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Electronic topological phase transitions (ETT) are predicted for any quantized metal films with a periodically modulated boundary commensurate with the bulk lattice. While the thickness of the film at which ETT occurs is determined almost exclusively by the period of the boundary modulation, the value of the band gaps and the amplitude of the singularities are proportional to the amplitude of the corrugation. The gaps in the energy spectrum lead to a strong anisotropy of conductivity. These novel quantum effects can be detected in measurements of the density of states and conductivity as a function of the film thickness. Experiments that could lead to these observations are proposed.

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© 2002 The American Physical Society