Reorganization of Edge Modes: Quantum Phase Transitions and Textures

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Notwithstanding earlier attempts at describing quantum phase transitions on the edge of quantum Hall systems, our proposed project opens new horizons. The proposal represents two main thrusts: 1. On the one hand, novel classes of naturally occurring (or induced) quantum phase transitions (QPTs) on the edge (e.g., spin switching transitions; spontaneous time reversal symmetry breaking). Why is this important? Beyond the basic physics importance of discovering and analyzing new classes of phase transitions in topological systems, the latter have implications on charge and spin transport through such setups. Moreover, the fact that spontaneous breakdown of time reversal symmetry may take place in otherwise time reversal invariant systems, may imply that renewed attention should be given to “topological protection” (e.g., in TRI topological insulators), necessary for quantum computation. 2. On the other hand, the physics of artificially engineered chiral and helical edges. Very recent experiments by the Heiblum group (the first batch of which has just been posted, see Y. Ronen et al., arXiv:1709.03976 (2017)), herald a new era: one can design a composite edge (made up of multiple chiral modes) both in the integer and the fractional regimes at will. Why is this important? One may then control the interaction and tunneling between edge chiral modes, and the spin content of each mode, tremendously enriching the scope of relevant one-dimensional problems to be studied. One can possibly entertain the idea of controlled interferometers, overcoming the evading physics of anyonic interferometry. Furthermore, the road to an on-demand large variety of (integer and fractional) topological insulators now seems to be open. The tools needed to attack these problems include field theoretical methods, analysis of symmetry breaking patterns, the theory of non-equilibrium quantum systems. The two PIs are well acquainted with these tools due to their previous experience in the fields of quantum Hall and topological insulator physics, with impactful achievements that include: the development and applications of non-equilibrium bosonization; the prediction of spontaneous time-reversal symmetry breaking in topological insulators, the first predictions of fractional statistics through Mach-Zender interferometry; the first analysis of fractional Aharonov-Bohm oscillations due to anyonic physics, including the analysis of interaction effects in Fabry-Perot interferometers. The two PIs have a long history of collaboration that results in several common publications. Their collaboration has included numerous mutual visits, and exchange of young members of their teams.