The Quantum Hall Effect of Field Induced Spin Density Wave Phases: the Physics of the Ultra Quantum Crystal

TL;DR

This paper explains the quantum Hall effect in field-induced spin density wave phases using a weak coupling Fermi liquid model, accounting for experimental anomalies and revealing complex collective excitations like skyrmions.

Contribution

It introduces a comprehensive theoretical framework that explains Hall plateaux sign inversion and collective excitations in ultra quantum crystals with SDW order.

Findings

Sign inversion of Hall plateaux explained by the Quantum Nesting model with perturbations.

Observation of superposition of SDW order parameters in phase diagram.

Identification of magneto-roton structures and topological excitations such as skyrmions.

Abstract

The Quantum Hall Effect of Field Induced Spin Density Wave Phases is accounted for within a weak coupling theory which assumes that in the relevant low temperature part of the phase diagram the quasi one dimensional conductor is well described by Fermi liquid theory. Recent experimental results show that sign inversion of the Hall Plateaux takes place all the way down from the instability line of the normal state. The Quantum Nesting model, when it takes into account small perturbations away from perfect nesting, describes well not only the usual sequence of Hall plateaux, but also the anomalies connected with sign inversion of the Hall Effect. Experimental observation of de-doubling of sub-phase to sub-phase transition lines suggests that superposition of SDW order parameters occurs in some parts of the phase diagram. The collective excitations of the Ultra Quantum Crystal have a specific magneto-roton structure. The SDW case exhibits,apart from the usual spin waves, topological excitations which are either skyrmions or half skyrmions. It is suggested that magneto-rotons may have been observed some years ago in specific heat experiments.