Towards realizing topological quantum physics in Condensed matter systems
Topology has become a guiding principle for discovering robust phenomena in quantum many-body physics. One of the most fascinating predictions of these principles is topological quantum computation, which is rooted in topological quantum field theory. I will start by reviewing briefly work that started during my postdoctoral research that led to the prediction of topological quantum computation using Majorana modes. Then I will summarize the part of my current work that focuses on understanding the slew of experimental data resulting from our prediction and making new predictions to definitively establish topological superconductivity and Majorana modes. In addition I will describe my results on existing experiments on other potentially topological superconducting systems. Following this I will discuss aspects of realizing parafermions, which are a generalization of Majorana modes that have been suggested to arise at the interface of a fractional quantum Hall and superconducting systems. Finally, I will describe my most recent interest in the role of emergent gauge fields that arise in ultra-cold atomic versions of the Majorana systems. Here we found interesting examples of interaction driven transitions that have low energy excitations that are neither Lorentz or Galilean invariant.