ with added charge to be 0.1 ${(\mathrm{C}/{\mathrm{m}}^2)}^{-1\mathrm{}}$ and 0.3 ${(\mathrm{C}/{\mathrm{m}}^2)}^{-1\mathrm{}}$.