Localized Impurity Research Articles

Impurity flat band states in the diamond chain

Flat band (FB) systems, featuring dispersionless energy bands, have garnered significant interest due to their compact localized states (CLSs). However, a detailed account on how local impurities affect the physical properties of overlapping CLSs is still missing. Here we study a diamond chain with a finite magnetic flux per plaquette that exhibits a gapped midspectrum FB with non-orthogonal CLSs, and develop a framework for projecting operators onto such non-orthogonal bases. This framework is applied to the case of an open diamond chain with small local impurities in the midchain plaquette, and analytical expressions are derived for FB states influenced by these impurities. For equal impurities in top and bottom sites under diagonal disorder, we show how the impurity states experience an averaged disorder dependent on their spatial extension, leading to enhanced robustness against disorder. For a single impurity, an exotic topological phase with a half-integer winding number is discovered, which is linked to a single in-gap edge state under open boundary conditions. Numerical simulations validate the analytical predictions.

Thermal boundary conductance of artificially and systematically designed grain boundaries of Silicon measured by laser heterodyne photothermal displacement method

The overall physical properties of polycrystalline materials vary depending on the microscopic individual grain boundary (GB) properties and their structures. Unlike previous studies that only examined the structure and properties of a specific GB, this study focuses on understanding the thermal boundary conductance (TBC) through artificial and systematic changes in the GB structures. This is achieved by combining an advanced technique to map local thermal expansion displacement using the laser heterodyne photothermal displacement method and a unique crystal growth method that induces spontaneous changes in the GB structures. As a result, we could quantify the TBC of the GB in silicon, considering the changes in three structural parameters of GB: azimuthal misorientation (α), asymmetry angle (β), and deviation angle (θ) from the growth direction. Our findings reveal that the TBC increases with increasing θ, whereas parameters α and β have negligible effects. The underlying physics of this relationship is discussed in terms of local carrier concentration and impurity segregation. These results demonstrate the crucial role of the GB structures in influencing the local TBC, shedding light on potential avenues for enhancing the macroscopic properties of polycrystalline materials by engineering GBs.

Unsupervised learning of effective quantum impurity models

Generalized quantum impurity models—which feature a few localized and strongly correlated degrees of freedom coupled to itinerant conduction electrons—describe diverse physical systems, from magnetic moments in metals to nanoelectronics quantum devices such as quantum dots or single-molecule transistors. Correlated materials can also be understood as self-consistent impurity models through dynamical mean-field theory. Accurate simulation of such models is challenging, especially at low temperatures, due to many-body effects from electronic interactions, resulting in strong renormalization. In particular, the interplay between local impurity complexity and Kondo physics is highly nontrivial. A common approach, which we further develop in this work, is to consider instead a simpler effective impurity model that still captures the low-energy physics of interest. The mapping from a bare to an effective model is typically done perturbatively, but even this can be difficult for complex systems, and the resulting effective model parameters can nevertheless be quite inaccurate. Here we develop a nonperturbative, unsupervised machine learning approach to systematically obtain low-energy effective impurity-type models, based on the renormalization-group framework. The method is shown to be general and flexible, as well as accurate and systematically improvable. We benchmark the method against exact results for the Anderson impurity model, and we provide an outlook for more complex models beyond the reach of existing methods. Published by the American Physical Society 2024

Study of the electronic structure and electron impact excitation cross section of helium impurities in spherical quantum dots

This manuscript is devoted to explore the atomic structure and electron impact excitation process of atom impurities in quantum dots. To achieve this goal, a method that solves the fully relativistic Dirac equation within the framework of relativistic configuration interaction is proposed. The Gaussian potential is used, which can accurately describe the location of impurities in quantum dots and their local effects on the surrounding electron cloud. The coupled Dirac equation is modified to include a new central potential, providing solutions that include both the continuous and bound state wave functions. The process of electron impact excitation is elucidated using the distorted wave method, all within the framework of relativistic Dirac theory. For illustrative purposes, a detailed investigation of the excitation energies, transition rates, wave functions, and excitation cross sections is carried out for a wide range of confinement strengths of the potential and quantum dot radii, using the helium impurities in spherical quantum dots as an example. Our results reveal that for a given confinement strength of the potential, the bound state wave functions are initially pulled into the inner region by the attractive Gaussian potential well, but eventually reflect the free atom scenario at large quantum dot radii. In contrast, the continuous electron wave functions exhibit monotonic variations as a function of the quantum dot radii. Such behavior of the wave functions gives rise to distinctive phenomena in the variation of excitation energies, transition rates, and excitation cross sections in relation to the potential parameters. Good agreement between the present results and existing data, where available, is obtained. This work holds importance not only for basic research in atomic physics but also for the optical and electronic applications of quantum dots. I.e., in the design and optimization of quantum dot lasers and quantum dot sensors.

First experimental confirmation of island SOL geometry effects in a high radiation regime on W7-X

Abstract This work characterizes the detachment behavior and radiation characteristics of the low
iota configuration in the Wendelstein 7-X (W7-X) stellarator. The island scrape-off layer (SOL) of the
low iota has a poloidal mode number of 6 islands surrounding the last closed flux surface (LCFS).
The island geometry of the low iota configuration is significantly different to that of the standard
magnetic field configuration, whose detachment characteristics have already been described in previous
work[2, 3, 4]. Experimental results show that the radiation pattern in the low iota configuration
is starkly different to that of the standard magnetic field configuration, with radiation concentrated
at the island SOL O-points, rather than the X-points. Additionally, this O-point localized radiation
pattern is associated with unstable detachment, with both radiation oscillations in experiments and the
lack of a self-consistent plasma solution at high radiated power fraction in EMC3-Eirene simulations.
EMC3-Eirene simulations are used to understand the radiation distribution. It was found that the O-
point localized radiation arises first from local impurity accumulation near the parallel flow stagnation,
which is located close to the geometrical center of the island (”O-point”). The local cooling in this
region leads to plasma condensation in the islands in closest magnetic connection to the divertor target
plates. The heat source to this region of the island, which is thermally isolated from the upstream heat
source in terms of parallel transport, must arise via perpendicular heat transport. This heat source is
expected to be large for the low iota configuration due to its very small internal island field line pitch.
This work highlights the importance (complementary to previous work, e. g. [5, 6]) of the internal
island field line pitch not only on the radiation pattern, but also the detachment performance of the
island divertor.

Unidirectional amplification in the frozen mode regime enabled by a nonlinear defect.

A stationary inflection point (SIP) is a spectral singularity of the Bloch dispersion relation ω(k) of a periodic structure where the first and the second derivatives of ω with respect to k vanish. An SIP is associated with a third-order exceptional point degeneracy in the spectrum of the unit-cell transfer matrix, where there is a collapse of one propagating and two evanescent Bloch modes. At the SIP frequency, the incident wave can be efficiently converted into the frozen mode with greatly enhanced amplitude and vanishing group velocity. This can be very attractive for applications, including light amplification. Due to its non-resonant nature, the frozen mode regime (FMR) has fundamental advantages over common cavity resonances. Here, we propose, a novel, to the best of our knowledge, scheme for FMR-based unidirectional amplifiers by leveraging a tailored amplification/attenuation mechanism and a single nonlinear defect. The defect breaks the directional symmetry of the periodic structure and enables nonlinearity-related unidirectional amplification/attenuation in the vicinity of the SIP frequency. We demonstrate the robustness of the amplification mechanism to local impurities and parasitic nonlinearity.

Validating and speeding up x-ray tomographic inversions in tokamak plasmas

X-ray tomography is a precious tool in tokamaks that provides rich information about the core plasma, such as local impurity concentration, electron temperature and density as well as magnetic equilibrium (ME) and magnetohydrodynamic activity. Nevertheless, inferring the local plasma emissivity from a sparse set of line-integrated measurements is an ill-posed problem that requires dedicated regularization and validation methods. Besides, speeding up the inversion algorithm in order to be compatible with real-time control systems is a challenging task with traditional approaches. In this contribution, in a first part we introduce tools aiming at validating and speeding up the x-ray tomographic inversions based on Tikhonov regularization, including ME constraint and parameter optimization, taking the WEST geometry as an example. In a second part, an alternative approach compatible with real-time, based on a set of neural networks is proposed and compared with the Tikhonov approach for an experimental case.

Charge exchange recombination spectroscopy on the alkali beam of Wendelstein 7-X.

Measurements of ion temperature profiles are required to assess the energy and particle transport processes in the Wendelstein 7-X stellarator. This device is equipped with a diagnostic alkali beam, which can be utilized to determine local impurity temperatures and densities by Charge Exchange Recombination Spectroscopy (CXRS). It could provide such profiles in the edge plasma, where other diagnostics are less efficient. With this contribution, first results of CXRS measurements on the sodium beam from the scientific operation phase OP2.1 are presented. The spectroscopic system was in commissioning phase lacking some of the final optical components. Thus, the aim of the diagnostics during this campaign was to explore the measurement capabilities. Based on the processed spectra, the prospects of C5+ and C6+ ion temperature and concentration measurements are discussed. The results indicate that with the final optical setup under installation, the diagnostics could provide ion temperature profiles in the edge with 3mm radial resolution and at least 1s temporal resolution.

Understanding the role of Niobium, Molybdenum and Tungsten in realizing of the transparent n-type SnO2

Based on the density functional theory, the defective band structures (DBSs), ionization energy and formation energy for Niobium (Nb), Molybdenum (Mo) and Tungsten (W)-doped SnO2 are calculated. The DBSs show Nb, Mo and W substituting Sn (labeled as NbSn, MoSn and WSn) could form the localized impurity states which are above the conduction band minimum (CBM). These characteristics can be attributed to the energy of dopants’ d-orbitals are much higher than that of Sn-s and -d orbital as well as O-2p orbitals, and the dopants with their neighboring atoms would form the non-bonding impurity states. The DBSs confirm NbSn, MoSn and WSn are typical n-type defects in SnO2. The ionization energies ϵ(0/+) for NbSn, MoSn and WSn are higher than 0.22 eV above CBM, indicating these defects could be fully ionized. We find the NbO and MoO3 are promising dopant sources, as the thermodynamic equilibrium fabrication scheme is considered. Taking Nb-doped SnO2 as an example, we find a few NbSn could induce high conductivity (541 S cm−1). These results suggest that SnO2 containing NbSn, MoSn and WSn are promising n-type semiconductors. Our findings would provide a better understanding of the n-type properties in Nb, Mo and W-doped SnO2.

Coherent exchange-coupled nonlocal Kondo impurities

Quantum dots exhibit a variety of strongly correlated effects, e.g., they can emulate localized magnetic impurities that form a Kondo singlet with their surrounding environment. Interestingly, in double-dot setups, such magnetic impurities couple to each other by direct Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, which wins over the Kondo physics. In this work, we investigate a double-dot device where the dots are coupled via off-resonant ballistic modes, dubbed electronic cavity modes. Within this cavity-double-dot system, we study, using variational matrix product state techniques, the competition between Kondo formation and the combined coherent orbital hybridization and RKKY-like interaction that the cavity facilitates. Specifically, we find that Kondo can form on each dot individually whereby the cavity can either (i) destroy the Kondo via the RKKY that mediates a singlet state on the two dots, or (ii) lead to an exotic orbital macrsoscopic superposition of the Kondo forming on each of the dots. We dub the latter “Kondo cat”. En route to this key finding, we rigorously study the many-body phase diagram of the system, as well as compare it with the case of coupling the dots via an incoherent RKKY channel. The realization of a Kondo cat can facilitate applications in metrology, and reveal the spin coherence length in mesoscopic devices. Published by the American Physical Society 2024

Ground state magnetic susceptibility of Kondo impurities

Impurity models describe localized impurities interacting with the spins of electrons. Strong correlations lead to non-trivial behaviours of the model. In this work we present 3 different impurity models: (1) the single-impurity Kondo model; (2) the two-impurity Kondo model; (3) the two-channel Kondo model. For each model we present a spin chain emulation and utilize the density matrix renormalization group (DMRG). We study the magnetization and zero-temperature susceptibility of the impurity when a local magnetic field is applied. We get the expected relations theoretically.

Differences in Kondo Splitting of Surface Quantum Systems Induced by Two Distinct Magnetic Tips: A Joint Method of DFT and HEOM.

The interactions between a magnetic tip and local spin impurities initiate unconventional Kondo phenomena, such as asymmetric suppression or even splitting of the Kondo peak. However, a lack of realistic theoretical models and comprehensive explanations for this phenomenon persists due to the complexity of the interactions. This research employs a joint method of density functional theory (DFT) and hierarchical equation of motion (HEOM) to simulate and contrast the modulation of the spin state and Kondo behavior in the Fe/Cu(100) system with two distinct magnetic tips. A cobalt tip, possessing a larger magnetic moment, incites greater atomic displacement of the iron atom, more notable alterations in electronic structure, and enhanced charge transfer with the environment compared with the control process utilizing a nickel tip. Furthermore, the Kondo resonance undergoes asymmetric splitting as a result of the ferromagnetic correlation between the iron atom and the magnetic tip. The Co tip's higher spin polarization results in a wider spacing between the splitting peaks. This investigation underscores the precision of the DFT + HEOM approach in predicting complex quantum phenomena and explaining the underlying physical principles. This provides valuable theoretical support for developing more sophisticated quantum regulation experiments.

Sub-nanosecond magnetic vortex reversal induced by localized resonant strain field in doped nanomagnets

The strain-induced magnetic vortex dynamics in nanomagnets with ring-shaped impurities are investigated by means of micromagnetic simulations. It is found that the type and location of impurities can modulate the strain-stimulated spin wave spectrum of the magnetic vortex. Compared with pure nanomagnets without doping, the scattering impurities make the eigenfrequency of nanomagnets higher, while the pinning impurities lead to lower eigenfrequency. Moreover, the spin wave oscillation amplitude in a doped nanomagnet is strengthened by the gradient of exchange energy at the interface between the impurity ring and nanomagnet. The magnetic vortex polarity in a nanomagnet with specific doping schemes can be reversed in a sub-nanosecond scale by a localized resonant strain signal. Besides the switching efficiency improvement, the threshold stress of sub-nanosecond polarity reversal in nanomagnets with specific doping schemes is also reduced compared to the counterpart of nanomagnets without impurities. These results indicate that doping engineering of nanomagnets is a significant method to achieve straintronic devices with higher operating frequency and lower energy consumption.

Studies of erosion-deposition of plasma-facing materials due to plasma-wall interactions in EAST tokamak

Material erosion, migration, mixing, dust formation, and co-deposition were investigated on plasma-facing materials in the experimental advanced superconducting tokamak (EAST). The test samples (TSs) of molybdenum (Mo), tungsten (W), and carbon (C) were irradiated during EAST operations. All exposed TS surfaces are modified by erosion and deposition processes resulting in the formation of thin layers containing a mixture of PFCs (Mo, W, Cu, Cr, Fe) and light elements (Li, C, Ca, N, O). The majority of chemical species are in a layer of thickness <650–900 nm. The particle size and structure of co-deposition were observed on each TS. Depth profiling by laser-induced breakdown spectroscopy (LIBS) suggests the presence of local and global impurities on the TSs resulting from the plasma-wall interaction (PWI). The processes involved in the PWI that caused erosion of EAST materials are heat flux and high energy excited impurity particles. The material is sputtered from the first wall plasma-facing components. Erosion and deposition processes occur simultaneously in the EAST. The migrated impurities get deposited globally on remote surfaces. A crack was observed in one of the W TSs due to a high heat load. The spectral intensity of co-deposition and substrate continuously changed during successive laser shots.

Page-curve-like entanglement dynamics in open quantum systems

The entanglement entropy of a black hole and that of its Hawking radiation are expected to follow the so-called Page curve: After an increase in line with Hawking’s calculation, it is expected to decrease back to zero once the black hole has fully evaporated, as demanded by unitarity. Recently, a simple system-plus-bath model has been proposed which shows a similar behavior. Here, we make a general argument as to why such a Page-curve-like entanglement dynamics should be expected to hold generally for system-plus-bath models at small coupling and low temperatures, when the system is initialized in a pure state far from equilibrium. The interaction with the bath will then generate entanglement entropy, but it eventually has to decrease to the value prescribed by the corresponding mean-force Gibbs state. Under those conditions, it is close to the system ground state. We illustrate this on two paradigmatic open-quantum-system models, the exactly solvable harmonic quantum Brownian motion and the spin-boson model, which we study numerically. In the first example we find that the intermediate entropy of an initially localized impurity is higher for more localized initial states. In the second example, for an impurity initialized in the excited state, the Page time—when the entropy reaches its maximum—occurs when the excitation has half decayed. Published by the American Physical Society 2024

Precipitation kinetics of Cu in FeCu and FeCuX (X=B, N, and BN) alloys using kinetic Monte Carlo simulations

We employed kinetic Monte Carlo simulations to investigate the precipitation of Cu in FeCu and FeCuX (X=B, N, and BN) alloys. The parameters of kinetic Monte Carlo simulations were obtained through first-principles calculations. In this study, we utilized a vacancy-mediated model that considers the migration barriers dependent on local impurity atomic environments. The dynamical stability of both FeCu and FeCuX (X=B, N, and BN) alloys was examined by the virtual crystal approximation method. Through the assessment of advancement factor, cluster number density, and mean cluster radius, the simulation results indicated that both B and N promote precipitation of Cu. While B doping has a minor effect, N doping significantly promotes Cu precipitation.

Perspective: Theory and simulation of highly mismatched semiconductor alloys using the tight-binding method

The electronic structure of highly mismatched semiconductor alloys is characterized by carrier localization and strongly influenced by the local alloy microstructure. First-principles calculations can deliver valuable quantitative insight, but their associated computational expense limits alloy supercell size and imposes artificial long-range ordering, which can produce misleading results. The empirical tight-binding method (ETBM) provides a transparent approach to investigate large-scale supercells on an atomistic level, to quantitatively predict the electronic structure of semiconductor alloys. Here, we overview key aspects and considerations for establishing ETBMs. Additionally, we discuss and highlight, given that the ETBM matrix elements are described in the language of overlaps between localized atomic orbitals, that ETBMs have proven highly successful in analyzing the impact of localized and resonant impurity states, as well as disorder, on the optoelectronic properties of highly mismatched alloys. The ETBM continues to provide valuable insight for emerging material systems, including two-dimensional materials, perovskites and their heterostructures, and provides a framework to address technologically relevant questions including the importance of short-range disorder for loss mechanisms such as non-radiative Auger–Meitner recombination. Moreover, the ETBM furnishes a quantitative basis for continuum models such as k⋅p or localization landscape theories, allowing to explicitly incorporate disorder effects in nanostructures to underpin predictive device-level analysis.

Magnon dispersion, magnetization, and thermodynamic properties of 2D-Sc/GaAs diluted magnetic semiconductor (DMS)

In this paper, the effect of magnon scattering, light–matter coupling strength, temperature, and applied dc field H0 on magnon dispersion, density of magnons, magnetization, and thermodynamic properties of 2D-Sc/GaAs DMS material is studied. The Green function formalism is used to find the magnon dispersion and density in single-mode excitation employing the quantum field theory. Our findings indicate that ferromagnetic phase change is obtained within a limited low-temperature range based on the product Ω0T5/2, which remains below unity and varies with the amount of magnon scattering factor Ω0. It was presumed that the density of localized magnetic impurities can be controlled by taking into account the numerical stability with the number of holes required for mediation, and therefore, a scandium (Sc) dopant and its kind, which have a double functionality of creating holes and adding magnetic impurities from their 3d suborbital, are the best choice to replace those with higher spin magnetic moments. We also observe that the magnetic curves broaden as the temperature further rises and decrease with the enhancement of the magnon scattering factor, perhaps, due to quenching of fermionic spins ceasing the interband excitation. However, in the absence of this factor, the magnetization decreases linearly with the increase in the temperature, breaking the Bloch T3/2 low, perhaps, introducing anomalous condition to such 2D materials. The light–matter coupling strength and the dc field H0 are alleged to be responsible for the formation of the energy gap and variation of magnon dispersion. This work suggests that there is a point above which the temperature TC may not rise with the increase in the impurity concentration x due to magnon scattering, distressing the entire thermodynamic property.

Testing validity of 1D models for impurity fraction scaling for divertor detachment with EDGE2D-EIRENE

Predictions of the Huber–Chankin (HC) scaling for the upstream impurity fraction were verified in a series of EDGE2D-EIRENE (‘code’) runs for highly radiating plasmas with nitrogen injection. The main quantity extracted from the code was poloidally averaged, from X-point to X-point, separatrix impurity fraction cZ in the main scrape-off layer (SOL). Variation of the main working gas (H, D and T) revealed a qualitative agreement between the model and code results owing to the very large isotope difference in the predicted cZ values caused primarily by the inverse isotope mass dependence of the H-mode power threshold assumed in the HC model and implemented in the code. At the same time, the variation of the toroidal field and safety factor in deuterium cases yielded no correlation between the model predictions and code results. The code showed much higher local impurity fractions (fZ ) in the divertor compared to the main SOL, as well as large case-to-case variations in the divertor to the main SOL ratio of impurity fractions. The analysis of code results has wide-ranging consequences not only for the HC model, but also for other similar 1D models which use simple geometry ignoring strong neutral recycling in the divertor/ Different topology makes plasma parameters in the divertor and main SOL very different, resulting in different impurity charge state composition. Missing mechanisms in 1D codes (e.g. friction and thermo-forces exerted on impurity ions by main working gas ions) lead to impurity density redistribution. Neglecting all above factors, 1D models assume a constant impurity fraction along field lines.

3D radiated power analysis of JET SPI discharges using the Emis3D forward modeling tool

Precise values for radiated energy in tokamak disruption experiments are needed to validate disruption mitigation techniques for burning plasma tokamaks like ITER and SPARC. Control room analysis of radiated power (P rad) on JET assumes axisymmetry, since fitting 3D radiation structures with limited bolometry coverage is an under-determined problem. In mitigated disruptions, radiation is toroidally asymmetric and 3D, due to fast-growing 3D MHD modes and localized impurity sources. To address this problem, Emis3D adopts a physics motivated forward modeling (‘guess and check’) approach, comparing experimental bolometry data to synthetic data from user-defined radiation structures. Synthetic structures are observed with the Cherab modeling framework and a best fit chosen using a reduced χ 2 statistic. 2D tomographic inversion models are tested, as well as helical flux tubes and 3D MHD simulated structures from JOREK. Two nominally identical pure neon shattered pellet injection (SPI) mitigated discharges in JET are analyzed. 2D tomographic inversions with added toroidal freedom are the best fits in the thermal quench (TQ) and current quench (CQ). In the pre-TQ, 2D reconstructions are statistically the best fits, but are likely over-optimized and do not capture the 3D radiation structure seen in fast camera images. The next-best pre-TQ fits are helical structures that extend towards the high-field side, consistent with an impurity flow under the magnetic nozzle effect also observed in JOREK simulations. Whole-disruption radiated fractions of 0.98+0.03/ −0.29 and 1.01+0.02/−0.17 are found, suggesting that the stored energy may have been fully mitigated by each SPI, although mitigation efficiencies well below ITER and SPARC requirements for high energy pulses are still within the large uncertainties. Emis3D is also used to validate JOREK SPI simulations, and confirms improvements in matching experiment from changes to impurity modeling. Time-dependent toroidal peaking factors are calculated and discussed.