Final Report Summary - OPTCHATRA (Optical charge transfer processes in early stages of photosynthesis from first-principle computational techniques) The OptChaTra project aims at improving the theoretical tools of understanding the reaction of matter to light with et aim at contributing to the design of new materials with specific optical properties. In particular the out-of-equilibrium behaviour of materials under laser irradiation offers an exciting new avenue towards ultrafast manipulation of material properties with implications for fundamental physics. The standard model of particle physics predicts that elementary Fermions come as three different kinds: Dirac-, Weyl- and Majorana-Fermions. However, despite being predicted hundred years ago, so far of these three kinds of fundamental particles only Dirac-Fermions have been found in nature. That is, until recently when with the discovery of graphene, it was realized that the behaviour of relativistic free particles can be observed in the electronic properties of materials. This sparked the search for materials where these elementary particles can be observed and only recently the first materials hosting Weyl Fermions have been discovered. However, a material in equilibrium can only host one kind of these Fermions. In the OptChaTra project it was demonstrated how one can transform within one material the kind of Fermion by using tailored light pulses.The observation of Dirac Fermions in the properties of graphene has at its origin the complex interaction of the large number of electrons and ions that compose a material. Each single electron interacts with the ions and the other electrons via the Coulomb interaction, but the particular pattern of Carbon ions in the graphene honey-comb crystal structure has the effect that together this soup of individual particles behaves collectively as if there were a single massless and free Fermion, a Dirac Fermion. These collective behaviour of many particles forming a single, new particle with different properties, is called a quasi-particle. The hunt for other materials hosting such quasiparticles that haves like fundamental particles has thus focused on the crystal structure of materials. However, by applying a laser field to the material, it is also possible to combine the quasiparticle with the photons of the laser field to form together a new quasiparticle that again can behave fundamentally differently.It has been recently proposed, however, that by irradiating a material with a laser, it is also possible to combine a quasiparticle with the photons of the laser field to form a new quasiparticle that, again, can behave fundamentally differently. In particular, the coupling to photons can affect the topology of quasiparticles. Topology is a property of the particles that leads to peculiar properties, for example metallic chiral edge states that form a collisionless one-way quantum highway along the edge of a topological insulator. This chirality, or handedness, is topological in the sense that right-handed and left-handed chiralities are discrete states that cannot be continuously deformed into each other. The 2016 Nobel Prize in Physics will soon be awarded to Michael Kosterlitz, Duncan Haldane, and David Thouless for the discovery of such topological phases of matter. Dirac and Weyl fermions differ by their chirality. Just like our left and right hands, Weyl fermions occur in pairs, where one particle is a mirrored version of the other. The two partners are almost identical, yet they cannot be superimposed. Dirac fermions, by contrast, do not have this property.The approach investigated in the OptChaTra project is to create chirality in a material is to drive it with a laser beam. It was realized about ten years ago that the so-called Floquet theory − a theory for laser-driven systems that oscillate periodically in time − allows us to engineer parameters and symmetries in materials that can change their topology. Inducing chirality into a Dirac fermion material by combining those fermions with photons from the laser beam to form new quasiparticles can thus transform it into a Weyl fermion material. Initially, in line with the aim of the OptChaTra project at improving the computational tools for the description of optically excited charge transfer, the theoretical formulation used by state-of-the-art techniques for the simulation of electronic excitants have been reformulated. Based on a recently proposed method for a compact representation of the electronic orbitals and efficient scheme for the computation of the exact exchange operator has been implemented in the OCTOPUS code. This implementation is a stepping stone within the reformulated theory which relies on a localised orbital presentation of the electronic states. Based on this implementation an novel computational scheme for the evaluation of electronic screening has been derived and a prototype has been implemented for local orbital basis in the SIESTA code.Systematic testing of the prototype revealed that the scheme, while theoretically more efficient than the standard approach and most other available approaches, suffered from numerical convergence issues that lead to an overall decrease of performance. Estimation of the possible usefulness of a full implementation of this prototype into the OCTOPUS code, yielded that it is unlikely to result in a widely used technique.The project then refocussed on a different aspect of light matter interaction, namely the real-time electronic dynamics in laser driven bulk materials instead of bio-molecules. Specifically, the recently discovered 3D Dirac materials Na3Bi2, a three-dimensional analogue of graphene, can undergo drastic changes in its electronic structure when subjected to circularly polarised light and can undergo a topological phase transition. Building on the experience gained in the first half of the project, a module was implemented in the OCTOPUS code, that performs Floquet-analysis of the time-evolution. With this tool, it was possible to show that circularly laser-driven Na3Bi2 undergoes a non-equilibrium phases transition from Dirac- to Weyl-semimetal.This kind of phase transition is purely electronic and can be achieved in ultrafast time-scales, allowing for a femto-second control of materials properties. Such a design of non-equilibrium phases of material with fundamentally changed properties can have important implications for electronics applications. The results of this project are a major advance in the field of topological materials and a manuscript describing them has been accepted for publication in Nature Communications.
