Layered antiferromagnetic semiconductors combine electronic correlations with pronounced metal-ligand hybridization, but how these competing interactions hierarchically shape their electronic structure remains largely unexplored. Here, we resolve the orbital-selective electronic structure of the van der Waals antiferromagnet chromium thiophosphate (CrPS4) using angle-resolved photoemission spectroscopy above and below its Néel temperature, complemented by density functional theory (DFT)+U calculations. We identify a clear orbital separation within the Cr 3d states: weakly hybridized, spin-polarized t2g states that stabilize robust local magnetism and strongly hybridized eg-ligand states forming bonding-antibonding pairs that govern covalency and optical activity. Systematic variation of U shows that the t2g-derived states are markedly correlation sensitive, whereas the nominally unoccupied eg-ligand manifold, populated partially via hybridization, remains comparatively U insensitive. This orbital-selective response unveils distinct control parameters within a single d shell and suggests promising pathways to tune magnetic and optical functionalities independently via external control of correlation strength and metal-ligand coupling.

Excitations between localized 3d states of transition metal ions within crystalline solids, commonly known as d-d transitions, play a pivotal role in diverse phenomena across solid-state physics, materials science, and chemistry. Until now, an experimental method to unravel the complex quasiparticle dynamics associated with d-d transitions has remained elusive. In this study, we bridge this gap by demonstrating that d-d transitions can be distinctly traced both in momentum space and in time using time- and angle-resolved photoelectron spectroscopy (trARPES). As a model system, we select FePS3, a two-dimensional van der Waals antiferromagnet with a rich array of quantum phenomena stemming from d-d transitions. Our investigation reveals the ultrafast dynamics of both a spin-allowed (5T2g → 5Eg) and a spin-forbidden (5T2g → 3T1g) d-d transition within the Fe2+ multiplet. We observe that for off-resonant excitation, the spin-allowed excitation exhibits a quicker buildup compared to the spin-forbidden transition, and it decays with a single exponential behavior over a timescale of 83 fs. For the spin-forbidden transition, we identify two independent decay channels with decay constants of 46 and 1,273 fs that we attribute to an exchange-mediated virtual hopping between neighboring Fe2+ ions and an on-site spin-orbit-mediated spin-flip process, respectively.

Chromium thiophosphate (CrPS_4) is a layered two-dimensional antiferromagnetic semiconductor exhibiting intriguing spintronic and magneto-optical properties, yet its electronic band structure has remained experimentally uncharacterized. Here, we employ momentum-resolved photoemission spectroscopy above and below the Néel temperature, complemented by density functional theory with Hubbard U corrections (DFT+U), to reveal a valence band dominated by Cr 3d and S 3p states with a ligand-to-metal charge-transfer band gap. We identify weakly hybridized t_2g orbitals responsible for magnetic ordering and strongly hybridized e_g orbitals that relax dipole selection rules, enabling optically active orbital transitions. These findings establish a foundational understanding of CrPS_4's electronic structure, providing a benchmark for theoretical models and informing future investigations into its orbital physics and potential device applications.

In this paper we consider a multi band extension to the periodic Anderson model. We use a single site DMFT(NRG) in order to study the impact of the conduction band mediated effective hopping of the correlated electrons between the correlated orbitals onto the heavy Fermi liquid formation. Whereas the hybridization of a single impurity model with two distinct conduction bands always adds up constructively, $T_{K}\propto \exp(-\mathrm{const}\, U/(\Gamma_1+\Gamma_2))$, we show that this does not have to be the case in lattice models, where, in remarkable contrast, also an low-energy Fermi liquid scale $T_0\propto \exp(-\mathrm{const}\, U/(\Gamma_1-\Gamma_2))$ can emerge due to quantum interference effects in multi band models, where $U$ denotes the local Coulomb matrix element of the correlated orbitals and $\Gamma_i$ the local hybridization strength of band $i$. At high symmetry points, heavy Fermi liquid formation is suppressed which is associated with a breakdown of the Kondo effect. This results in an asymptotically scale-invariant (i.e., power-law) spectrum of the correlated orbitals $\propto|\omega|^{1/3}$, indicating non-Fermi liquid properties of the quantum critical point, and a small Fermi surface including only the light quasi-particles. This orbital selective Mott phase demonstrates the possibility of metallic local criticality within the general framework of ordinary single site DMFT.

Excitations between localized 3d states of transition metal ions within crystalline solids, commonly known as d-d transitions, play a pivotal role in diverse phenomena across solid state physics, materials science, and chemistry. These transitions contribute to the coloration in transition metal oxides, catalytic processes on oxide surfaces, and high-temperature superconductivity. They also couple optical excitation to quantized collective phenomena such as phonons and magnons in magnetic systems. Until now, an experimental method to unravel the complex quasiparticle dynamics associated with d-d transitions has remained elusive. We bridge this gap by demonstrating that d-d transitions can be distinctly traced in momentum space and time using time- and angle-resolved photoelectron spectroscopy (trARPES). Through this approach, we can assign specific momentum-dependent characteristics and elucidate the decay mechanisms of specific d-d transitions in FePS$_{3}$, a two-dimensional van der Waals antiferromagnet with a rich array of quantum phenomena stemming from d-d transitions. This study pioneers the use of ARPES in probing the dynamics of d-d transitions across a wide spectrum of solid-state systems.

We report on time-resolved nonlinear terahertz spectroscopy of a strongly correlated ruthenate, CaRuO$_3$, as a function of temperature, frequency and terahertz field strength. Third-harmonic radiation for frequencies up to 2.1 THz is observed evidently at low temperatures below 80 K, where the low-frequency linear dynamical response deviates from the Drude model and a coherent heavy quasiparticle band emerges by strong correlations associated with the Hund's coupling.Phenomenologically, by taking an experimentally observed frequency-dependent scattering rate, the deviation of the field driven kinetics from the Drude behavior is reconciled in a time-dependent Boltzmann description, which allows an attribution of the observed third-harmonic generation to the terahertz field driven nonlinear kinetics of the heavy quasiparticles.

Two-color spin-noise spectroscopy of interacting electron spins in singly charged semiconductor quantum dots provides information on the inter quantum dot interactions. We investigate the spin cross-correlation function in a quantum dot ensemble using a modified semiclassical approach. Spin-correlation functions are calculated using a Hamilton quaternion approach maintaining local quantum mechanical properties of the spins. This method takes into account the effects of the nuclear-electric quadrupolar interactions, the randomness of the coupling constants, and the electron g factor on the spin-noise power-spectra. We demonstrate that the quantum dot ensemble can be mapped on an effective two-quantum dot problem and discuss how the characteristic length scale of the inter-dot interaction modifies the low-frequency cross-correlation spectrum. We argue that details on the interaction strength distribution can be extracted from the cross-correlation spectrum when applying a longitudinal or a transversal external magnetic field.

The antiferromagnetic ordering in Mott insulators upon lowering the temperature is accompanied by a transfer of the single-particle spectral weight to lower energies and a shift of the Mott gap to higher energies (magnetic blue shift, MBS). The MBS is governed by the double exchange and the exchange mechanisms. Both mechanisms enhance the MBS upon increasing the number of orbitals. By performing a polynomial fit to numerical dynamical mean-field theory data we provide an expansion for the MBS in terms of hopping and exchange coupling of a prototype Hubbard-Kondo-Heisenberg model and discuss how the results can be generalized for application to realistic Mott or charge-transfer insulator materials. This allows estimating the MBS of the charge gap in real materials in an extremely simple way avoiding extensive theoretical calculations. The approach is exemplarily applied to $α$-MnTe, NiO, and BiFeO$_3$ and an MBS of about $130$ meV, $360$ meV, and $157$ meV is found, respectively. The values are compared with the previous theoretical calculations and the available experimental data. Our ready-to-use formula for the MBS simplifies the future studies searching for materials with a strong coupling between the antiferromagnetic ordering and the charge excitations, which is paramount to realize a coupled spin-charge coherent dynamics at a femtosecond time scale.

We present a microscopic model for a singly charged quantum dot (QD) ensemble to reveal the origin of the long-range effective interaction between the electron spins in the QDs. Wilson's numerical renormalization group (NRG) is used to calculate the magnitude and the spatial dependency of the effective spin-spin interaction mediated by the growth-induced wetting layer. Surprisingly, we found an antiferromagnetic Heisenberg coupling for very short inter-QD distances that is caused by the significant particle-hole asymmetry of the wetting layer band at very low filling. Using the NRG results obtained from realistic parameters as input for a semiclassical simulation for a large QD ensemble, we demonstrate that the experimentally reported phase shifts in the coherent spin dynamics between single- and two-color laser pumping can be reproduced by our model, solving a long-standing open problem of the microscopic origin of the inter-QD electron spin-spin interaction.

We study theoretically the formation of the nuclear-spin polaron state in semiconductor nanosystems within the Lindblad equation approach. To this end, we derive a general Lindblad equation for the density operator that complies with the symmetry of the system Hamiltonian and address the nuclear-spin polaron formation for localized charge carriers subject to an arbitrarily anisotropic hyperfine interaction when optically cooling the nuclei. The steady-state solution of the density matrix for an anisotropic central spin model is presented as a function of the electron and nuclear spin bath temperature. Results for the electron-nuclear spin correlator as well as data for the nuclear spin distribution function serve as a measure of spin-entanglement. The features in both of them clearly indicate the formation of the nuclear polaron state at low temperatures where the crossover regime coincides with an enhancement of quantum fluctuations and agrees with the mean-field prediction of the critical temperature line. We can identify two distinct polaron states dependent upon the hyperfine anisotropy which are separated by a quantum phase transition at the isotropic point. These states are reflected in the temporal spin auto-correlation functions accessible in experiment via spin-noise measurements.

By combining Wilson's numerical renormalization group with a modified Bloch-Redfield approach we are able to eliminate the artificial broadening of the Lehmann representation of quantum impurity spectral functions required by the standard numerical renormalization group algorithm. Our approach is based on the exact reproduction of the continuous coupling function in the original quantum impurity model. It augments each chain site of the Wilson chain by a coupling to an additional reservoir. This open Wilson chain is constructed by a continuous fraction expansion and the coupling function is treated in second order in the context of the Bloch-Redfield approach. The eigenvalues of the resulting Bloch-Redfield tensor generate a finite life time of the numerical renormalization group excitations that leads to a natural broadening of the spectral functions. We combine this approach with z-averaging and an analytical exact expression for the correlation part of the self-energy to obtain an accurate representation of the spectral function of the original continuum model in the absence and presence of an external magnetic field.

We investigate the real-space spectral properties of strongly-correlated multi-impurity arrays in the Kondo insulator regime. Employing a recently developed mapping onto an effective correlated cluster problem makes the problem accessible to the numerical renormalization group. The evolution of the spectrum as function of cluster size and cluster site is studied. We applied the extended Lieb-Mattis theorem to predict whether the spectral function must vanish at the Fermi energy developing a true pseudo-gap or whether the spectral function remains finite at $\w=0$. Our numerical renormalization group spectra confirm the predictions of the theorem and shows a metallic behavior at the surface of a cluster prevailing in arbitrary spatial dimensions. We present a conventional minimal extension of a particle-hole symmetric Anderson lattice model at $U=0$ that leads to a gapped bulk band but a surface band with mainly $f$-orbital character for weak and moderate hybridization strength. The change in the site-dependent spectra upon introducing a Kondo hole in the center of the cluster are presented as a function of the hole-orbital energy. In particular the spectral signatures across the Kosterlitz-Thouless type quantum phase transition from a singlet to a local moment fixed point are discussed.

A substantial energy gap of charge excitations induced by strong correlations is the characteristic feature of Mott insulators. We study how the Mott gap is affected by long-range antiferromagnetic order. Our key finding is that the Mott gap is increased by the magnetic ordering: A magnetic blue shift (MBS) occurs. Thus the effect is proportional to the exchange coupling in the leading order in the Hubbard model. In systems with additional localized spins the double-exchange mechanism induces an additional contribution to the MBS which is proportional to the hopping in the leading order. The coupling between spin and charge degrees of freedom bears the potential to enable spin-to-charge conversion in Mott systems on extreme time scales determined by hopping and exchange only, since a spin-orbit-mediated transfer of angular momentum is not involved in the process. In view of spintronic and magnonic applications, it is highly promising to observe that several entire classes of compounds show exchange and double-exchange effects. Exemplarily, we show that the magnetic contribution to the band-gap blue shift observed in the optical conductivity of α-MnTe is correctly interpreted as the MBS of a Mott gap.

D. Bossini, 2, ∗ S. Dal Conte, 4 M. Terschanski, G. Springholz, A. Bonanni, K. Deltenre, F. Anders, G.S. Uhrig, G. Cerullo, 4 and M. Cinchetti Department of Physics and Center for Applied Photonics, University of Konstanz, D-78457 Konstanz, Germany. Lehrstuhl für Experimentalphysik VI, Technische Universität Dortmund, Otto-Hahn Straße 4, 44227 Dortmund, Germany Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, Milano, Italy Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche, Piazza Leonardo da Vinci 32, Milano, Italy Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz, Altenbergerstr. 69, 4040 Linz, Austria Lehrstuhl für Theoretische Physik II, Technische Universität Dortmund, Otto-Hahn Straße 4, 44227 Dortmund, Germany Lehrstuhl für Theoretische Physik I, Technische Universität Dortmund, Otto-Hahn Straße 4, 44227 Dortmund, Germany (Dated: October 29, 2021)

The emerging and screening of local magnetic moments in solids has been investigated for more than 60 years. Local vacancies as in graphene or in Heavy Fermions can induce decoupled bound states that lead to the formation of local moments. In this paper, we address the puzzling question how these local moments can be screened and what determines the additionally emerging low temperature scale. We review the initial problem for half-filled conduction bands from two complementary perspectives: By a single-particle supercell analysis in the uncorrelated limit and by the Lieb-Mathis theorem for systems with a large Coulomb interaction $U$. We proof that the stable local moments are subject to screening by three different mechanisms. Firstly the local moments are delocalized by a finite $U$ beyond the single-particle bound state. We find a Kosterlitz-Thouless type transition governed by an exponentially suppressed low energy scale of a counterintuitive Kondo form with $J_{\rm eff} \propto U^n$ for small $U$, where $n>1$ depends on the precise model. Secondly, we show that away from half-filling the local moment phase becomes unstable and is replaced by two types of singlet phases that are adiabatically connected. At a critical value for the band center, the physics is governed by an exponentially suppressed Kondo scale approaching the strong coupling phase that is replaced by an singlet formation via antiferromagnetic RKKY interaction for large deviation from the critical values. Thirdly, we show that the local magnetic moment can be screened by a Kondo hole orbital at finite energy, even though the orbital occupation is negligible: An additional low energy scale emerges below which the localized moment is quenched. Similarities to the experimental findings in Ce$_{1-x}$La$_x$Pd$_3$ are pointed out.

The light-induced femtosecond dynamics of the sublattice magnetizations in the antiferromagnetically ordered phase of the semiconductor α-MnTe is investigated theoretically as function of an external driving field. The electromagnetic field is coupled to optical modes and the concomitant atomic displacements modulate the Heisenberg exchange couplings. We derive the equations of motion for the time-dependent sublattice magnetization in spin wave theory and analyze the contributions from the driven magnon modes. The antiferromagnetic order parameter exhibits coherent longitudinal oscillations determined by the external driving frequency which decay due to dephasing. Including a phenomenological dissipative term to mimic spin-lattice relaxation processes leads to relaxation back to thermal equilibrium. We provide approximate analytic solutions of the resulting differential equations which allow us to understand the effect of the driving light pulse on the amplitude, frequency, and lifetime of the coherent spin dynamics.

Under optical cooling of nuclei, a strongly correlated nuclear-spin polaron state can form in semiconductor nanostructures with localized charge carriers due to the strong hyperfine interaction of the localized electron spin with the surrounding nuclear spins. Here we develop a kinetic-equation formalism describing the nuclear-spin polaron formation. We present a derivation of the kinetic equations for an electron-nuclear spin system coupled to reservoirs of different electron and nuclear spin temperatures which generate the exact thermodynamic steady state for equal temperatures independent of the system size. We illustrate our approach using the analytical solution of the central spin model in the limit of an Ising form of the hyperfine coupling. For homogeneous hyperfine coupling constants, i.e., the box model, the model is reduced to an analytically solvable form. Based on the analysis of the nuclear-spin distribution function and the electron-nuclear spin correlators, we derive a relation between the electron and nuclear spin temperatures, where the correlated nuclear-spin polaron state is formed. In the limit of large nuclear baths, this temperature line coincides with the critical temperature of the mean-field theory for polaron formation. The criteria of the polaron formation in a finite-size system are discussed. We demonstrate that the system's behavior at the transition temperature does not depend on details of the hyperfine-coupling distribution function but only on the effective number of coupled bath spins. In addition, the kinetic equations enable the analysis of the temporal formation of the nuclear-polaron state, where we find the build-up process predominated by the nuclear spin-flip dynamics.

The continuous coupling function in quantum impurity problems is exactly partitioned into a part represented by a finite-size Wilson chain and a part represented by a set of additional reservoirs, each coupled to one Wilson chain site. These additional reservoirs represent high-energy modes of the environment neglected by the numerical renormalization group and are required to restore the continuum limit of the original problem. We present a hybrid time-dependent numerical renormalization group approach which combines an accurate numerical renormalization group treatment of the nonequilibrium dynamics on the finite-size Wilson chain with a Bloch-Redfield formalism to include the effect of these additional reservoirs. Our approach overcomes the intrinsic shortcoming of the time-dependent numerical renormalization group approach induced by the bath discretization with a Wilson parameter Lambda > 1. We analytically prove that for a system with a single chemical potential, the thermal equilibrium reduced density operator is the steady-state solution of the Bloch-Redfield master equation. For the numerical solution of this master equation, a Lanczos method is employed which couples all energy shells of the numerical renormalization group. The presented hybrid approach is applied to the real-time dynamics in correlated fermionic QISs. An analytical solution of the resonant-level model serves as a benchmark for the accuracy of the method which is then applied to nontrivial models, such as the interacting resonant-level model and the single-impurity Anderson model.

We study the conductance of a time-reversal symmetric helical electronic edge coupled antiferromagnetically to a magnetic impurity, employing analytical and numerical approaches. The impurity can reduce the perfect conductance $G_0$ of a noninteracting helical edge by generating a backscattered current. The backscattered steady-state current tends to vanish below the Kondo temperature $T_K$ for time-reversal symmetric setups. We show that the central role in maintaining the perfect conductance is played by a global $U(1)$ symmetry. This symmetry can be broken by an anisotropic exchange coupling of the helical modes to the local impurity. Such anisotropy, in general, dynamically vanishes during the renormalization group (RG) flow to the strong coupling limit at low-temperatures. The role of the anisotropic exchange coupling is further studied using the time-dependent Numerical Renormalization Group (TD-NRG) method, uniquely suitable for calculating out-of-equilibrium observables of strongly correlated setups. We investigate the role of finite bias voltage and temperature in cutting the RG flow before the isotropic strong-coupling fixed point is reached, extract the relevant energy scales and the manner in which the crossover from the weakly interacting regime to the strong-coupling backscattering-free screened regime is manifested. Most notably, we find that at low temperatures the conductance of the backscattering current follows a power-law behavior $G\sim (T/T_K)^2$, which we understand as a strong nonlinear effect due to time-reversal symmetry breaking by the finite-bias.

We present a mapping of correlated multi-impurity Anderson models to a cluster model coupled to a number of effective conduction bands capturing its essential low-energy physics. The major ingredient is the complex single-particle self energy matrix of the uncorrelated problem that encodes the influence to the host conduction band onto the dynamics of a set of correlated orbitals. While the real part of the self-energy matrix generates an effective hopping between the cluster orbitals, the imaginary part determines the coupling to the effective conduction bands in the mapped model. The rank of the imaginary part determines the number of independent screening channels of the problem, and allows the replacement of the phenomenological exhaustion criterion by a rigorous mathematical statement. This rank provides a distinction between multi-impurity models of first kind and of second kind. For the latter, there are insufficient screening channels available, so that a singlet ground state must be driven by the inter-cluster spin correlations. This classification provides a fundamental answer to the question of why ferromagnetic correlations between local moments are irrelevant for the spin compensated ground state in dilute impurity models, whereas they compete with the Kondo-scale in dense impurity arrays, without evoking a spin density wave. The low-temperature physics of three examples taken from the literature are deduced from the analytic structure of the mapped model, demonstrating the potential power of this approach. NRG calculations are presented for up to five site cluster. We investigate the appearance of frustration induced non-Fermi liquid fixed points in the trimer, and demonstrate the existence of several critical points of KT type at which ferromagnetic correlations suppress the screening of an additional effective spin-$1/2$ degree of freedom.