PEIERLS STABILIZATION OF MAGNETIC-FLUX STATES OF 2-DIMENSIONAL LATTICE ELECTRONS

The problem of two-dimensional lattice electrons in a uniform magnetic field is reduced to a one-dimensional Peierls system which is an off-diagonal tight-binding model. Thus, this off-diagonal equation and the usual Harper equation, which has a diagonal modulation, give the same energy spectrum. The stabilization of the state in which the magnetic field gives one flux unit per electron is formally equivalent to the Peierls instability of lattice deformation. © 1990 The American Physical Society.