Works on a range of problems within the field of theoretical condensed matter physics. Among those are problems related to topological phases of quantum matter, including the study of materials such as topological insulators, metals, and superconductors, the application and development of topological band theory, and strongly correlated phases such as the fractional quantum Hall effect. In addition, Dr. Ilan is interested in mesoscopic systems and devices and specializes in quantum transport phenomena, and studies novel metamaterials that realize topological phenomena in (semi) classical settings.
Research achievements include: the prediction of robust transport signatures of topological superconductivity in topological insulator nanowires. The prediction for the emergence of axial fields in Weyl semimetals under deformations and inhomogeneous conditions recently corroborated in experiments carried out on acoustic metamaterials.
Future directions include: studying high energy analogs in topological metals; designing systems with large Berry curvatures and anomalous transport, and studying topology and correlated states in twisted bi-layer systems; exploring novel systems with topological superconductivity and their probes; studying topology in non-Hermitian systems.