Abstract

The Schrodinger equation in a spatially periodic system has eigenstates in the form of Bloch waves, plane waves with amplitudes modulated periodically in space. We will consider in this chapter geometric phases associated with the Bloch waves. Crystalline solids are naturally occuring periodic systems in which an electron sees a periodic potential due to the nuclei and other electrons. Periodic systems also include artificial structures such as superlattices, networks of microwires, and arrays of quantum dots or antidots. A perfect periodic potential can also be produced on cold atoms by an interference pattern of laser beams of suitable frequency. Throughout this chapter, we will treat the periodic potentials as given and focus on the properties of particles in the Bloch states under external forces.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.