Out-of-equilibrium dynamics in real band structures - Wadgaonkar, Indrajit Pradeepchandra (Nanyang Technological University, 2023)
In recent times the ability to investigate timescales during which materials perform out-of- equilibrium dynamics has led to the realisation that several new effects arise from the complex interplay of excited quasiparticles. It becomes hence necessary to describe all the elements participating into out-of-equilibrium dynamics within the same approach to be able to model properly a number of emergent processes. Such a task however faces severe bottlenecks. A full quantum mechanical analysis which involves the description of the electronic and phononic degrees of freedom and the interaction with electromagnetic fields, over extended and possibly heterogeneous systems, is inherently too complex to be feasible. The full Time Dependent Boltzmann Equation (TDBE) seems to be the only feasible way to treat the full complexity of out-of-equilibrium dynamics involving heterogeneous systems and several quasiparticles. However, in spite of being a lot cheaper than a full quantum mechanical analysis, the TDBE still faces a steep challenge due to the presence of its scattering integral term which has an impractical scaling with precision. The usual approximations to this collision integral term circumvent this issue by reducing the order of the term (usually to linear or to at most quadratic order) but also brutally limit the application of the TDBE to regimes which are either relatively close to equilibrium or which impose the presence of thermal baths. This often overshadows the proper description of energy transfer through subsystems. Recently a novel solver has been developed for the numerical solution of the full scattering integral term of TDBE, which is free of approximations like linearisation of the scattering operator or close-to-equilibrium regime and which can work with arbitrary dispersions with a full account of the Pauli factors. In this thesis, I present two major modifications to this solver. First, I extend the formulation of the solver to achieve a higher order momentum space convergence by using second degree basis functions. I demonstrate the application of the improved solver to a test 2D material which is analogous to doped graphene. Next, I present a customisation of an adaptive time stepping algorithm, Dormand Prince 853, to suit our solver. The inclusion of an adaptive time stepping routine in the solver prevents intrinsic instabilities in the time propagation of the Boltzmann scattering operator and makes the solver efficient, robust, stable and minimally dependent on human supervision. I present comparison between the time propagation of an initial excitation in (6,5) carbon nanotubes (CNT), with both routines: standard Runge Kutta-4 (RK4) and our customised adaptive time stepping routine and I show conclusively that our routine outperforms RK4 on all criteria viz. accuracy, wall time and stability. Next, I present the application of our solver to unravel the thermalization pathways in ferroelectric Rashba semiconductor, α-GeTe which is an emerging ferroelectric low band gap semiconductor with a giant Rashba parameter. This unique combination of properties make it an ideal candidate for future spintronics device developments. A recent experimental study on this material displayed a counter-intuitive temperature dependence of the ultrafast thermalisation dynamics. The thermalisation could be split into three sub-timescales: electronic intraband, electronic interband and electron-phonon thermalisation. Interestingly, while the latter showed an expected increase in dynamics with temperature, the second timescale instead, counter-intuitively, showed a slowing down of dynamics with increasing temperature. Using our improved solver we were able to conclusively explain this anomalous behaviour and pinpoint it to electron-electron scattering channels with the largest phase space. This segregation of the scattering channels to unravel the emergent thermalisation characteristics truly showcases our solver's ability to decipher real materials of interest. Finally, I present results of our recent work on decoding spin relaxation mechanisms in caesium lead bromide perovskites. The unique exciton fine structure splitting in caesium lead bromide perovskites is responsible for a robust spin coherence, evident through quantum beating, even at high temperatures. Coherent optical control of exciton spins is critical for future quantum information applications and hence understanding the underlying spin physics in these materials becomes important. Using Monte Carlo simulations we were able to quantitatively reproduce the evolution of magnetisation which is driven by two competing types of spin dynamics. We found an excellent agreement between the oscillation frequency of the observed quantum beating and the fine structure splitting energies. The oscillation frequencies were found to be independent of temperature but they varied with the nanocrystal size. We also identify the temperature resolved regimes of dominant spin relaxation mechanisms. These findings establish the robust nature of the observed quantum beating and pave way for engineering size dependent coherent spin dynamics in future quantum information devices.