POSSIBLE ELECTRON-PHONON INSTABILITIES IN 2-DIMENSIONAL BLOCH-ELECTRON SYSTEMS IN MAGNETIC-FIELDS

The spectrum of a two-dimensional electron system in a square lattice potential subject to a perpendicular magnetic field is considered. Wel l known symmetry considerations show that if the magnetic field flux p er unit cell (measured in units of the flux quantum hc/\e\) is rationa l and non-integer, the electron energy can be expressed as a function of a generalized momentum kappa and the spectrum consists of translati onally degenerate bands in kappa-space. In this work it is shown that if the chemical potential is located at a logarithmic Van Hove singula rity of the density of states then it is possible that a periodic latt ice distortion is energetically favourable. This instability persists when the flux is changed within a small interval. The width of this in terval as well as the critical temperature marking the onset of the in stability can be estimated with logarithmic accuracy. The effects of e lectron-electron interactions are considered in the Hartree approximat ion.