Resonance Raman (RR) peaks of and stretching modes and their higher harmonics have been observed superimposed on photoluminescence (PL) spectrum of thin films. Commercial fluorine doped thin films deposited by sputtering on glass and thin films deposited on Si by laser ablation have been studied. The dispersions of CO and OH stretching RR modes are ~ 600 cm-1/eV and 800 cm-1 respectively. The dispersion of the third harmonic of CO stretching mode is ~ 2000 cm-1/eV. Similar dispersion of RR peak of stretching modes and higher harmonics superimposed on PL spectra has been observed in Mo1-xFexO2 thin films and SiO2 bulk glass. Large dispersion of RR peaks seems to be a common property of oxides with impurities of and .
Near-bandgap Raman scattering was used to induce and study photostructural changes in AsxS100-x bulk glasses revealing a new photoinduced polymerization effect. Raman spectra were recorded also in off-resonant conditions allowing for a detailed comparison between the equilibrium glass structure and the metastable one induced by illumination. It is shown that in S-rich glasses structural changes involve the athermal scission of S8 rings and their polymerization to Sn chains. The fraction of bonds involved in this effect is surprisingly high, being one order of magnitude higher than the correspo…
The glassy structure of reactive supplementary cementitious materials (SCMs) and recycled glass: Contribution of XRD and Raman spectroscopy to their characterization
We report a study of long-range MoS2-substrate interaction using resonant Raman imaging. We observed a strong thickness-dependent peak shift of a Raman-forbidden mode that can be used as a new method of determining the thickness of multilayered MoS2 flakes. In addition, dependence of the Raman scattering intensity on thickness is explained by the interference enhancement theory. Finally, the resonant Raman spectra on different substrates are analysed.
In this work we present our findings performing low frequency Raman measurements over temperature in a tellurite-tungstate glass sample. The spectra could be fitted by using only two log-Gaussians, which suggests that quasi-elastic light scattering is negligible. The positions of the peaks have the same temperature behavior, being the higher frequency one refered as Boson Peak in literature. The similar temperature behavior and depolarization ratio indicates that the peaks may have the same origin, being linked to the tranversal and longitudinal vibrations of some unit.
Raman spectra of thin solid electrolyte films obtained by sputtering a lithium sulfate target in nitrogen plasma are measured and compared to ab initio electronic structure calculations for clusters composed of 28 atoms. Agreement between measured and calculated spectra is obtained when oxygen atoms are replaced by nitrogen atoms and when the nitrogen atoms form bonds with each other. This suggests that the incorporation of nitrogen during the sputtering process leads to structures in the film, which prevent crystallization of these thin film salt glasses.
The room-temperature Raman signatures from graphene layers on sapphire and glass substrates were compared with those from graphene on GaAs substrate and on the standard Si/SiO2 substrate, which served as a reference. It was found that while G peak of graphene on Si/SiO2 and GaAs is positioned at 1580 cm-1 it is down-shifted by ~5 cm-1 for graphene-on-sapphire (GOS) and, in many cases, splits into doublets for graphene-on-glass (GOG) with the central frequency around 1580 cm-1. The obtained results are important for graphene characterization and its proposed graphene applications in electronic …
About two hundred coloured glass beads (red, yellow, green, blue, white, black, pink, plum) were selected among the thousands of beads excavated on Mapungubwe hill and at K2, archaeological sites in the Limpopo valley South Africa, and have been studied with Raman scattering. The glass matrix of the beads was classified according to its Raman signature into 3 main sub-groups and corroded glass could also be identified. At least seven different chromophores or pigments (lazurite, lead tin yellow type II, Ca/Pb arsenate, chromate, calcium antimonate, Fe-S "amber" and a spinel) have been identifi…
We present an analysis of deep-UV Raman measurements of graphite, graphene and carbon nanotubes. For excitation energies above the strong optical absorption peak at the $M$ point in the Brillouin zone ($\approx 4.7\,\text{eV}$), we partially suppress double-resonant scattering processes and observe the two-phonon density of states of carbon nanomaterials. The measured peaks are assigned to contributions from LO, TO, and LA phonon branches, supported by calculations of the phonon dispersion. Moreover, we gain access to the infrared-active $E_{1u}$ mode in graphite. By lowering the excitation en…
We present a detailed calculation of intensities of two-phonon and four-phonon Raman peaks in graphene. Writing the low-energy hamiltonian of the interaction of electrons with the crystal vibrations and the electromagnetic field from pure symmetry considerations, we describe the system in terms of just a few independent coupling constants, considered to be parameters of the theory. The electron scattering rate is introduced phenomenologically as another parameter. The results of the calculation are used to extract information about these parameters from the experimentally measured Raman peak i…
We have developed a theory of Raman scattering with single and double spin flips of localized resident electrons and holes as well as nonequilibrium localized excitons in semiconductor perovskite crystals under optical excitation in the resonant exciton region. Scattering mechanisms involving localized excitons, biexcitons and exciton polaritons as intermediate states has been examined, the spin-flip Raman scattering by polaritons being a novel mechanism. The derived equations are presented in the invariant form allowing one for the analysis of the dependence of scattering efficiency on the po…
We present a practical method to compute the vibrational resonant Raman spectra in solids with delocalized excitations. We apply this approach to the study of tetrahedrous amorphous carbon. We determine the vibrational eigenmodes and eigenvalues using density functional theory in the local density approximation, and the Raman intensities using a tight binding approximation. The computed spectra are in good agreement with the experimental ones measured with visible and UV lasers. We analyze the Raman spectra in terms of vibrational modes of microscopic units. We show that, at any frequency, the…
The resonant Raman scattering in N-IR - UV range from amorphous hydrogenated carbon (a-C:H) reveal inclusions of trans-polyacetylene (trans-(CH)x) chains with approximate length of up to 120 C=C units and inclusions of poly(p-phenylene vinylene) (PPV) polymer chains. The PPV is evidenced by a strong dispersive mode at ca. 1175 cm-1. It was found that the Raman response from core Ag trans-(CH)x modes incorporated into a-C:H to changing excitation energy is identical to of free-standing chains thus facilitating identification of trans-(CH)x in complex carbonaceous materials spectra.
Knowledge of the electronic band structure of multiferroic oxides, crucial for the understanding and tuning of photo-induced effects, remains very limited even in the model and thoroughly studied BiFeO3. Here, we investigate the electronic band structure of BiFeO3 using Raman scattering with twelve different excitation wavelengths ranging from the blue to the near infrared. We show that resonant Raman signatures can be assigned to direct and indirect electronic transitions, as well as in-gap electronic levels, most likely associated to oxygen vacancies. Their temperature evolution establishes …
Resonant Raman spectroscopies beyond density-functional theory
École polytechnique fédérale de Lausanne（洛桑联邦理工学院）；University of Bremen（不来梅大学）；PSI Center for Scientific Computing, Theory and Data（瑞士保罗谢勒研究所科学计算、理论与数据中心）
We report non-resonant x-ray Raman scattering (XRS) measurements from hexagonal boron nitride for transferred momentum from 2 to 9 $\mathrmÅ^{-1}$ along directions both in and out of the basal plane. A symmetry-based argument, together with real-space full multiple scattering calculations of the projected density of states in the spherical harmonics basis, reveals that a strong pre-edge feature is a dominantly $Y_{10}$-type Frenkel exciton with no other \textit{s}-, \textit{p}-, or \textit{d}- components. This conclusion is supported by a second, independent calculation of the \textbf{q}-depen…
Raman spectroscopy is a useful experimental tool to investigate local deformation and structural changes in SiO$_2$-based glasses. Using a semi-classical modelling of Raman spectra in large samples of silica glasses, we show in this paper that shear plastic flow affects the Raman measurement in the upper part of the spectrum. We relate these changes to structural modifications, as well as a detailed analysis of the vibration modes computed in the same frequency range. These results opens the door to in situ monitoring of plastic damage in silica-based structures.
Microscopic mechanism of structural and volume relaxation below glass transition temperature in a soda-lime silicate glass revealed by Raman spectroscopy and its first principle calculations
Raman scattering on bulk AsxS1-x glasses showes that vibrational modes of As4S4 monomer first appear near x=0.38, and their concentration increases precipitously with increasing x, suggesting that the stoichiometric glass (x=0.40) is intrinsically phase seperated into small As-rich(As4S4) and large S-righ clusters. Support for the Raman-active vibrational modes of the orpiment-like and realgar-like nanophases is provided by ab-initio density functional theory calculations on appropriate clusters. Nanoscale phase seperation provides a basis for understanding the global maximum in the glass tran…
Layered inorganic materials, such as the transition metal dichalcogenides (TMDs), have attracted much attention due to their exceptional electronic and optical properties. Reliable synthesis and characterization of these materials must be developed if these properties are to be exploited. Herein, we present low-frequency Raman analysis of MoS2, MoSe2, WSe2 and WS2 grown by chemical vapour deposition (CVD). Raman spectra are acquired over large areas allowing changes in the position and intensity of the shear and layer-breathing modes to be visualized in maps. This allows detailed characterizat…
We report a detailed study of the strong near-field Raman scattering enhancement which takes place in tip-enhanced Raman scattering (TERS) in indium nitride. In addition to the well-known first-order optical phonons of indium nitride, near-field Raman modes, not detectable in the far-field, appear when approaching the plasmonic probe. The frequencies of these modes coincide with calculated energies of second order combinational modes consisting of optical zone center phonons and acoustic phonons at the edge of the Brillouin zone. The appearance of strong combinational modes suggests that TERS …
We calculate the resonant electronic Raman scattering for the Falicov-Kimball model near the Mott transition on a hypercubic lattice. The solution is exact, and employs dynamical mean field theory.
We perform tunable resonant Raman scattering on 17 semiconducting and 7 metallic singly resonant single wall carbon nanotubes. The measured scattering cross-section as a function laser energy provides information about a tube's electronic structure, the lifetime of intermediate states involved in the scattering process and also energies of zone center optical phonons. Recording the scattered Raman signal as a function of tube location in the microscope focal plane allows us to construct two-dimensional spatial maps of singly resonant tubes. We also describe a spectral nanoscale artifact we hav…
We calculate low-frequency Raman scattering from the confined acoustic phonon modes of CdS1-xSex nanoparticles embedded in borosilicate glass. The calculation of the Raman scattering by acoustic phonons in nanoparticles has been performed by using third-order perturbation theory. The deformation potential approximation is used to describe the electronphonon interaction. The Raman-Brillouin electronic density and the electron-phonon interaction are found to increases with decreasing size of nanoparticle. A good agreement between the calculated and reported low-frequency Raman spectra is found.
Raman spectra obtained by the inelastic scattering of light by crystalline solids contain contributions from first-order vibrational processes (e.g. the emission or absorption of one phonon, a quantum of vibration) as well as higher-order processes with at least two phonons being involved. At second order, coupling with the entire phonon spectrum induces a response that may strongly depend on the excitation energy, and reflects complex processes more difficult to interpret. In particular, excitons (i.e. bound electron-hole pairs) may enhance the absorption and emission of light, and couple str…
We present an exact solution for electronic Raman scattering in a single-band, strongly correlated material, including nonresonant, resonant and mixed contributions. Results are derived for the spinless Falicov-Kimball model, employing dynamical mean field theory; this system can be tuned through a Mott metal-insulator transition.
Resonance Raman scattering, which probes electrons, phonons and their interplay in crystals, is extensively used in two-dimensional materials. Here we investigate Raman modes in MoSe$_2$ at different laser excitation energies from 2.33 eV down to the near infrared 1.16 eV. The Raman spectrum at 1.16 eV excitation energy shows that the intensity of high-order modes is strongly enhanced if compared to the first-order phonon modes intensity due to resonance effects with the MoSe$_2$ indirect band gap. By comparing the experimental results with the two-phonon density of states calculated with dens…
The appearance of a broad peak at $\sim$1550 cm$^{-1}$ (G$^{-}$ peak) in carbon nanotube resonant Raman scattering spectra has been conventionally attributed to the presence of metallic nanotubes. Here, we present resonant Raman measurements on macroscopic nanotube ensembles enriched in armchair species prepared through density gradient ultracentrifugation. Our data clearly demonstrate that the broad G$^{-}$ mode is absent for armchair structures and appears only when the excitation laser is resonant with non-armchair "metals." Due to the large number ($\sim$10$^{10}$) of nanotubes across seve…
Phonon modes found in low frequency Raman scattering from $CdS_{1-x}Se_x$ nanocrystals embedded in borosilicate glass arising from confined acoustic phonons are investigated. In addition to the breathing modes and quadrupolar modes, two additional modes are found in the spectra. In order to assign the new modes, confined acoustic phonon frequencies are calculated using CFM, CSM and the Lamb model. Based on the ratio of the frequencies of the new modes to those of the quadrupolar mode, the new modes are assigned to first overtone of the quadrupolar mode (l=2, n=1) and l=1, n=0 torsional mode. T…
We systematically study the high-resolution and polarized Raman spectra of multilayer (ML) MoTe2. The layer-breathing (LB) and shear (C) modes are observed in the ultralow-frequency region, which are used to quantitatively evaluate the interlayer coupling in ML MoTe2 based on the linear chain model, in which only the nearest interlayer coupling is considered. The Raman spectra on three different substrates verify the negligible substrate effect on the phonon frequencies of ML MoTe2. Ten excitation energies are used to measure the high-frequency modes of N-layer MoTe2 (NL MoTe2; N is an integer…
Inclusions of sp-hybridised, trans-polyacetylene [trans-(CH)x] and poly(p-phenylene vinylene) (PPV) chains are revealed using resonant Raman scattering (RRS) investigation of amorphous hydrogenated carbon (a-C:H) films in the near IR - UV range. The RRS spectra of trans-(CH)x core Ag modes and the PPV CC-H phenylene mode are found to transform and disperse as the laser excitation energy \hbarωL is increased from near IR through visible to UV, whereas sp-bonded inclusions only become evident in UV. This is attributed to \hbarωL probing of trans-(CH)x chain inhomogeneity and the distribution of …
The weakly screened electron-hole interactions in an atomically thin semiconductor not only downshift its excitation spectrum from a quasiparticle one, but also redistribute excitation energies and wavefunction characters with profound effects on diverse modes of material response, including the exciton-phonon scattering processes accessible to resonant Raman measurements. Here we develop a first-principles framework to calculate frequency-dependent resonant Raman intensities that includes excitonic effects and goes beyond the Placzek approximation. We show how excitonic effects in MoS2 strong…
The temperature evolution of the resonant Raman scattering from high-quality bilayer 2H-MoS$_{2}$ encapsulated in hexagonal BN flakes is presented. The observed resonant Raman scattering spectrum as initiated by the laser energy of 1.96 eV, close to the A excitonic resonance, shows rich and distinct vibrational features that are otherwise not observed in non-resonant scattering. The appearance of 1$^{st}$ and 2$^{nd}$ order phonon modes is unambiguously observed in a broad range of temperatures from 5 K to 320 K. The spectrum includes the Raman-active modes, $i.e.$ E$_\textrm{1g}^{2}$($Γ$) and…
We present a detailed study of the Ti 3$d$ carriers at the interface of LaAlO$_3$/SrTiO$_3$ heterostructures by high-resolution resonant inelastic soft x-ray scattering (RIXS), with special focus on the roles of overlayer thickness and oxygen vacancies. Our measurements show the existence of interfacial Ti 3$d$ electrons already below the critical thickness for conductivity and an increase of the total interface charge up to a LaAlO$_3$ overlayer thickness of 6 unit cells before it levels out. By comparing stoichiometric and oxygen deficient samples we observe strong Ti 3$d$ charge carrier dop…
EXAFS and confocal Raman microscopy have been used to study 50SnF2.(20-x)SnO.30P2O5.xEr2O3 (x=0, 0.1, 0.25) glasses. EXAFS data reveal an average coordination of Sn to O of 1.5 in both undoped glass and Er-doped glass samples. The first coordination sphere of Er in glasses doped with Er2O3 was found to have 9 F atom neighbours at an average bond length of 2.292+/-0.005 Å, indicating that Er preferentially bonds with F. Raman spectra clearly show the emergence of orthophosphate Q0 units on addition of Er2O3. The saturation of Er solubility is found to be between 0.25 and 0.5 mol$\%$ Er2O3. An i…
We report two new first-order Raman modes in the spectra of few-layer MoS$_2$ at 286~cm$^{-1}$ and 471~cm$^{-1}$ for excitation energies above 2.4~eV. These modes appear only in few-layer MoS$_2$; therefore their absence provides an easy and accurate method to identify single-layer MoS$_2$. We show that these modes are related to phonons that are not observed in the single layer due to their symmetry. Each of these phonons leads to several nearly degenerate phonons in few-layer samples. The nearly degenerate phonons in few-layer materials belong to two different symmetry representations, showi…
Resonant Raman signatures of bright and momentum-dark exciton coupled by intervalley phonon scattering in monolayer WSe2
University of Münster（明斯特大学）；Center for Soft Nanoscience (SoN), University of Münster（明斯特大学软纳米科学中心）；Technical University of Munich（慕尼黑工业大学）；Walter Schottky Institut and Physics Department, Technical University of Munich（慕尼黑工业大学沃尔特·肖特基研究所与物理系）；MCQST, München（慕尼黑量子科学与技术中心）
Resonant soft X-ray Raman scattering measurements on NiO have been made at photon energies across the Ni 2p absorption edges. The details of the spectral features are identified as Raman scattering due to d-d and charge-transfer excitations. The spectra are interpreted within the single impurity Anderson model, including multiplets, crystal-field and charge-transfer effects. At threshold excitation, the spectral features consists of triplet-triplet and triplet-singlet transitions of the 3d8 configuration. For excitation energies corresponding to the charge-transfer region in the Ni 2p X-ray ab…
The electronic states at the direct band gap of monolayer WSe2 at the $K^+$ and $K^-$ valleys are related by time reversal and may be viewed as pseudo-spins. The corresponding optical interband transitions are governed by robust excitons. In double resonant Raman spectroscopy, we uncover that the 2s exciton state energy differs from the 1s state energy by exactly the energy of the combination of several prominent phonons. Superimposed on the exciton photoluminescence (PL) we observe the double resonant Raman signal. This spectrally narrow peak shifts with the excitation laser energy as incomin…
The Raman effect -- inelastic scattering of light by lattice vibrations (phonons) -- produces an optical response closely tied to a material's crystal structure. Here we show that resonant optical excitation of IR and Raman phonons gives rise to a Raman scattering effect that can induce giant shifts to the refractive index and induce new optical constants that are forbidden in the equilibrium crystal structure. We complete the description of light-matter interactions mediated by coupled IR and Raman phonons in crystalline insulators -- currently the focus of numerous experiments aiming to dyna…
We present a theoretical model to describe the double-resonant scattering process in arbitrary carbon nanotubes. We use this approach to investigate the defect-induced $D$ mode in CNTs and unravel the dependence of the $D$-mode frequency on the CNT diameter and on the energy of the resonant optical transition. Our approach is based on the symmetry of the hexagonal lattice and geometric considerations, hence the method is independent of the exact model that is chosen to describe the electronic band structure or the phonon dispersion. We finally clarify the diameter dependence of this Raman mode…
We study the effects of chemical bonding on Raman scattering from benzenethiol chemisorbed on silver clusters using time-dependent density functional theory (TDDFT). Raman scattering cross sections are computed using a formalism that employs analytical derivatives of frequency-dependent electronic polarizabilities, which treats both off-resonant and resonant enhancement within the same scheme. In the off-resonant regime, Raman scattering into molecular vibrational modes is enhanced by one order of magnitude and shows pronounced dependence on the orientation and the local symmetry of the molecu…
University of Warsaw（华沙大学）；Wrocław University of Science and Technology（弗罗茨瓦夫科技大学）；Peking University Shenzhen Graduate School（北京大学深圳研究生院）；CNRS（法国国家科学研究中心）
In order to deepen in the knowledge of the vibrational properties of 2-dimensional MoS2 atomic layers, a complete and systematic Raman scattering analysis has been performed using both bulk single crystal MoS2 samples and atomically thin MoS2 layers. Raman spectra have been measured under non-resonant and resonant conditions using seven different excitation wavelengths from near-infrared (NIR) to ultraviolet (UV). These measurements have allowed to observe and identify 41 peaks, among which 22 have not been previously experimentally observed for this compound, characterizing the existence of d…
Understanding the stability limitations and defect formation mechanisms in 2D magnets is essential for their utilization in spintronic and memory technologies. Here, we correlate defects in mono- to multilayer CrSBr with their structural, vibrational and magnetic properties. We use resonant Raman scattering to reveal distinct vibrational defect signatures. In pristine CrSBr, we show that bromine atoms mediate vibrational interlayer coupling, allowing for distinguishing between surface and bulk defect modes. We show that environmental exposure causes drastic degradation in monolayers, with the …
We develop a general, fully quantum mechanical theory of Raman scattering from first principles in terms of many-body correlation functions. In order to arrive at expressions that are practically useful in the context of condensed matter physics, we adopt the Lehmann-Symanzik-Zimmermann reduction formula from high-energy physics and formulate in the modern language of many-body perturbation theory. This enables us to derive a general and practically useful expression for the Raman scattering rate in terms of quantities that can be computed \textit{ab initio}. Our work paves the way toward a co…
The nature of the interface in lateral heterostructures of 2D monolayer semiconductors including its composition, size, and heterogeneity critically impacts the functionalities it engenders on the 2D system for next-generation optoelectronics. Here, we use tip-enhanced Raman scattering (TERS) to characterize the interface in a single-layer MoS2/WS2 lateral heterostructure with a spatial resolution of 50 nm. Resonant and non-resonant TERS spectroscopies reveal that the interface is alloyed with a size that varies over an order of magnitude-from 50-600 nm-within a single crystallite. Nanoscale i…
A detailed pressure-dependence study of the low-energy excitations of glassy As2S3 is reported over a wide pressure range, up to 10 GPa. The spectral features of Boson peak are analysed as a function of pressure. Pressure effects on the Boson peak are manifested as an appreciable shift of its frequency to higher values, a suppression of its intensity, as well as a noticeable change of its asymmetry leading to a more symmetric shape at high pressures. The pressure-induced Boson peak frequency shift agrees very well with the predictions of the soft potential model over the whole pressure range s…
Resonant Raman spectra (RRS) of O-H and O-D vibration and libration modes, their combinations and higher harmonics have been observed in LiTaO3 polycrystalline thin films. RRS peaks are superimposed on photoluminescence (PL) spectrum. Monochromatic light from a xenon lamp is used as excitation source. PL spectrum shows two broad peaks, first near the band gap in UV (4.4-4.8eV) and another in the sub band gap region (< 4.0 eV). Band gap PL along with RRS peaks are reported for the first time. Photoluminescence excitation spectrum (PLE) shows a peak at 4.8 eV. Peak positions and full width at ha…
Transition metal dichalcogenides (TMDs) are layered materials which show excellent potential for nanoelectronic and optoelectronic applications. However, as many of the exciting features of these materials are controlled by the anharmonic effects, a proper understanding of the phonon properties and anharmonicity associated with these materials is essential for the proposed applications to be realized. We present here a comprehensive study on the phonon properties of two different TMDs; viz., MoS2 and MoTe2, as a function of temperature, laser excitations, and polarization, as well as flake-thi…
Excitation of four coherent phonon modes of different symmetries has been realized in copper metaborate CuB$_2$O$_4$ via impulsive stimulated Raman scattering (ISRS). Phonons were detected by monitoring changes in the linear optical birefringence using the balanced-detection (BD) technique. We compare the results of BD-ISRS experiment to the polarized spontaneous Raman scattering spectra. We show that the agreement between the two sets of data obtained by these allied techniques in a wide phonon frequencies range of 4-14 THz can be achieved by rigorously taking into account the symmetry of the…
The interaction between excitons and phonons in semiconductor nanocrystals plays a crucial role in the exciton energy spectrum and dynamics, and thus in their optical properties. We investigate the exciton2 phonon coupling in giant-shell CdSe/CdS core-shell nanocrystals via resonant Raman spectroscopy. The Huang-Rhys parameter is evaluated by the intensity ratio of the longitudinal-optical (LO) phonon of CdS with its first multiscattering (2LO) replica. We used four different excitation wavelengths in the range from the onset of the CdS shell absorption to well above the CdS shell band edge to…
We present measurements of the $D''$ Raman mode in graphene and carbon nanotubes at different laser excitation energies. The Raman mode around 1050 - 1150\,cm$^{-1}$ originates from a double-resonant scattering process of longitudinal acoustic (LA) phonons with defects. We investigate its dependence on laser excitation energy, on the number of graphene layers and on the carbon nanotube diameter. We assign this Raman mode to so-called 'inner' processes with resonant phonons mainly from the $Γ-K$ high-symmetry direction. The asymmetry of the $D''$ mode is explained by additional contributions fr…
Resonantly-enhanced Raman response in graphene-capped bismuthene on SiC
Universität Würzburg（维尔茨堡大学）；Würzburg-Dresden Cluster of Excellence ctd.qmat, Universität Würzburg（维尔茨堡大学 würtzburg-dresden 卓越集群 ctd.qmat）；Sapienza University of Rome（罗马第一大学）；RWTH Aachen University（亚琛工业大学）；Forschungszentrum Jülich（于利希研究中心）；Institut für Theoretische Physik und Astrophysik, Universität Würzburg（维尔茨堡大学理论与天体物理研究所）；TUD Dresden University of Technology（德累斯顿工业大学）
