Possible new long-range order in spin-compensated fractional quantum hall effect

Abstract

We discuss the even-denominator fractional quantized Hall effect using halperin's wave functions, and explain how this type of wave function becomes almost a spin singlet, even though it is not an eigenstate of the total spin operator. The SU(2) global spin rotational symmetry (valid in the absence of the spin-orbit interaction and Zeeman terms), is argued, based on this variational wave function, to break down to Z₂⊗ U(1), indicating a "nematic" type of order. As a consequence of this symmetry breaking a Goldstone mode is predicted. Apart from this, for both the even- and odd-denominator Halperin wave functions, the spins are shown to have a chirality in the sense S(0)·(S(z) × S(z')) ≠ 0.