Quantum Hall effect in quasi-one-dimensional conductors

The integer topological invariant called the Chern number is calculated for a quasi-one-dimensional conductor in the magnetic-field-induced spin-density-wave state. Due to the nonzero value of the Chern number the Hall conductivity per layer has the quantized value ${\mathrm{\sigma }}_{\mathit{x}\mathit{y}}$=2${\mathit{Le}}^2$/h and in the effective action of the system there is a so-called Hopf term, which describes topologically nontrivial configurations of the spin-density-wave polarization vector. The dependence of the integer number L on magnetic field H is calculated in the parquette approximation. The theory is applied to the Bechgaard-salt family of organic conductors (TMTSF${)}_2$X, where TMTSF is tetramethyltetraselenafulvalene.