A New Phase in the Bilayers of Semiconductors in Quantum Hall Effect

Recently, Spielman et al have found a new type of Goldstone boson in quantum Hall effect in bilayers. The Goldstone boson is accompanied with a phase transition or broken symmetry. In the vacuum state if there is a broken symmetry, then a massless particle is emitted. Spielman et al have discovered such a quasiparticle. However, it remains to be proved that there is a phase transition associated with the new quasiparticle. Usually the Hall resistivity is quantized in units of h/ie where i is an integer. It has been reported that i need not be an integer. In particular, it can be equal to 1/3 or some other fraction. We have found that the experimentally observed fractions can be accurately predicted by a special spin-orbit interaction based on a pseudoscalar which describes a ~v.~s type interaction, where ~v is the velocity of the electron and ~s the spin. Thus there is a new spin-dependent force on the electron. This spin-orbit interaction is of the order of v/c whereas the usual spin-orbit interaction in atoms is of the order of v/c. It has been found experimentally that the masses of some of the quasiparticles are equal. This equality of masses has been understood by using the particle-hole symmetry. Further