Solving the time-dependent Schrödinger equation using complex-coordinate contours

Theory of electronic resonances: fundamental aspects and recent advances

Electronic resonances are states that are unstable towards loss of electrons. They play critical roles in high-energy environments across chemistry, physics, and biology but are also relevant to processes under ambient conditions that involve unbound electrons. This feature article focuses on complex-variable techniques such as complex scaling and complex absorbing potentials that afford a treatment of electronic resonances in terms of discrete square-integrable eigenstates of non-Hermitian Hamiltonians with complex energy. Fundamental aspects of these techniques as well as their integration into molecular electronic-structure theory are discussed and an overview of some recent developments is given: analytic gradient theory for electronic resonances, the application of rank-reduction techniques and quantum embedding to them, as well as approaches for evaluating partial decay widths.

Interlayer excitons in van der Waals heterostructures: Binding energy, Stark shift, and field-induced dissociation

Photoexcited intralayer excitons in van der Waals heterostructures (vdWHs) with type-II band alignment have been observed to tunnel into interlayer excitons on ultrafast timescales. Such interlayer excitons have sufficiently long lifetimes that inducing dissociation with external in-plane electric fields becomes an attractive option of improving efficiency of photocurrent devices. In the present paper, we calculate interlayer exciton binding energies, Stark shifts, and dissociation rates for six different transition metal dichalcogenide (TMD) vdWHs using a numerical procedure based on exterior complex scaling (ECS). We utilize an analytical bilayer Keldysh potential describing the interaction between the electron-hole pair, and validate its accuracy by comparing to the full multilayer Poisson equation. Based on this model, we obtain an analytical weak-field expression for the exciton dissociation rate. The heterostructures analysed are MoS₂/MoSe₂, MoS₂/WS₂, MoS₂/WSe₂, MoSe₂/WSe₂, WS₂/MoSe₂, and WS₂/WSe₂ in various dielectric environments. For weak electric fields, we find that WS₂/WSe₂ supports the fastest dissociation rates among the six structures. We, furthermore, observe that exciton dissociation rates in vdWHs are significantly larger than in their monolayer counterparts.

Dynamical Processes in Open Quantum Systems from a TDDFT Perspective: Resonances and Electron Photoemission

We present a review of different computational methods to describe time-dependent phenomena in open quantum systems and their extension to a density-functional framework. We focus the discussion on electron emission processes in atoms and molecules addressing excited-state lifetimes and dissipative processes. Initially we analyze the concept of an electronic resonance, a central concept in spectroscopy associated with a metastable state from which an electron eventually escapes (electronic lifetime). Resonances play a fundamental role in many time-dependent molecular phenomena but can be rationalized from a time-independent context in terms of scattering states. We introduce the method of complex scaling, which is used to capture resonant states as localized states in the spirit of usual bound-state methods, and work on its extension to static and time-dependent density-functional theory. In a time-dependent setting, complex scaling can be used to describe excitations in the continuum as well as wave packet dynamics leading to electron emission. This process can also be treated by using open boundary conditions which allow time-dependent simulations of emission processes without artificial reflections at the boundaries (i.e., borders of the simulation box). We compare in detail different schemes to implement open boundaries, namely transparent boundaries using Green functions, and absorbing boundaries in the form of complex absorbing potentials and mask functions. The last two are regularly used together with time-dependent density-functional theory to describe the electron emission dynamics of atoms and molecules. Finally, we discuss approaches to the calculation of energy and angle-resolved time-dependent pump-probe photoelectron spectroscopy of molecular systems.

Simulation of sub-femtosecond response in laser-assisted field emission

Numerical methods are used to simulate the response of field emission to incident pulses of optical radiation, with the objective of determining the criteria to reduce the time for response of the emitted current to the radiation. The results of these simulations suggest that a sub-femtosecond response may be achieved by increasing the power flux density of the radiation, and decreasing the applied static field. An intrinsic delay in the response is shown to correspond to the semiclassical time for traversal of the barrier by quantum tunneling.