Analytic properties of band functions

✍ Scribed by J.E Avron; B Simon

• Publisher: Elsevier Science
• Year: 1978
• Tongue: English
• Weight: 959 KB
• Volume: 110
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(78)90143-4

✦ Synopsis

We consider the analytic properties of Bioch Hamiltonians and their energy levels as functions of quasi-momentum k. Among other results are: (1) The only entire band is the trivial free electron parabola. (2) The only isolated singularities allowed are branch points.

(3) In one dimension, no natural boundaries or logarithmic branch points occur. (4) The periodic attractive screened Coulomb lattice has a nondegenerate lowest band (i.e., the "direct gap" is strictly positive for all k).