The Broken Symmetry of Two-Component $\nu =1/2$ Quantum Hall States

Abstract

We show that the recently discovered $\nu =1/2$ quantum Hall states in bilayer systems are triplet p-wave pairing states of composite Fermions, of exactly the same form as ${}^3$He superfluids. The observed persistence (though weakening) of the $\nu =1/2$ state in the two- to one-component crossover region corresponds to a continuous deformation of the so-called (331) state towards the ``Pfaffian" state, identical to the well known A to A${}_1$ transition in ${}^3$He. This deformation also demonstrates the remarkable fact that electrons can release and capture ``vortices" in a continuous and incompressible manner through spin rotations. The broken symmetry of the triplet pairing state is a ``pairing" vector $\mathbf{d}$. It also implies a (pseudo-spin) magnetization $\propto i\mathbf{d}\times {\mathbf{d}}^{\ast }$. In the presence of layer tunneling, the (331) state ({\bf d} real) is unstable against other states with a magnetization ({\bf d} complex). The recently observed persistence of the $\nu =5/2$ state in single layer systems in the two- to one-component crossover region is also consistent with triplet pairing interpretation.

Misprints in a paragraph on p.7 of previous version corrected. All results remain indentical.