Density wave orders and their interplay with superconductivity.
My work explores how symmetry breaking in quantum materials gives rise to new and often surprising electronic behaviors, particularly in connection with superconductivity. A major focus has been on charge, spin, and pair density wave (PDW) orders, phenomena that frequently appear in unconventional superconductors. To tackle these problems, I developed advanced hybrid momentum-real space techniques designed to capture the physics of periodic inhomogeneities.
In weakly correlated systems, I studied how superconductivity coexists with disordered charge density waves (CDW). I discovered that disorder fragments CDWs into distinct domains, creating domain walls where superconductivity emerges. Interestingly, in magnetic vortex cores, charge patterns replace the expected metallic state, which in turn helps protect superconductivity and allows it to survive under stronger magnetic fields. I also uncovered a new particle–hole proximity effect, where CDW correlations spread into otherwise metallic regions.
Moving into strongly correlated regimes, I led a detailed variational study of the t–J model, demonstrating that density wave states can energetically compete with uniform d-wave superconductivity. As doping increases, these density waves weaken, giving way to a nematic phase that breaks rotational—but not translational—symmetry. More recently, I used the composite operator method (COM) to identify CDWs in the doped Hubbard model, which arise from modulated half-filled Mott domains. To guide experiments, I also calculated distinct Josephson tunneling signatures that can differentiate between intertwined PDW states and coexisting superconducting and CDW phases.
Development of Real-Space Hubbard Operator Method
In my current postdoctoral position, I have worked independently with Ph.D. students Dr. Louis Haurie and Emile Pangburn, leading the implementation of the Hubbard operator method (HOM) in real space. This approach treats the interaction part of the Hamiltonian exactly, while incorporating kinetic (hopping) terms through the equation of motion framework. Our group is currently the only one capable of applying this method in real space, creating a unique opportunity to expand its applications.
After benchmarking the method against uniform systems, we applied it to the bilayer Hubbard model and uncovered spontaneous selective Mott insulating phases. In studies of doped single-layer Mott insulators, we observed that translation symmetry breaking and charge order naturally arise through the formation of local Mott regions. More recently, we investigated the role of impurities in doped Hubbard systems and found that the Friedel oscillation wavevector deviates from conventional predictions, providing clear evidence that Luttinger’s theorem is violated in the strongly correlated regime.
Superconductivity – effect of disorder, magnetic fields, and strong correlations.
Topological phases in strongly correlated Mott insulators.
Non-Fermi liquids and the strange metal phase.
Non-equilibrium dynamics in classical athermal systems.