Organic Superconductors and Spin Density Waves

Abstract

The energy dispersion of a 1-D electron gas depends only on a single component of the wave vector k and the Fermi surface consists of two points at ± k_F (with $2{{k}_{{F = }}}\rho \tfrac{\pi }{{{{a}^{,}}}}$, where a is the 1-D unit cell and ρ the density of carriers per unit cell) [1]. An array of non-interacting chains will thus give rise to two planar Fermi surface sheets, (Fig 1). In the vicinity of the Fermi level, the energy spectrum can be linearized and leads to the particular property, (Fig 1),

$$ {{\varepsilon }_{ + }}(k) = - {{\varepsilon }_{ - }}(k - 2{{k}_{F}}) $$

((1))

when the energy is counted from the Fermi energy and where + and - refer to right and left moving electrons. Equation (1) provides the essential peculiarity of the 1-D electron gas, i.e. the symmetry between electron and hole states near the Fermi level.