arXiv subjects

Jörg Main

Publications and source records attributed to Jörg Main.

At least 19 recordsLinked to original sources

arXiv2026

Impact of the valence band on Rydberg excitons in cuprous oxide quantum wells

The complex valence band structure of bulk cuprous oxide necessitates going beyond the parabolic approximation to precisely estimate exciton binding energies. The same is true for excitons in cuprous oxide quantum wells, for which many effects have been obtained so far only qualitatively within a hydrogenlike two-band model. Here, we derive the complete Hamiltonian for excitons in cuprous oxide quantum wells based on the Luttinger-Kohn model, taking into account the full complex valence band structure. Symmetry properties of the system are discussed. Numerical results based on the diagonalization of the Hamiltonian using B-spline functions reveal the energy shifts and the lifting of degeneracies due to the nondiagonal coupling terms of the complex valence band. The relative oscillator strengths of the excitonic transitions induced by circularly polarized light are also calculated.

cond-mat.mes-hall↗

arXiv2025

Wavefunctions and oscillator strengths of Rydberg excitons in cuprous oxide quantum wells

We investigate the eigenstates, that is, the wavefunctions of Rydberg excitons in cuprous oxide quantum wells and derive expressions relating them to the oscillator strengths of different exciton states. Using the B-spline expansion, we compute the wavefunctions in coordinate space and estimate the oscillator strengths. The symmetry properties of the states and the non-separability of the wavefunctions are illustrated. Wavefunctions associated with resonances above the scattering threshold, in particular those of bound states in the continuum as well as their partner states, are also given.

cond-mat.mes-hall↗

arXiv2025

Quantum defects of Rydberg excitons in cuprous oxide: A semiclassical spherical model

Excitons, i.e. the bound states of an electron and a positively charged hole are the solid state analogue of the hydrogen atom. As such they exhibit a Rydberg series, which in cuprous oxide has been observed up to high principal quantum numbers by T. Kazimierczuk et al. [Nature 514, 343 (2014)]. In this energy regime the quantum mechanical properties of the system can be understood in terms of classical orbits by the application of semiclassical techniques. In fact the first theoretical explanation of the spectrum of the hydrogen atom within Bohr's atomic model was a semiclassical one using classical orbits and a quantization condition for the angular momentum. Contrary to the hydrogen atom, the degeneracy of states with the same principal quantum number $n$ is lifted in exciton spectra. This is similar to the situation in alkali atoms, where these splittings are caused by the interaction of the excited electron with the ionic core. For excitons in cuprous oxide, these splittings occur due to the influence of the complex band structure of the crystal. Using an adiabatic approach and analytically derived energy surfaces, we develop a semiclassical spherical model and determine, via semiclassical torus quantization, the quantum defects of various angular momentum states.

cond-mat.mes-hall↗

arXiv2025

Bound states in the continuum in cuprous oxide quantum wells

We propose a realistic semiconductor system containing bound states in the continuum (BICs) which allows for a practical realization. By varying the confinement strength of excitons in cuprous oxide quantum wells, we show that long-lived Rydberg states of the confined electron-hole pairs appear in the continuum background. The accuracy of calculations of the linewidths based on the coupled-channel Schrödinger equation with three channels and only few basis states is confirmed by a numerically exact solution employing a B-spline basis and the complex coordinate-rotation method. We argue that finite-sized cuprous oxide crystals, due to their large exciton binding energies, are a convenient platform for experimental identification of BICs.

cond-mat.mes-hall↗

arXiv2024

Rydberg excitons in cuprous oxide: A two-particle system with classical chaos

When an electron in a semiconductor gets excited to the conduction band the missing electron can be viewed as a positively charged particle, the hole. Due to the Coulomb interaction electrons and holes can form a hydrogen-like bound state called exciton. For cuprous oxide a Rydberg series up to high principle quantum numbers has been observed by Kazimierczuk et al. [Nature 514, 343 (2014)] with the extension of excitons up to the $μ$m-range. In this region the correspondence principle should hold and quantum mechanics turn into classical dynamics. Due to the complex valence band structure of Cu$_2$O the classical dynamics deviates from a purely hydrogen-like behavior. The uppermost valence band in cuprous oxide splits into various bands resulting in a yellow and green exciton series. Since the system exhibits no spherical symmetry, the angular momentum is not conserved. Thus, the classical dynamics becomes non-integrable, resulting in the possibility of chaotic motion. Here we investigate the classical dynamics of the yellow and green exciton series in cuprous oxide for two-dimensional orbits in the symmetry planes as well as fully three-dimensional orbits. The analysis reveals substantial differences between the dynamics of the yellow and green exciton series. While it is mostly regular for the yellow series large regions in phase space with classical chaos do exist for the green exciton series.

cond-mat.mes-hall↗

arXiv2024

Energy states of Rydberg excitons in finite crystals: From weak to strong confinement

Due to quantum confinement, excitons in finite-sized crystals behave rather differently than in bulk materials. We investigate the dependence of energies of Rydberg excitons on the strengths of parabolic as well as rectangular confinement potentials in finite-sized crystals. The evolution of the energy levels of hydrogen-like excitons in the crossover region from weak to strong parabolic confinement is analyzed for different quantum numbers by numerical solution of the two-dimensional Schrödinger equation. The energy spectrum of hydrogen-like excitons in Cu$_{2}$O-based rectangular quantum wells is, in turn, obtained numerically from the solution of the three-dimensional Schrödinger equation as a function of the quantum well width. Various crossings and avoided crossings of Rydberg energy levels are observed and categorized based on the symmetry properties of the exciton wave function. Particular attention is paid to the two limiting cases of narrow and wide quantum wells attributed to strong and weak confinement, respectively. The energies obtained with the pure Coulomb interaction are compared with the results originating from the Rytova-Keldysh potential, i.e., by taking into account the dielectric contrast in the quantum well and in the barrier.

cond-mat.mes-hall↗

arXiv2024

Resonance energies and linewidths of Rydberg excitons in Cu$_2$O quantum wells

Rydberg excitons are the solid-state analog of Rydberg atoms and can, e.g., for cuprous oxide, easily reach a large size in the region of $μ$m for principal quantum numbers up to $n=25$. The fabrication of quantum well-like structures in the crystal leads to quantum confinement effects and opens the possibility to study a crossover from three-dimensional to two-dimensional excitons. For small widths of the quantum well (QW) there are several well separated Rydberg series between various scattering thresholds leading to the occurrence of electron-hole resonances with finite lifetimes above the lowest threshold. By application of the stabilization method to the parametric dependencies of the real-valued eigenvalues of the original three-dimensional Schrödinger equation we calculate the resonance energies and linewidths for Rydberg excitons in QWs in regimes where a perturbative treatment is impossible. The positions and finite linewidths of resonances at energies above the third threshold are compared with the complex resonance energies obtained within the framework of the complex-coordinate-rotation technique. The excellent agreement between the results demonstrates the validity of both methods for intermediate sizes of the QW-like structures, and thus for arbitrary widths.

cond-mat.mes-hall↗

arXiv2024

Classical dynamics and semiclassical analysis of excitons in cuprous oxide

Excitons, as bound states of electrons and holes, embody the solid state analogue of the hydrogen atom, whose quantum spectrum is explained within a classical framework by the Bohr-Sommerfeld atomic model. In a first hydrogenlike approximation the spectra of excitons are also well described by a Rydberg series, however, due to the surrounding crystal environment deviations from this series can be observed. A theoretical treatment of excitons in cuprous oxide needs to include the band structure of the crystal, leading to a prominent fine-structure splitting in the quantum spectra. This is achieved by introducing additional spin degrees of freedom into the system, making the existence and meaningfulness of classical exciton orbits in the physical system a non-trivial question. Recently, we have uncovered the contributions of periodic exciton orbits directly in the quantum mechanical recurrence spectra of cuprous oxide [J. Ertl et al., Phys. Rev. Lett. 129, 067401 (2022)] by application of a scaling technique and fixing the energy of the classical dynamics to a value corresponding to a principle quantum number $n=5$ in the hydrogenlike case. Here, we present a comprehensive derivation of the classical and semiclassical theory of excitons in cuprous oxide. In particular, we investigate the energy dependence of the exciton dynamics. Both the semiclassical and quantum mechanical recurrence spectra exhibit stronger deviations from the hydrogenlike behavior with decreasing energy, which is related to a growing influence of the spin-orbit coupling and thus a higher velocity of the secular motion of the exciton orbits. The excellent agreement between semiclassical and quantum mechanical exciton recurrence spectra demonstrates the validity of the classical and semiclassical approach to excitons in cuprous oxide.

cond-mat.mes-hall↗

arXiv2024

Gaussian-process-regression-based method for the localization of exceptional points in complex resonance spectra

Resonances in open quantum systems depending on at least two controllable parameters can show the phenomenon of exceptional points (EPs), where not only the eigenvalues but also the eigenvectors of two or more resonances coalesce. Their exact localization in the parameter space is challenging, in particular in systems, where the computation of the quantum spectra and resonances is numerically very expensive. We introduce an efficient machine learning algorithm to find exceptional points based on Gaussian process regression (GPR). The GPR-model is trained with an initial set of eigenvalue pairs belonging to an EP and used for a first estimation of the EP position via a numerically cheap root search. The estimate is then improved iteratively by adding selected exact eigenvalue pairs as training points to the GPR-model. The GPR-based method is developed and tested on a simple low-dimensional matrix model and then applied to a challenging real physical system, viz., the localization of EPs in the resonance spectra of excitons in cuprous oxide in external electric and magnetic fields. The precise computation of EPs, by taking into account the complete valence band structure and central-cell corrections of the crystal, can be the basis for the experimental observation of EPs in this system.

quant-ph↗

arXiv2022

Transition state theory characterizes thin film macrospin dynamics driven by an oscillatory magnetic field: Inertial effects

Understanding the magnetization switching process in ferromagnetic thin films is essential for many technological applications. We investigate the effects of periodic driving via magnetic fields on a macrospin system under explicit consideration of inertial dynamics. This is usually achieved by extending the Landau-Lifshitz-Gilbert equation with a term including the second time derivative of the magnetization. The dynamics of the magnetization switching can then be characterized by its switching rate. We apply methods from transition state theory for driven systems to resolve the rate of magnetization switching in this general case. In doing so, we find that magnetization exhibits resonance-like behavior under certain driving conditions, and it can be affected strongly by the system's relaxation rate.

cond-mat.mtrl-sci↗

arXiv2022

Signatures of exciton orbits in quantum mechanical recurrence spectra of Cu$_2$O

The seminal work by T. Kazimierczuk et al. [Nature 514, 343 (2014)] has shown the existence of highly excited exciton states in a regime, where the correspondence principle is applicable and quantum mechanics turns into classical mechanics, however, any interpretation of exciton spectra based on a classical approach to excitons is still missing. Here, we close this gap by computing and comparing quantum mechanical and semiclassical recurrence spectra of cuprous oxide. We show that the quantum mechanical recurrence spectra exhibit peaks, which, by application of semiclassical theories and a scaling transformation, can be directly related to classical periodic exciton orbits. The application of semiclassical theories to exciton physics requires the detailed analysis of the classical exciton dynamics, including three-dimensional orbits, which strongly deviate from hydrogenlike Keplerian orbits. Our findings illuminate important aspects of excitons in semiconductors by directly relating the quantum mechanical band-structure splittings of excitons to the corresponding classical exciton dynamics.

cond-mat.mes-hall↗

arXiv2022

Mean first-passage times for solvated LiCN isomerization at intermediate to high temperatures

The behavior of a particle in a solvent has been framed using stochastic dynamics since the early theory of Kramers. A particle in a chemical reaction reacts slower in a diluted solvent because of the lack of energy transfer via collisions. The flux-over-population reaction rate constant rises with increasing density before falling again for very dense solvents. This Kramers turnover is observed in this paper at intermediate and high temperatures in the backward reaction of the LiNC $\rightleftharpoons$ LiCN isomerization via Langevin dynamics and mean first-passage times (MFPTs). It is in good agreement with the Pollak-Grabert-Hänggi (PGH) reaction rates at lower temperatures. Furthermore, we find a square root behavior of the reaction rate at high temperatures and have made direct comparisons of the methods in the intermediate- and high- temperature regimes; all suggesting increased ranges in accuracy of both the PGH and MFPT approaches.

physics.chem-ph↗

arXiv2021

On the stability of satellites at unstable libration points of sun-planet-moon systems

The five libration points of a sun-planet system are stable or unstable fixed positions at which satellites or asteroids can remain fixed relative to the two orbiting bodies. A moon orbiting around the planet causes a time-dependent perturbation on the system. Here, we address the sense in which invariant structure remains. We employ a transition state theory developed previously for periodically driven systems with a rank-1 saddle in the context of chemical reactions. We find that a satellite can be parked on a so-called time-periodic transition state trajectory -- which is an orbit restricted to the vicinity of the libration point L2 for infinitely long time -- and investigate the stability properties of that orbit.

astro-ph.EP↗

arXiv2021

Transition state dynamics of a driven magnetic free layer

Magnetization switching in ferromagnetic structures is an important process for technical applications such as data storage in spintronics, and therefore the determination of the corresponding switching rates becomes essential. We investigate a free-layer system in an oscillating external magnetic field resulting in an additional torque on the spin. The magnetization dynamics including inertial damping can be described by the phenomenological Gilbert equation. The magnetization switching between the two stable orientations on the sphere then requires the crossing of a potential region characterized by a moving rank-1 saddle. We adopt and apply recent extensions of transition state theory for driven systems to compute both the time-dependent and average switching rates of the activated spin system in the saddle region.

cond-mat.mtrl-sci↗

arXiv2021

Controlling reaction dynamics in chemical model systems through external driving

The rate of a chemical reaction can often be determined by the properties of a rank-1 saddle and the associated transition state separating reactants and products. We have found evidence that such rates can be controlled and even enhanced by external driving in at least one such system. Specifically, we analyze a reactive model in two degrees of freedom that has been used earlier to describe driven chemical reactions. Therein, changes in the external driving can lead to a local maximum of the decay rate constant or even to bifurcations of periodic trajectories on the normally hyperbolic invariant manifold (NHIM) corresponding to the transition state. Inspired by these bifurcations, we show that in this case, the dynamics on the NHIM can be connected to the geometry of reactive trajectories and to reaction probabilities of Maxwell-Boltzmann distributed reactant ensembles.

physics.chem-ph↗

arXiv2021

Interseries dipole transitions from yellow to green excitons in cuprous oxide

We study dipole interseries transitions between the yellow and green exciton series in cuprous oxide including the complex valence band structure. To this end, we extend previous studies of the spectrum of complex green exciton resonances [Phys. Rev. B 101, 075208 (2020)] to optical transitions between different exciton states in addition to transitions from the crystal ground state. This allows us to augment the calculations on interseries transitions using a hydrogen-like model [Phys. Rev. B 100, 085201 (2019)] by a more comprehensive treatment of the valence band structure.

cond-mat.mes-hall↗

arXiv2021

Dynamics and decay rates of a time-dependent two-saddle system

The framework of transition state theory (TST) provides a powerful way for analyzing the dynamics of physical and chemical reactions. While TST has already been successfully used to obtain reaction rates for systems with a single time-dependent saddle point, multiple driven saddles have proven challenging because of their fractal-like phase space structure. This paper presents the construction of an approximately recrossing-free dividing surface based on the normally hyperbolic invariant manifold in a time-dependent two-saddle model system. Based on this, multiple methods for obtaining instantaneous (time-resolved) decay rates of the underlying activated complex are presented and their results discussed.

physics.chem-ph↗

arXiv2021

Exchange interaction in the yellow exciton series of cuprous oxide

We experimentally and numerically investigate the exchange interaction of the yellow excitons in cuprous oxide. By varying the material parameters in the numerical calculations, we can interpret experimental findings and understand their origin in the complex band structure and central-cell corrections. In particular, we experimentally observe the reversal of the ortho- and paraexciton for the $2S$ yellow exciton, and explain this phenomenon by an avoided crossing with the green $1S$ orthoexciton in a detailed numerical analysis. Furthermore, we discuss the exchange splitting as a function of the principal quantum number $n$ and its deviation from the $n^{-3}$ behavior expected from a hydrogenlike model. We also explain why the observed exchange splitting of the green $1S$ exciton is more than twice the splitting of the yellow $1S$ state.

cond-mat.mtrl-sci↗