Peierls instability
The Peierls transition (after its discoverer Rudolf Peierls ; also Peierls transition or Peierls distortion called, the postulate .. U g instability is also Peierls theorem ) describes the solid-state physics , the instability of a one-dimensional metal (described in band model ) against lattice suggestions with is the wave vector , where is the Fermi wave vector . This means that the originally equal distances between the lattice atoms increase and decrease alternately in the form of a charge density wave . This doubles the size of the grid cell ; each now contains not just a single but a pair of atoms ( dimerization ).
If the grid positions are occupied by magnetic moments , the magnetic interaction leads to the same effect; in this case the transition is called a Spin-Peierls transition .
In one dimension, the Fermi surface (corresponding to the energy up to which the energy levels of the electrons are occupied in the ground state ) consists of the two points in k-space . A lattice excitation with a wave vector , which exactly connects the two points of the Fermi surface, creates, according to the degenerate perturbation theory of quantum mechanics, a lowering of the energy levels on the Fermi surface: a band gap arises . This can increase further (Peierls instability) until it is stopped by the elastic energy of the grid.
The Peierls instability leads to the fact that the Landau quasiparticle theory of excitations in Fermi liquids , which is common in two and three dimensions, fails in one dimension. Instead, Tomonaga-Luttinger fluids are available.
See also
literature
- Charles Kittel : Introduction to Solid State Physics. Oldenbourg 1980, p. 343 f.