Quantized Hall conductance and its sign reversal in field-induced spin-density waves

The sign-reversal phenomenon of the quantized Hall conductance as a function of an external magnetic field (H) observed in (TMTSF${)}_2$X is investigated theoretically. After giving a general Hall-conductance formula written in terms of order parameters of the field-induced spin-density wave (FISDW), we have done extensive mean-field calculations for a simplified standard model. It is shown that the many competing order parameters ${\mathrm{\Delta }}_{\mathit{n}}$ (n=0,±1,±2, . . .) which coexist in a FISDW state can make the sign of the Hall constant change particularly near the subphase boundary of the FISDW and that numbering of the integer subphases (N=0,1,2, . . . stabilized in this order from high fields) does not necessarily coincide with the Hall number L defined by L=${\mathrm{\sigma }}_{\mathit{x}\mathit{y}}$/(${\mathit{e}}^2$/h). We have found that the jumps of the Hall constant are accompanied by the spin-density wave gap closing when a FISDW is continuously evolving as H varies. In order for the sign reversal to occur a FISDW must contain many order parameters ${\mathrm{\Delta }}_{\mathit{n}}$ with n being both signs.