Order by Disorder and by Doping in Quantum Hall Valley Ferromagnets

TL;DR

This paper explores the complex symmetry-breaking phenomena in multi-valley quantum Hall systems, revealing how thermal fluctuations and doping influence the emergence of nematic and other ordered phases.

Contribution

It introduces the concept of 'order by doping' to explain symmetry selection mechanisms in multi-valley quantum Hall ferromagnets.

Findings

Discrete ${D}_3$ symmetry breaks at finite temperature.

Symmetry breaking involves 'order by disorder' and 'order by doping'.

Analogous phenomena observed in Si(110) system.

Abstract

We examine the Si(111) multi-valley quantum Hall system and show that it exhibits an exceptionally rich interplay of broken symmetries and quantum Hall ordering already near integer fillings $\nu$ in the range $\nu=0-6$. This six-valley system has a large $[SU(2)]^3\rtimes D_3$ symmetry in the limit where the magnetic length is much larger than the lattice constant. We find that the discrete ${D}_3$ factor breaks over a broad range of fillings at a finite temperature transition to a discrete nematic phase. As $T \rightarrow 0$ the $[SU(2)]^3$ continuous symmetry also breaks: completely near $\nu =3$, to a residual $[U(1)]^2\times SU(2)$ near $\nu=2$ and $4$ and to a residual $U(1)\times [SU(2)]^2$ near $\nu=1$ and $5$. Interestingly, the symmetry breaking near $\nu=2,4$ and $\nu=3$ involves a combination of selection by thermal fluctuations known as "order by disorder" and a selection by the energetics of Skyrme lattices induced by moving away from the commensurate fillings, a mechanism we term "order by doping". We also exhibit modestly simpler analogs in the four-valley Si(110) system.