Quantized Hall Effect in Ultrathin Metallic Films

The Hall coefficient $R_H$ of ultrathin epitaxial Pb films is determined experimentally. A comparison with electrical conductivity data leads to the conclusion that the investigated Pb layers behave like a size-quantized metal. Pronounced variations of $R_H$ with the film thickness were found. The observed reversal of the sign of $R_H$ is discussed within the available theory of the quantum size effect describing the galvanomagnetic properties of metals. We find that the observed phenomenon cannot be explained by the free electron model of a quantized layer.