We examine the Si(111) multivalley quantum Hall system and show that it exhibits an exceptionally rich interplay of broken symmetries and quantum Hall ordering already near integer fillings ν in the range ν=0-6. This six-valley system has a large [SU(2)]3D3 symmetry in the limit where the magnetic length is much larger than the lattice constant. We find that the discrete D3 factor breaks over a broad range of fillings at a finite-temperature transition to a discrete nematic phase. As T→0, the [SU(2)]3 continuous symmetry also breaks: completely near ν=3, to a residual [U(1)]2×SU(2) near ν=2 and 4, and to a residual U(1)×[SU(2)]2 near ν=1 and 5. Interestingly, the symmetry breaking near ν=2,4 and ν=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.
All Science Journal Classification (ASJC) codes
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics