Bound Electron States on a Curved Surface

Abstract

We examine electrons bound in quantum-mechanical states in the surface region of a cylindrically curved surface. As predicted by Prange, the energy-level scheme for such states is formally identical with that of a flat-surface sample, except for the replacement of magnetic field $H$ by an effective field $H_{\mathrm{eff}}=H(1+\frac{R_c}{R_s})$, where $R_c$ and $R_s$ are the cyclotron and surface-curvature radii, respectively. The predicted field shift of the microwave impedance-oscillation spectrum of a (100)-plane Cu sample in weak magnetic fields has been observed and measured; this has allowed us to determine both the curvature radius $K$ and the Fermi velocity $v_F$ at the [100] point of the Cu Fermi surface. We find $K=0.36\mathrm{}\times {10}^8$ ${\mathrm{cm}}^{-1\mathrm{}}$ and $v_F=1.11\mathrm{}\times {10}^8$ cm/sec.