When electrons are subject to a potential with two incommensurate periods, translational invariance is lost, and no periodic band structure is expected. However, model calculations based on nearly free one-dimensional electrons and experimental results from high-resolution photoemission spectroscopy on a quasi-one-dimensional material do show dispersing band states with signatures of both periodicities. Apparent band structures are generated by the nonuniform distribution of electronic spectral weight over the complex eigenvalue spectrum.

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Using angle-resolved photoemission and linearly polarized synchrotron radiation, we measured the electronic band structure of electronic states of CuO 2 plane materials ranging from insulators ͑Sr 2 CuO 2 Cl 2) to overdoped superconductors ͑Bi 2 Sr 2 CaCu 2 O 8ϩx). We report three results: ͑i͒ The CuO 2 containing insulator possesses a spin-density-wave ͑SDW͒ ground state; ͑ii͒ there are precursors of the SDW state for underdoped Bi 2 Sr 2 CaCu 2 O 8ϩx ; ͑iii͒ an extended saddle-point-type van Hove singularity is neither a necessary nor a sufficient condition for a high superconducting transition temperature, T c. ͓S0163-1829͑97͒50226-8͔ RAPID COMMUNICATIONS