Edge States And Quasiparticles In 2DEG

The fractional quantum Hall effect, discovered in 1982 in two-dimensional electron systems, has generated a wealth of successful theories and new concepts in condensed matter physics. The possibility of having non-abelian quasiparticle statistics in fractional quantum Hall states such as the Moore-Read state is extremely exciting, especially due to its relevance to topological quantum computation.This thesis focuses on quasiparticle and edge excitations of fractional quantum Hall states. Quasiparticles in fractional quantum Hall liquids are anyons, having fractional charge and satisfying fractional statistics or non-abelian statistics. In v=1/3 fractional quantum Hall liquids, individual quasihole or quasiparticle can be created and trapped by a tip potential with a finite width, which may be generated by a biased atomic force microscopy tip in experiment. These excitations have±e/3 charge and satisfy abelian statistics. Their presence has no effect on the edge spectrum of the system. At filling factor v=5/2, by using a similar tip potential, we can create both e/4 and e/2 quasiholes. The e/4 quasihole is believed to satisfy the non-abelian statistics and the presence of such a single quasihole in the system can lead to nontrivial change of the edge spectrum. The study of edge excitations in v=5/2 fractional quantum Hall liquids reveals a neutral fermionic mode as well as a chiral bosonic mode, whose velocity difference leads to de-coherence in quasiparticle interference experiments. Ground states and edge excitations have also been studied in v=2/3 fractional quantum Hall liquids, which can be described as the v=1/3 Laughlin state formed by holes embedded in a integer-filling background. In this case, there are two counter-propagating edge modes. The outer mode has a larger (3 times) velocity than the inner edge. The quasihole and quasiparticle excitation in v=2/3 also have fractional charge±e/3 and satisfy abelian statistics.Other than semiconductor heterojunctions, the quantum Hall effect can also be ob-served in graphene systems. Graphene is an ideal two-dimensional electron gas system, with Dirac electrons are living in a honeycomb lattice structure. The structure of the edge of a graphene sheet, zigzag edge or armchair edge, has an important effect on the transportation properties of the graphene. While graphene with zigzag edge has zero en-ergy surface state, there is none in graphene with armchair edge. This can be detected in the scanning tunneling microscopy experiments. Nevertheless, in a realistic finite system, there are mixed edges and anisotropic interaction. It is, therefore, possible that surface states can also appear in the armchair-edge graphene while disappear in the zigzag-edge graphene.