PROPAGATION OF BAND ELECTRONS ON COUPLED CHAINS IN A MAGNETIC-FIELD

The problem of propagation of a tight-binding electron on coupled chains in a magnetic field is studied. The exact solution for the mean-square displacement is obtained, from which the coherent evolution of the band electron is found to be tuned periodically by the ratio of the flux passing through a unit cell to the flux quantum. The electron will escape to infinity rapidly when the ratio becomes an integer. When it approaches a half-integer, the electron motion will have a tendency towards localization. These theoretical findings are confirmed by numerical ones.