Research

Excitations in strongly-correlated and exotic materials with time dependent density functional theory (TDDFT)

This project offers ab initio techniques based mostly on time dependent density functional theory (TDDFT) and many-body theory to understand and control quantum phenomena at the macroscopic level. The project targets mostly excitations in two-dimensional quantum materials such as HfTe2, Ta2NiSe5 and some others. These materials exhibit a broad variety of emergent quantum phenomena from ground to excited states. Harnessing and controlling the exotic physics of quantum materials for technological applications require state of the art theoretical modeling. But the complexity of these quantum phenomena calls for continuous development and improvement of theoretical models. Physical properties of quantum materials require highly accurate methods, often beyond ground state density functional theory (DFT). These materials provide an excellent platform to improve theory so that theoretical models become predictive enough for technological applications.

We particularly focus on excitonic insulators (EI). In EI materials, the exciton (bound electron-hole pair) binding energy exceeds the fundamental band gap, so that excitons are present even in the ground or lowest-energy state.  Electronic interactions lead to intriguing features in EIs like long-range coherence of excitons, analogous to coherence in superconductors. While it is known that the excitonic condensation leads to a broken-symmetry phase, the driving mechanism is often not well understood. To gain more information about the phase transitions we are performing a comprehensive exploration of the excitations and lattice dynamics.  

Over time, we aim to extend the impact of external control such as strain on EI phases, and explore the corresponding response in exciton binding energies, exciton dispersion, electron-phonon coupling and collective excitations such as plasmons. If feasible, a materials search for EIs will be undertaken.

Our methodology is largely based on TDDFT combined with the GW+BSE method. We are exploring model exchange-correlation kernels for collective excitation in model and real systems as well. Besides, dielectric-dependent hybrid functionals will be applied to electron-hole excitations and exciton binding energies and will be compared to GW+BSE results. 

Development and applications of meta generalized gradient (meta-GGA) approximations 

Density functional theory is very widely used in chemistry, physics, materials science and engineering, and even geology and pharmaceutical design. The five rungs of the ladder of approximations to the exact density functional for the exchange-correlation energy of a many-electron system provide a range of options for electronic structure calculations for molecules and materials, from the more affordable first three rungs (local spin density approximation or LSDA, generalized gradient approximation or GGA, and meta-GGA) to the more expensive but often more accurate fourth and fifth rungs (hybrids and self-interaction corrections that use the full non-interacting one-electron density matrix, and random phase approximation RPA-like functionals that employ even the unoccupied Kohn-Sham orbitals). The first two rungs have been widely explored, but the more numerous and complex ingredients of the third, fourth, and fifth rungs deserve and even demand further exploration. Recently our SCAN and r2SCAN meta-GGAs, based on exact constraints, appropriate norms, and a simple construction principle (smoothness), have been improved in unexpected ways by the LAK meta-GGA, which exploits an overlooked degree of freedom in the limit to which it interpolates for slowly varying densities. We are exploiting this degree of freedom in a different way in order to add the Laplacian of the density to the other meta-GGA ingredients: the local spin densities, their gradients, and the spin-resolved positive orbital kinetic energy densities. Alternative possibilities for meta-GGAs are also explored.