Man. Araujo et De. Khmelnitskii, POSSIBLE ELECTRON-PHONON INSTABILITIES IN 2-DIMENSIONAL BLOCH-ELECTRON SYSTEMS IN MAGNETIC-FIELDS, Journal of physics. Condensed matter, 6(42), 1994, pp. 8839-8852
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.