Negative quantum Hall effect in field-induced spin-density-wave states: Dependence on shape of the quasi-one-dimensional Fermi surface

Abstract

The successive transitions of the field-induced spin-density wave, which is labeled by the quantum number $N$ of the Hall conductivity and the nesting vector, are known to depend on the shape of the quasi-one-dimensional Fermi surface. We study the condition for the appearance of the negative $N$ states, where the quantized Hall conductivity changes the sign. We obtain the phase diagram for the negative $N$ states in the parameter space of the higher harmonics in the Fermi surface (${t}_{b}^{\ensuremath{'}}$, ${t}_{3}$, and ${t}_{4}$) to be stabilized with and without the periodic anion potential $V$ in the perpendicular direction to the conducting axis, which are the cases in ${(\text{TMTSF})}_{2}{\text{ClO}}_{4}$ and ${(\text{TMTSF})}_{2}{\text{PF}}_{6}$, respectively. The negative $N$ phase is shown to be stabilized for the smaller values of ${t}_{3}$ and ${t}_{4}$ in the case of the finite $V$. Comparing with the experiment by Matsunaga et al. [J. Phys. IV 131, 269 (2005)], where the quantum Hall effect is observed in ${(\text{TMTSF})}_{2}{\text{ClO}}_{4}$ with various cooling rates, we obtain the parameter regions of ${t}_{3}$ and ${t}_{4}$ for ${(\text{TMTSF})}_{2}{\text{ClO}}_{4}$ ($0.06\ensuremath{\lesssim}{t}_{3}/{t}_{b}^{\ensuremath{'}}\ensuremath{\lesssim}0.23$, $0\ensuremath{\lesssim}{t}_{4}/{t}_{b}^{\ensuremath{'}}\ensuremath{\lesssim}0.08$, and $V/{t}_{b}^{\ensuremath{'}}\ensuremath{\lesssim}2.0$).