Quantum Hall tunnel junctions: Luttinger liquid physics, quantum coherence effect and fractional quantum numbers

This thesis is devoted to the investigation of non-conventional effects of quantum Hall fluids such as fractional quantum numbers, nontrivial quantum coherence and Luttinger liquid physics of their edge states. Tunneling transport studies in various quantum Hall tunnel junctions were done as a means of exploring these effects and four types of tunnel junctions are covered.; First, a line junction in the presence of a single point contact is discussed as a possible scenario for a recent experimental observations on tunneling between laterally coupled quantum Hall liquids. The experimental system is modeled as a pair of coupled chiral Luttinger liquids with a point contact tunneling center. Salient features of published and unpublished data are explained.; This study of the quantum Hall line junction is then extended to include the possible presence of multiple tunneling centers. Non-trivial Aharonov-Bohm (AB) oscillations in the tunneling conductance is predicted as a result of a coherence between multiple point contacts. A comparison with a recent experimental data is given to confirm theoretical predictions discussed in this thesis and an estimate of the coherence length based on the theory is given.; Tunnel junctions between a Hall bar and a superconducting lead are proposed as a tool for investigating Cooper-pair tunneling into singlet fractional quantum Hall edge states. It is shown that the low energy regime of one of the set-ups is governed by a quantum entangled fixed point.; Finally, a three-terminal "T-junction" is proposed as an experimental setup for directly detecting fractional charge and statistics of fractional quantum Hall quasiparticles via cross current noise measurements. The elementary excitations of fractional quantum Hall (FQH) fluids are vortices with fractional statistics; yet this fundamental prediction has remained an open experimental challenge. It is shown that the noise at finite temperature reveals signatures of generalized exclusion principles, fractional exchange statistics and fractional charge. Furthermore the vortices of Laughlin states are predicted to exhibit a "bunching" effect, while for higher states in the Jain sequences they are predicted to exhibit an "anti-bunching" effect.