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At least 361 records · Page 20

Frontier Orbital Degeneracy: A New Concept for Tailoring the Magnetic State in Organic Semiconductor Adsorbates

Kondo resonances in molecular adsorbates are an important building block for applications in the field of molecular spintronics. Here, we introduce the novel concept of using frontier orbital degeneracy for tailoring the magnetic state, which is demonstrated for the case of the organic semiconductor 1,4,5,8,9,11-Hexaazatriphenylenehexacarbonitrile (HATCN, C 18 N 12 ) on Ag(111). Low-temperature scanning tunneling microscopy/spectroscopy (LT-STM/STS) measurements reveal the existence of two types of adsorbed HATCN molecules with distinctly different appearances and magnetic states, as evident from the presence or absence of an Abrikosov-Suhl-Kondo resonance. Our DFT results show that HATCN on Ag(111) supports two almost isoenergetic states, both with one excess electron transferred from the Ag surface, but with magnetic moments of either 0 or 0.65 μ B . Therefore, even though all molecules undergo charge transfer of one electron from the Ag substrate, they exist in two different molecular magnetic states that resemble a free doublet or an entangled spin state. We explain how the origin of this behavior lies in the twofold degeneracy of the lowest unoccupied molecular orbitals of gas phase HATCN, lifted upon adsorption and charge-transfer from Ag(111). In conclusion, our combined STM and DFT study introduces a new pathway to tailoring the magnetic state of molecular adsorbates on surfaces, with significant potential for spintronics and quantum information science.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Readout of Oriented Triplet Excitons in Linear Acenes via Room-Temperature Electrically Detected Magnetic Resonance

In this study, optically generated molecular spin centers offer an attractive platform for room-temperature spintronic and quantum applications. The linear acene family of molecules are especially good candidates due to their efficient generation of highly polarized triplet excitons via singlet fission. However, the direct detection and manipulation of these spin centers in thin films via the electrical means desirable for ultimate microelectronic devices has proven challenging. In particular, highly oriented triplet features have previously been detected in crystalline anthracene but longer acenes reveal only doublet features in Electrically-Detected Magnetic Resonance (EDMR). In this work we present EDMR spectra of highly oriented triplet excitons in pentacene for the first time, using a host-guest style device made of tetracene and pentacene. The guest acts as an energetic trap site, permitting the isolation and detection of molecular triplets at room temperature. Modeling of these results shows that the observed resonance features correspond to triplet sublevel transitions on isolated pentacene guest molecules. Rotation of the applied field confirms the tendency of the linear acenes to self-orient with the longest molecular axis perpendicular to the device substrate. Lastly, we find the disappearance of resonant triplet features in the neat acenes is not primarily due to the effects of exciton delocalization, but a broader mechanism of spin relaxation primarily influenced by exciton diffusivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Excited State Exchange Control of Photoinduced Electron Spin Polarization in Electronic Ground States

Ground-state electron spin polarization (ESP) is generated in radical elaborated (bpy)Pt(CAT-NN) and (bpy)Pt(CAT- p -Me 2 PhMe 2 -NN) (bpy = 5,5'-di- tert -butyl-2,2'-bipyridine, CAT = 3- tert -butylcatecholate, p -Ph = para -phenylene, NN = nitronylnitroxide). Photoexcitation produces an exchange-coupled, three-spin, charge-separated doublet 2 S 1 (S = chromophore excited spin singlet configuration) excited state that rapidly decays to a 2 T 1 (T = chromophore excited spin triplet configuration) excited state. The SQ-bridge-NN bond torsions affect the magnitude of the excited state exchange interaction ( J SQ-NN ), which determines the 2 T 1 – 4 T 1 energy gap. Ground state ESP is dependent on the magnitude of J SQ-NN , and we postulate that this results from differences in 2 T 1 and 4 T 1 state mixing. Mechanisms that lead to the rapid transfer of the excited state ESP to the ground state are discussed. Although subnanosecond 2 T 1 state lifetimes are measured optically in solution, the ground state ESP decays very slowly at 20 K and is observable for more than a millisecond.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Vibrational Fermi Resonance in Atomically Thin Black Phosphorus

Fermi resonance is a phenomenon involving the hybridization of two coincidentally quasi-degenerate states that is observed in the vibrational or electronic spectra of molecules. Despite numerous examples in molecular systems, vibrational Fermi resonances in dispersive semiconducting systems remain largely unexplored due to the rarity of occurrence. Here we report a vibrational Fermi resonance in atomically thin black phosphorus. The Fermi resonance arises via anharmonic mixing of a fundamental Raman mode and a Davydov component of an infrared mode, leading to a doublet with mixed character. The extent of Fermi coupling can be modulated by the application of external biaxial strain. The consequences of Fermi hybridization are revealed by electronic resonance effects in the thickness-dependent and excitation-wavelength-dependent Raman spectrum, which is predicted by ab initio hybrid functional simulations including excitonic interactions. This work reveals new insight into electron–phonon coupling in black phosphorus and demonstrates a novel method for modulating Fermi resonances in 2D semiconductors.

74 ATOMIC AND MOLECULAR PHYSICS↗

Exchange Coupling Determines Metal-Dependent Efficiency for Iron- and Cobalt-Catalyzed Photochemical CO 2 Reduction

Catalysts promoting multielectron charge delocalization offer selectivity for the CO 2 reduction reaction (CO 2 RR) over the competing hydrogen evolution reaction. Here, we show metal–ligand exchange coupling as an example of charge delocalization that can determine the efficiency for photocatalytic CO 2 RR. A comparative evaluation of iron and cobalt complexes supported by the redox-active ligand tpyPY2Me establishes that the two-electron reduction of [Co(tpyPY2Me)] 2+ ([Co] 2+ ) occurs at potentials 770 mV more negative than the [Fe(tpyPY2Me)] 2+ ([Fe] 2+ ) analogue by maximizing the exchange coupling in the latter compound. The positive shift in the reduction potential promoted by metal–ligand exchange coupling drives [Fe] 2+ to be among the most active and selective molecular catalysts for photochemical CO 2 RR reported to date, maintaining up to 99% CO product selectivity with total turnover numbers (TONs) and initial turnover frequencies exceeding 30,000 and 900 min –1 , respectively. In contrast, [Co] 2+ shows much lower CO 2 RR activity, reaching only ca. 600 TON at 83% CO product selectivity under similar conditions accompanied by rapid catalyst decomposition. Further, the spin density plots of the two-electron reduced [Co] 0 complex implicate a paramagnetic open-shell doublet ground state compared to the diamagnetic open-shell singlet ground state of reduced [Fe] 0 , rationalizing the observed negative shift in two-electron reduction potentials from the [M] 2+ species and lowered CO 2 RR efficiency for the cobalt complex relative to its iron congener. This work emphasizes the contributions of multielectron metal–ligand exchange coupling in promoting effective CO 2 RR and provides a starting point for the broader incorporation of this strategy in catalyst design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effect of Co/SiO 2 Single-Site Heterogeneity on Small Alkane Dehydrogenation Kinetics

Atomically dispersed, high-spin Co(II) atoms in distorted tetrahedral coordination to an amorphous silica (am-SiO 2 ) support, and more recently in zeolite frameworks, are active and selective for light alkane dehydrogenation. This paper investigates how variations in the geometry of the active sites affect the ethane dehydrogenation activity of atomically dispersed Co(II) on an am-SiO 2 support. We generate a distribution of sites and determine the geometric parameters that exhibit the strongest correlation with the coordination geometry and activity of the metal atom by means of linear dimensionality reduction techniques. We perform electronic structure calculations and microkinetic modeling and deduce the mechanism and kinetics for a representative sample of sites. Irrespective of the active site geometry, the rate of ethane dehydrogenation is governed by the β-hydride elimination, which involves quartet-doublet spin-crossing and proceeds adiabatically due to strong spin-orbit coupling. Informed by the complete microkinetic analysis of the sites, we derive the reduced rate expression as a function of three site-dependent quantities. We show that these site-dependent quantities correlate with the energy of formation of the ethyl intermediate that forms via C-H bond activation. This correlation allows us to derive the site-averaged rate for the entire distribution of sites. Among various sites, the tri-coordinate and planar tetra-coordinate Co sites exhibit higher Lewis acidity than the tetrahedral sites, and consequently, higher initial rates. Finally, we discuss the implications for more active catalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Electrical Control of the Nuclear Spin States of Rare-Earth Adatoms

Rare-earth adatoms on surfaces have been studied for potential atomic-scale magnetic storage, quantum sensing, and quantum computing applications. Despite accumulating experimental efforts, a comprehensive description of the electronic configurations of the adatoms remains elusive. Here, we investigate two charge states and several electronic configurations, including 5d and 6s valence shells, for a Sm adatom on a MgO substrate using multiconfigurational ab initio methods, for the possibility of using the Sm nuclear spin levels as qubits. For the configurations in a neutral charge state, we find that the electronic ground state is a singlet, and thus the hyperfine interaction associated with the 147 Sm nucleus is absent, which may greatly enhance nuclear spin coherence time. The degeneracy of the nuclear levels is lifted by the nuclear quadrupole interaction. We show that the splitting of the nuclear levels can be controlled by a static electric field, and that Rabi oscillations between the nuclear levels can be induced by a time-dependent electric field. For the configurations in a singly charged state, electronic Kramers doublets are formed. The electronic configurations including an unpaired 6s orbital exhibit a strong hyperfine Stark effect due to a large Fermi contact contribution to the hyperfine interaction. In these configurations, electric-field-induced Rabi oscillations between the electronic-nuclear levels can occur at frequencies up to 3 orders of magnitude higher than those for the neutral charge state. The proposed system may be experimentally observed within scanning tunneling microscopy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Discrete Open-Shell Tris(bipyridinium radical cationic) Inclusion Complexes in the Solid State

In the solid state the properties of organic radicals depend heavily on radical-radical interactions that are influenced by the superstructure of the crystalline phase. Here, we report the synthesis and characterization of a substituted tetracationic cyclophane, cyclobis(paraquat-p-1,4- dimethoxyphenylene), and outline how its bisradical dicationic redox state associates with the methyl viologen radical cation (MV •+ ) to give a trisradical tricationic inclusion complex. The (super)structures of the reduced cyclophane and this 1:1 complex in the solid-state deviate from the analogous (super)structures observed for the reduced state of cyclobis(paraquat-p-phenylene) and that of its trisradical tricationic complex. Titration experiments with a range of guests reveal that the methoxy substituents on the para-xylenyl do not influence significantly of the binding affinity of the cyclophane for small neutral guests, whereas the affinity decreases by an order of magnitude for larger radical cationic guests such as MV •+ . X-Ray diffraction reveals that the solid- state structures of the tricationic trisradical complexes to be a discrete entity with weak intermolecular orbital overlap between the neighboring complexes. Transient nutation EPR experiment and DFT calculations confirm that the complex has a doublet spin configuration in the ground state as a result of the strong orbital overlap within the complex, while the quartet-state spin configuration is higher in energy and so is inaccessible at ambient temperature. The superconducting quantum interference device (SQUID) measurement reveals that trisradical tricationic complexes interact antiferromagnetically (J/k = - 2.33 K) and form a 1D Heisenberg antiferromagnetic chain along the a-axis in the crystal. Furthermore, these results offer new insights into the design and synthesis of organic magnetic materials based on host-guest inclusion complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Large Hyperfine Coupling Arising from Pseudo- 2 S Ground States in a Series of Lutetium(II) Metallocene Complexes

The synthesis of molecules with strong coupling between electronic and nuclear spins represents an important challenge in molecular quantum information science. Here, we report the synthesis and characterization of the divalent lutetium metallocene complexes Lu(Cp Me 5 )(Cp iPr 5 ) (Cp Me 5 = pentamethylcyclopentadienyl; Cp iPr 5 = pentaisopropylcyclopentadienyl), Lu(Cp iPr 4 Et ) 2 (Cp iPr 4 Et = ethyltetraisopropylcyclopentadienyl), and Lu(Cp iPr 4 ) 2 (Cp iPr 4 = tetraisopropylcyclopentadienyl). The molecular structures of these complexes, as determined through singlecrystal X-ray diffraction, feature a common bent sandwich geometry, with average Cp–Lu–Cp angles ranging from 159.9° to 152.6°. Analysis of continuous-wave electron paramagnetic resonance (EPR) spectra for the complexes reveals nearly isotropic g tensors with only a slight deviation from that of a free electron. Moreover, an extremely large splitting of the eight-line spectra indicates the presence of strong hyperfine coupling, and simulations provide isotropic hyperfine coupling constants of A iso = 4.38, 4.30, and 4.17 GHz across the series, where the value of A iso is found to decrease as the Cp–Lu–Cp angle becomes more acute. Notably, these values are the largest yet observed for any lanthanide complex. Moreover, EPR and computational analysis show that the large values of A iso stem from large s-orbital character up to 41.2% in the corresponding singly occupied molecular orbitals. To our knowledge, this degree of s-character in a molecular orbital is the largest yet reported for an open-shell isolable complex. These results outline a general strategy toward the isolation of paramagnetic molecules with strong hyperfine coupling and highly isotropic doublet electronic ground states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Charge-Transfer States Enable Spin-Selective Formation of Quartet State Qudits in Luminescent Radical-Chromophore Dyads

Luminescent tris(2,4,6-trichlorophenyl)methyl (TTM) radicals are promising doublet emitters that have been used to generate spin-optical interfaces in molecular electron spin qudits. In particular, photoexcitation of covalent TTM-chromophore dyads can generate quartet spin states that can be detected via photoluminescence. However, the mechanism of quartet spin initialization is complicated by competing charge-transfer (CT) and energy-transfer (EnT) pathways between the radical and the chromophore. Here, we demonstrate the role of CT intermediates by engineering a covalent dyad of TTM and naphthalene-(1,4:5,8)-bis(dicarboximide) (NDI), a well-known electron acceptor chromophore. Transient absorption spectroscopy indicates that photoexcitation of TTM results in ultrafast electron transfer from 2* TTM to NDI, which kinetically outcompetes EnT. Electron paramagnetic resonance spectroscopy reveals that charge recombination proceeds via spin–orbit charge-transfer intersystem crossing to generate 3* NDI, followed by spin mixing with 2TTM to form the quartet state. Furthermore, this process uniquely spin-polarizes the quartet state, providing fundamental design principles to purify the initial wave function for quantum information processing.

Charge transfer↗

Role of the Character of the Excited State of Singly Reduced Rh 2 (II,II) Intermediates on Photocatalytic Activity

Singly reduced intermediates have recently been implicated as photoactive intermediates in a number of important reactions; however, their photophysical properties remain poorly understood. A series of dirhodium(II,II) complexes, cis-[Rh 2 (p-R-Form) 2 (bncn) 2 ] 2+ (bncn = benzo[c]cinnoline; p-R-Form = N,N′-di-p-R-phenylformamidinate), where R = −OCH 3 (1), −CH 3 (2), −H (3), −F (4), −Cl (5), and −CF 3 (6), and their respective radical anions were prepared and their excited state properties were investigated. Complex 3 acted as a singlemolecule photocatalyst for H 2 production with red light. Substitution on the formamidinate ligands in 1−6 affected the energy of the Rh 2 (δ*)/Form(π,nb) highest occupied molecular orbital (HOMO), consistent with the metal/ligand-to-ligand charge transfer ( 1 ML-LCT) absorption maxima and the 3 ML-LCT excited state lifetime, ranging from 1.6 ns in 1 to 54 ns in 6 in CH 3 CN. The highest turnover number for photocatalytic H 2 evolution was observed for 3, and the lowest values were for 1 and 6. The radical anion, [Rh 2 ] − , formed during photocatalysis, was shown to absorb a photon and undergo a second reduction. The lifetimes of the doublet excited states of [3] − and [6] − were 0.49 and 0.24 ns, respectively. Calculations showed that the lowest energy excited state in [3] − was 2 ML-LCT, whereas that in [6] − was a bncn − → Rh 2 (σ*) ligand-to-metal charge transfer ( 2 LMCT) state. The 2 LMCT state stabilized across the series from [1] − to [6] − , pointing at its role in modulating the photophysical properties. This work highlights the importance of the reductive quenching of [Rh 2 ] − and the generation of the doubly reduced species to effectively catalyze hydrogen evolution.

Absorption↗

Gas-Phase Formation of Fulvenallene (C 7 H 6 ) via the Jahn–Teller Distorted Tropyl (C 7 H 7 ) Radical Intermediate under Single-Collision Conditions

The fulvenallene molecule (C 7 H 6 ) has been synthesized via the elementary gas-phase reaction of the methylidyne radical (CH) with the benzene molecule (C 6 H 6 ) on the doublet C 7 H 7 surface under single collision conditions. The barrier-less route to the cyclic fulvenallene molecule involves the addition of the methylidyne radical to the π-electron density of benzene leading eventually to a Jahn–Teller distorted tropyl (C 7 H 7 ) radical intermediate and exotic ring opening–ring contraction sequences terminated by atomic hydrogen elimination. The methylidyne-benzene system represents a benchmark to probe the outcome of the elementary reaction of the simplest hydrocarbon radical—methylidyne—with the prototype of a closed-shell aromatic molecule—benzene—yielding nonbenzenoid fulvenallene. Combined with electronic structure and statistical calculations, this bimolecular reaction sheds light on the unusual reaction dynamics of Hückel aromatic systems and remarkable (polycyclic) reaction intermediates, which cannot be studied via classical organic, synthetic methods, thus opening up a versatile path to access this previously largely obscure class of fulvenallenes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Direct laser writing of volumetric gradient index lenses and waveguides

Abstract Direct laser writing (DLW) has been shown to render 3D polymeric optical components, including lenses, beam expanders, and mirrors, with submicrometer precision. However, these printed structures are limited to the refractive index and dispersive properties of the photopolymer. Here, we present the subsurface controllable refractive index via beam exposure (SCRIBE) method, a lithographic approach that enables the tuning of the refractive index over a range of greater than 0.3 by performing DLW inside photoresist-filled nanoporous silicon and silica scaffolds. Adjusting the laser exposure during printing enables 3D submicron control of the polymer infilling and thus the refractive index and chromatic dispersion. Combining SCRIBE’s unprecedented index range and 3D writing accuracy has realized the world’s smallest (15 µm diameter) spherical Luneburg lens operating at visible wavelengths. SCRIBE’s ability to tune the chromatic dispersion alongside the refractive index was leveraged to render achromatic doublets in a single printing step, eliminating the need for multiple photoresins and writing sequences. SCRIBE also has the potential to form multicomponent optics by cascading optical elements within a scaffold. As a demonstration, stacked focusing structures that generate photonic nanojets were fabricated inside porous silicon. Finally, an all-pass ring resonator was coupled to a subsurface 3D waveguide. The measured quality factor of 4600 at 1550 nm suggests the possibility of compact photonic systems with optical interconnects that traverse multiple planes. SCRIBE is uniquely suited for constructing such photonic integrated circuits due to its ability to integrate multiple optical components, including lenses and waveguides, without additional printed supports.

36 MATERIALS SCIENCE↗

Observation of magnetic adatom-induced Majorana vortex and its hybridization with field-induced Majorana vortex in an iron-based superconductor

Braiding Majorana zero modes is essential for fault-tolerant topological quantum computing. Iron-based superconductors with nontrivial band topology have recently emerged as a surprisingly promising platform for creating distinct Majorana zero modes in magnetic vortices in a single material and at relatively high temperatures. The magnetic field-induced Abrikosov vortex lattice makes it difficult to braid a set of Majorana zero modes or to study the coupling of a Majorana doublet due to overlapping wave functions. Here we report the observation of the proposed quantum anomalous vortex with integer quantized vortex core states and the Majorana zero mode induced by magnetic Fe adatoms deposited on the surface. We observe its hybridization with a nearby field-induced Majorana vortex in iron-based superconductor FeTe 0.55 Se 0.45 . We also observe vortex-free Yu-Shiba-Rusinov bound states at the Fe adatoms with a weaker coupling to the substrate, and discover a reversible transition between Yu-Shiba-Rusinov states and Majorana zero mode by manipulating the exchange coupling strength. The dual origin of the Majorana zero modes, from magnetic adatoms and external magnetic field, provides a new single-material platform for studying their interactions and braiding in superconductors bearing topological band structures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Spin/valley pumping of resident electrons in WSe2 and WS2 monolayers

Abstract Monolayers of transition metal dichalcogenides are ideal materials to control both spin and valley degrees of freedom either electrically or optically. Nevertheless, optical excitation mostly generates excitons species with inherently short lifetime and spin/valley relaxation time. Here we demonstrate a very efficient spin/valley optical pumping of resident electrons in n-doped WSe 2 and WS 2 monolayers. We observe that, using a continuous wave laser and appropriate doping and excitation densities, negative trion doublet lines exhibit circular polarization of opposite sign and the photoluminescence intensity of the triplet trion is more than four times larger with circular excitation than with linear excitation. We interpret our results as a consequence of a large dynamic polarization of resident electrons using circular light.

36 MATERIALS SCIENCE↗

Slow magnetic relaxation in a europium(II) complex

Single-ion anisotropy is vital for the observation of Single-Molecule Magnet (SMM) properties (i.e., a slow dynamics of the magnetization) in lanthanide-based systems. In the case of europium, the occurrence of this phenomenon has been inhibited by the spin and orbital quantum numbers that give way to J = 0 in the trivalent state and the half-filled population of the 4f orbitals in the divalent state. Herein, by optimizing the local crystal field of a quasi-linear bis(silylamido) Eu II complex, the [Eu II (N{SiMePh 2 } 2 ) 2 ] SMM is described, providing an example of a europium complex exhibiting slow relaxation of its magnetization. This behavior is dominated by a thermally activated (Orbach-like) mechanism, with an effective energy barrier of approximately 8 K, determined by bulk magnetometry and electron paramagnetic resonance. Ab initio calculations confirm second-order spin-orbit coupling effects lead to non-negligible axial magnetic anisotropy, splitting the ground state multiplet into four Kramers doublets, thereby allowing for the observation of an Orbach-like relaxation at low temperatures.

36 MATERIALS SCIENCE↗

Controlling crystal-electric field levels through symmetry-breaking uniaxial pressure in a cubic super heavy fermion

Abstract YbPtBi is one of the heavy-fermion systems with largest Sommerfeld coefficient γ and is thus classified as a ‘super’-heavy fermion material. In this work, we resolve the long-debated question about the hierarchy of relevant energy scales, such as crystal-electric field (CEF) levels, Kondo and magnetic ordering temperature, in YbPtBi. Through measurements of the a.c. elastocaloric effect and generic symmetry arguments, we identify an elastic level splitting that is unambiguously associated with the symmetry-allowed splitting of a quartet CEF level. This quartet, which we identify to be the first excited state at Δ/ k B ≈ 1.6 K above the doublet ground state at ambient pressure, is well below the proposed Kondo temperature T K ≈ 10 K. Consequently, this analysis of the energy scheme can provide support models that predict that the heavy electron mass is a result of an enhanced degeneracy of the CEF ground state, i.e., a quasi-sextet in YbPtBi. At the same time, our study shows the potential of the a.c. elastocaloric effect to control and quantify strain-induced changes of the CEF schemes, opening a different route to disentangle the CEF energy scales from other relevant energy scales in correlated quantum materials.

36 MATERIALS SCIENCE↗

Field-tunable valley coupling in a dodecagonal semiconductor quasicrystal

Quasicrystals are characterized by atomic arrangements having long-range order without periodicity. Van der Waals bilayers provide an opportunity to controllably vary the atomic alignment between two layers from a periodic moiré crystal to an aperiodic quasicrystal. Here, in this work, we reveal that in a dodecagonal WSe 2 quasicrystal, two separate valleys in separate layers are brought arbitrarily close in momentum space through higher-order Umklapp scatterings. A modest perpendicular electric field is then sufficient to induce strong interlayer valley hybridization, manifested as another hybrid excitonic doublet. Concurrently, we observe the disappearance of the trion that exists at low field, which we attribute to a modified spatial distribution of the wavefunction due to the quasicrystal potential. This is possibly a precursor to localization. Our findings highlight the ability of incommensurate systems to bring any pair of momenta into close proximity, thereby introducing opportunities for valley engineering.

electronic properties and materials↗