Topological Phases

1. Topological phases and fractionalization in one-dimensional systemsSmitha Vishveshwara, University Illinois Urbana-Champaign, DMR 0644022 • Topological Phases • Studied spin ladders and superconductors for hosting ‘topological phases’ that have exotic (Majorana fermion) bound states at the ends • Found that applying potentials that are periodic, quasiperiodic, or disordered give rise to rich topological phase diagrams • Charge fractionalization in rings • Found that ring geometries are well suited to explore splintering of electron due to interactions. Predict clear signatures in magnetic field profile. • Findings contribute to strongly correlated physics, nanoscience and potentially topological quantum computation. Can be directly tested by experiments Spin ladder systems and superconducting wires in periodic potentials: host new topological regions Hofstadter butterfly pattern for normal systems in quasiperiodic potentials (left panel) mirrored in superconducting topological phases (grey, right panel) Geometry to measure charge fractionalization in ring geometries

2. Topological phases and fractionalization in one-dimensional systemsSmithaVishveshwara, University Illinois Urbana-Champaign, DMR 0644022 International collaboration at Indian Institute of Science (IISc), Bangalore, India Prof. Diptiman Sen Collaborator at IISc • BROADER IMPACTS • International collaboration at IISc, a premier Indian institute, leading to liaisons with physics dept., graduate student exchange, and several papers • Development of special topics graduate course largely based on research from this grant • Fostering Women in Physics ventures on several fronts • Mentoring of undergraduates DeGottardi, Graduate Student of PI Visited IISc – training, collaboration PI discusses with undergraduates