Bound on the Group Velocity of an Electron in a 1D Periodic Potential

Details Bound on the Group Velocity of an Electron in a 1D Periodic Potential Bound on the Group Velocity of an Electron in a 1D Periodic Potential

1994-08-22

arxiv.org/abs/cond-mat/9408067v1

Physics

Condensed Matter

6 pages in Tex

Scientific paper

10.1103/PhysRevB.51.2616

By using a recently derived upper bound on the allowed equilibrium current in a ring, it is proved that the magnitude of the group velocity of a Bloch electron in a one-dimensional periodic potential is always less than or equal to the group velocity of the same Bloch state in an empty lattice. Our inequality also implies that each energy band in a one-dimensional crystal always lies below the corresponding free-electron band, when the minima of those bands are aligned.

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