ARE BLOCH BANDS AT FINITE ELECTRIC FIELD ADIABATICALLY CONNECTED TO THOSE AT ZERO FIELD,
Abstract
If a potential consists of a superposition of a periodic part and a uniform electric field than for a particle moving in this field there are Bloch bands closed in time. The present report addresses itself to the question whether these bands may be identified with the field-free bands. The most natural thing is to expect that the bands are slightly field dependent, but converge toward the field-free bands as E goes to zero. Bands for which this is true are said to be adiabatically connected to corresponding bands at zero field. Two model cases are given for which this adiabatic connection pertains. It is shown that the answer to the question in the report title is almost always negative. In this proof the positive cases serve an essential function. It is shown that the parameters of the periodic potential must obey at least one upple mentary condition to allow adiabatic connection, and that the collected cases precisely obey this condition. Adiabatic connection is thus generally not possible. An explicitly soluble case is pre sented which does not allow adiabatic connection. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1963
- Accession Number
- AD0413307
Entities
People
- G.h. Wannier
- J.p. Vandyke
Organizations
- University of Oregon