Topological Excitations in Low-Dimensional Space and Fractional Statistics

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Because there exists no intrinsic spin-statistics relation in the planar system, it is possible that electrons condense without making Cooper pairs and that quasiparticles possesses fractional statistics. A concrete example is the fractional quantum Hall (QH) system, which is obtained by applying a strong magnetic field to a planar electron gas. The fractional QH system is most easily understood based on the composte-boson picture. Composite bosons are electrons bound to odd units of Dirac flux quanta.Though the composite-boson picture is an excellent way of viewing the system, its field-theoretical formulation has so far many unsatisfactory points. We have constructed a self-consistent field theoretical framework, which allows us to investigate all excitation modes confined within the lowest Landau level (LLL) . Any state in the LLL is described by the wave function omega [z]PSI_<LN> [chi] , where PSI_<LN> [chi] is the Laughlin wave function describing the ground state. Here, omega [z … More ] is an analytic function of symmetric N variables. It is the wave function of composite bosons in my theory. Using this scheme, I have analyzed Skyrmion excitations in QF ferromagnets. Our theoretical results account for observed activation energies of Skyrmions quite well.I have also conducted experiments on a bilayr QH system. We have measured the Hall-plateau width and the activation energy in the bilayr quantum Hall state at filling factor nu=2,1 and 2/3, by changing the total electron density and the density ratio in the two quantum wells. Their behavior are remarkably different from one to another. The nu=1 state is found stable over all measured range of the density difference, while the nu=2/3 state is stable only around the balanced point. The nu=2 state, on the other hand, shows a phase transition between these two types of the states as the electron density is changed. I have interpreted these experimental facts based on the composit-boson picture. In particular, the phase transion in the nu=2 state is understood as the one between the spin ferromagnet and the pseudospin ferromagnet. Less