Resistivity and transverse magnetoresistance in ultrathin films of pure bismuth

Electrical resistivity and transverse magnetoresistance were measured at liquid-helium temperatures in thin films of pure bismuth ranging from 101 to 4504 A{} in magnetic fields up to a maximum of 80 kG. The films could be divided into two groups, above and below a thickness of about 250 A{}. The resistivity (in zero magnetic field) and the magnetoresistance were found to be drastically different, both in magnitude and variation as a function of field strength, for the two groups. Interpretation is given in terms of a transition, due to the quantum size effect, of the charge carriers from states of three-dimensional motion in the thicker films to states of two-dimensional motion in the thinner films.