Nematic valley ordering in quantum Hall systems

The interplay between quantum Hall ordering and spontaneously broken "internal" symmetries in two-dimensional electron systems with spin or pseudospin degrees of freedom gives rise to a variety of interesting phenomena, including novel phases, phase transitions, and topological excitations. Here we develop a theory of broken-symmetry quantum Hall states, applicable to a class of multivalley systems, where the symmetry at issue is a point-group element that combines a spatial rotation with a permutation of valley indices. The anisotropy of the dispersion relation, generally present in such systems, favors states where all electrons reside in one of the valleys. In a clean system, the valley "pseudospin" ordering occurs via a finite-temperature transition accompanied by a nematic pattern of spatial symmetry breaking. In weakly disordered systems, domains of pseudospin polarization are formed, which prevents macroscopic valley and nematic ordering; however, the resulting state still asymptotically exhibits the quantum Hall effect. We discuss the transport properties in the ordered and disordered regimes, and the relation of our results to recent experiments in AlAs.