Abstract
The origin of a “flat band” as defined in the “flat band–steep band” model for superconductivity has been studied. A “local inversion center” is derived mathematically as the necessary and sufficient condition for an occurrence of a “flat band” at an arbitrary k → point. From the k → -dependent part of E( k → j) , a “pseudo-inversion center” is demonstrated to be a sufficient condition based on the Patterson symmetry. The chemical bonding origin of a “flat band” is also studied analytically with a tight-binding approach.
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