Broken symmetry states characterizing density waves of higher angular momentum in correlated electronic systems are intriguing objects. In the scheme of characterization by angular momentum, conventional charge and spin density waves correspond to zero angular momentum. Here, we explore a class of exotic density wave states that have topological properties observed in recently discovered topological insulators. These rich topological density wave states deserve closer attention in not only high temperature superconductors but in other correlated electron states, as in heavy fermions, of which an explicit example will be discussed. The state discussed has nontrivial charge [Formula: see text] skyrmionic spin texture. These skyrmions can condense into a charged superfluid. Alternately, they can fractionalize into merons and anti-merons. The fractionalized particles that are confined in skyrmions in the insulating phase, can emerge at a deconfined quantum critical point, which separates the insulating and the superconducting phases. These fractional particles form a two-component spin-singlet chiral [Formula: see text] wave superconducting state that breaks time reversal symmetry. Possible connections of this exotic order to the superconducting state in the heavy-fermion material [Formula: see text] are suggested. The direct evidence of such a chiral superconducting state is polar Kerr effect that was observed recently.
Density-wave states of nonzero angular momentum