Effect of umklapp scattering on the magnetic-field-induced spin-density waves in quasi-one-dimensional organic conductors

TL;DR

This paper investigates how umklapp scattering influences the FISDW phases in quasi-one-dimensional organic conductors, revealing effects on transition temperatures, SDW polarization, and the quantum Hall effect, including the stabilization of negative QHE phases.

Contribution

It introduces a modified Stoner criterion incorporating umklapp scattering and analyzes its impact on SDW polarization and quantum Hall phenomena in FISDW phases.

Findings

Umklapp scattering stabilizes phases with sign reversal of QHE.

Negative QHE phases involve two SDWs with similar amplitudes.

Helicoidal SDWs emerge with increased umklapp strength, affecting QHE and magnetoelectric effects.

Abstract

We study the effect of umklapp scattering on the magnetic-field-induced spin-density-wave (FISDW) phases which are experimentally observed in the quasi-one-dimensional organic conductors of the Bechgaard salts family. Within the framework of the quantized nesting model, we show that the transition temperature is determined by a modified Stoner criterion which includes the effect of umklapp scattering. We determine the SDW polarization (linear or circular) by analyzing the Ginzburg-Landau expansion of the free energy. We also study how umklapp processes modify the quantum Hall effect (QHE) and the spectrum of the FISDW phases. We find that umklapp scattering stabilizes phases which exhibit a sign reversal of the QHE, as experimentally observed in the Bechgaard salts. These ``negative'' phases are characterized by the simultaneous existence of two SDWs with comparable amplitudes. As the umklapp scattering strength increases, they may become helicoidal (circularly polarized SDWs). The QHE vanishes in the helicoidal phases, but a magnetoelectric effect appears. These two characteristic properties may be utilized to detect the magnetic-field-induced helicoidal SDW phases experimentally.