Our laboratory’s main theme is the first-principles quantum mechanical calculations of light-matter interactions or full ab initio description of materials’ quantum states under a strong or weak light field. To materialize this vision, we have worked on the electron-correlation part of the time-dependent density functional theory (DFT) and explored the limitation and capability of DFT-based methods.
Since Schrödinger’s and Dirac’s formulation of quantum mechanics at around the late 1920s, diverse branches of theories have developed to deal with quantum mechanics of condensed matters in a way as ab initio as possible. The relativistic or non-relativistic Hamiltonian consists of two-body interactions of every pair of many bodies, which gives rise to enormous complexity in the ab initio treatment. One of the most common approaches is the density functional theory (DFT), in which an effective one-body Hamiltonian is solved self-consistently, and various hierarchical treatments have been introduced to overcome the limitations of such an effective one-body theory. While these methods have been remarkably successful for the ground state or the excited state within the linear response regime, the ab initio description for the non-linear regime of the excited state has remained challenging. On the other hand, the experimental side’s community is rapidly growing toward non-equilibrium or transient phenomena, mainly through the femtosecond pump and probe techniques. Such measurements include perturbations, such as photons or electrons colliding with a condensed matter, and the transient phenomena at the boundary of static phases of multiferroic structures. In this perspective, the extension of the ab initio theory framework into a time-dependent regime is essential, and such a method is required to account for the correlation and phase switching between variously ordered states of a solid.
To respond to this requirement of scientific communities, we developed the package of real-time time-dependent density functional theory (rt-TDDFT), in which the Kohn-Sham orbitals evolve along with the self-consistent evolution of density and Hamiltonian. As stated above, we are mostly concerned with DFT limitation, particularly the overestimation of long-range charge transfer and underestimation of the fundamental bandgap. There have been several suggestions to mitigate the limitation of continuous functional approximation of DFT. For example, the method of restoring derivative discontinuities by using perturbative approaches or implementing the orbital-dependent potentials, such as LDA-SIC and hybrid functionals. In our developments, we choose to combine the Hubbard U potential with the rt-TDDFT. To construct the time-propagating operator, the nonlocal Hubbard U potential was implemented as a split exponential form, as suggested by Suzuki and Trotter (ST), or using an inversion scheme through the Crank–Nicholson (CN) algorithm. All the implementation details were published in JCTC (2016), Nature Communications (2018, 2019), PNAS (2019).
Through these developments, we are now able to calculate the electron-phonon coupled dynamics in a strong spin-orbit coupled system. One of the best examples is the spin-phonon-valley dynamics in two-dimensional transition metal dichalcogenides (Nat. Comm. (2018, 2019)). Among the structures of two-dimensionally layered transition metal dichalcogenides, the monolayer MoS2 has been mostly investigated in terms of the coupling between magnetization and the momentum vector, so-called spin-valley coupling. The valence band maximum (VBM) on those valleys reveals a quite sizable splitting between spin-up and spin-down state, while those of conduction band minima (CBM) are almost degenerate. Owing to this spin-valley coupled VBM structure, the circularly polarized photons matched with the bandgap can excite electrons only at a particular valley. The pump-probe measurements have been performed on the valley-selective excited state, and it was reported that the electron spin relaxation is far faster than the valley relaxation. This indicates that the spin-valley polarized state in MoS2 is vulnerable to an easier spin relaxation, which is likely to be decoupled from inter-valley scattering. In our work, we studied ultrafast spin relaxation of electron valley in monolayer MoS2 through density functional theory (DFT) and real-time propagation time-dependent density functional theory (rtp-TDDFT) calculations. Very interestingly, we found that the spin-precession is delicately coupled with the lowest-lying optical phonon. Based on this result, we can suggest that the ultrafast spin relaxation mechanism of CBM valley comes from the correlation between non-collinear spin state and mirror-asymmetric optical phonon.