Topological Excitations in Low-Dimensional Space and Fractional Statistics

由于平面系统中不存在本征自旋统计关系，因此电子在不形成库珀对的情况下凝聚，准粒子可能具有分数统计性质。一个具体的例子是分数量子霍尔(QH)系统，它是通过在平面电子气中施加强磁场而获得的。基于合成玻色子的图像，分数QH系统是最容易理解的。复合玻色子是束缚在狄拉克磁通量子奇数单位上的电子。尽管复合玻色子图像是观察系统的一种很好的方式，但它的场论公式到目前为止还有许多不满意的地方。我们建立了一个自洽的场论框架，它允许我们研究限制在最低朗道能级(LLL)内的所有激发模。LLL中的任何状态都由波函数omega[z]psi；lt；ln&gt；[chi]描述，其中psi&lt；ln&gt；[chi]是描述基态的Laughlin波函数。这里，omega[z…More]是对称N个变量的解析函数。在我的理论中，它是复合玻色子的波函数。用这个方案分析了QF铁磁体中的Skyrmion激发。我们的理论结果很好地解释了观察到的Skyrmions的激活能，我还在一个双层QH系统上进行了实验。通过改变两个量子阱中的总电子密度和密度比，测量了填充因子nu=2，1和2/3时，双分子层量子霍尔态的霍尔坪宽度和激活能。他们的行为各不相同。在密度差的所有测量范围内，nu=1状态是稳定的，而nu=2/3状态仅在平衡点附近稳定。另一方面，随着电子密度的变化，nu=2态显示出这两种态之间的相变。我根据复合玻色子的图景解释了这些实验事实。特别地，nu=2态的相变可以理解为自旋铁磁体和伪自旋铁磁体之间的相变。较少

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