Diophantine equation for the three-dimensional quantum Hall effect
Abstract
When the Fermi level lies in a gap, the Hall conductivity of three-dimensional electrons in a periodic potential is expressed in a topologically invariant form with a set of three integers. If the magnetic fluxes through the three independent areas of the periodic lattice are rational numbers, one obtains a Diophantine equation relating these numbers and the integers which characterize the Hall conductivity.
- Publication:
-
Physical Review B
- Pub Date:
- June 1992
- DOI:
- Bibcode:
- 1992PhRvB..4513488K
- Keywords:
-
- 73.20.Dx;
- 71.20.-b;
- 02.40.+m;
- Electron density of states and band structure of crystalline solids