Showed how Wannier functions of electrons in 1-dimensional crystal are eigenfunctions of non-Abelian Berry phase matrices. These quantities are now used in analysis of topological insulators.
Developed the formalism of phonon Wannier functions for construction of model Hamiltonian of structural phase transitions in crystals. This has been demonstrated in ferroelectrics, shape memory alloys and multiferroics.
Developed a “polarization-stat” which can be used within molecular dynamics and thermodynamic integration to obtain free energies and Landau theory of ferroelectrics.
Contributed to generalization of the technique to model site occupancy disorder in crystals to grand-canonical ensembles.
Developed mixed-space molecular dynamics for efficient simulations of model hamiltonians of ferroelectrics (contributed to release of free software FERAM).