Amorphous solids represent the extreme limit of structural disorder, in which broken translational symmetry challenges the Bloch description of electronic states. In strictly two dimensions (2D), lattice disorder should lead to complete localization electronic states. In stark contrast, here we show that 2D monolayer amorphous carbon (MAC)– a chemically uniform but maximally disordered random network of π-conjugated carbon retains a quantum-critical extended state at the band centre (E ∼ 0)despite the absence of crystalline order. This is confirmed by correlating lattice disorder with local wavefunction structure in atomic-resolution scanning tunnelling microscopy and spectroscopy. Our statistical analysis of the wavefunction probability density reveals a diverging correlation length and verifies the multifractal scaling relation η = −∆ 2 – characteristic of Anderson criticality– in agreement with atomistic tight-binding calculations. We attribute the presence of this critical state to an emergent chiral symmetry of the continuous random network, described by a Wess-Zumino Witten (WZW) topological term that protects the band-centre. Our results thus identify topological disorder as stabilizing agent for quantum criticality in a strictly 2D amorphous system.

We investigate the emergence of correlated electron phases in rhombohedral N-layer graphene due to two-valley Coulomb interactions within a low-energy k · p framework. Analytical expressions for Lindhard susceptibilities in intra- and intervalley channels are derived, and the critical temperatures for phase transitions are estimated using both the random phase approximation (RPA) and the parquet approximation (PA). Within RPA, only Stoner and intervalley coherent (IVC) phases are supported, while the PA reveals a richer phase structure including particle-particle (PP) channel instabilities. We establish a general scaling law for the critical temperature with respect to layer number N, highlighting an upper bound as N →∞, and demonstrate a non-monotonic decrease of the critical temperature with increasing chemical potential. The PA uncovers the role of interaction symmetry: SU(4)-symmetric interactions favor intervalley Stoner order in the density channel, whereas SU(2) × SU(2)-symmetric interactions permit a broader set of phases. A crossover in the dominant instability occurs in the particle-hole channel at a critical layer number, suggesting the emergence of magnetic or IVC phases in thicker systems. We also identify conditions under which pair-density wave (PDW) order could form in the PP channel, though its physical realization may be constrained.

Spin defects in two-dimensional materials hold significant potential for quantum information technologies and sensing applications. The negatively charged boron vacancy (VB-) in hexagonal boron nitride (hBN) has attracted considerable attention as a quantum sensor due to its demonstrated sensitivity to temperature, magnetic fields, and pressure.1 However, its applications have thus far been limited by inherently dim photoluminescence (PL). By fabricating a van der Waals heterostructure with a sensitizing donor layer, lead iodide (PbI2), we effectively enhance the PL intensity from the VB- by 5-45x, while maintaining compatibility with other heterostructures and vdW optoelectronic platforms. The type-I band alignment at the heterojunction enables efficient exciton migration while suppressing back-electron transfer, and the strong spectral overlap between the PbI2 emission and defect absorption supports efficient fluorescence resonance energy transfer. Ab initio density functional theory (DFT) predicts a photon-ratcheting mechanism that boosts absorption and emission while maintaining magnetic resonance (ODMR) contrast through minimal hybridization. Experimentally, the heterostructure exhibits enhanced continuous-wave ODMR sensitivity and functions as a precise probe of external magnetic fields. This work establishes a proof-of-concept for amplifying weak defect signals in nanomaterials, highlighting a new strategy for engineering their optical and magnetic responses.

This study investigates spin decoherence in large disordered carbon nanosphere (CNS) particles with a focus on predicting and extending the electron spin qubit decoherence time (T2). We present and experimentally validate a simple analytical model that predicts T2 and reveal how defects─such as carbon vacancies, hydrogen chemisorption, and substitutional impurities─along with their concentration and distribution, impact T2. This model offers insights into the interplay among spin density distribution, structural defects, and isotopic composition, demonstrating the role of defect minimization through controlled annealing in enhancing spin coherence. Through comparison with experimental data, we validate our model and demonstrate that spin polarization in the CNS is likely evenly distributed over a characteristic region of approximately 5 nm for T2 ∼ 200 ns. Based on these findings, we propose a synthetic protocol involving a confined annealing procedure that extends the spin lifetime in the CNS to up to 362 ns. With observed improvements in T2, our findings provide valuable guidelines for optimizing electron spin coherence time in quantum devices and spintronic applications.

We present a comprehensive first-principles study of the magnetoresistance in ZrSiX (X= S, Se, Te) topological nodal-line semimetals. Our study demonstrates that all primary features of the experimentally measured magnetoresistance in these materials are captured by our calculations, including the unusual butterfly-shaped anisotropic magnetoresistance. This anisotropic magnetoresistance can be accurately reproduced using the semiclassical Boltzmann transport theory without introducing any information on the topological nature of bands or the concepts of topological phase transition. Considering the complex structure of the Fermi surface in these topological materials, we develop a theoretical description explaining the features observed in magnetoresistance measurements. Additionally, the atypical Hall resistance can be interpreted by the same semiclassical approach. Our findings establish magnetotransport as a powerful tool for analyzing the geometry of the Fermi surface, complementing angle-resolved photoemission spectroscopy and quantum oscillation measurements. This approach is demonstrated to be particularly useful for determining the role of non-trivial topology in transport properties.

Exotic quantum phases, arising from a complex interplay of charge, spin, lattice and orbital degrees of freedom, are of immense interest to a wide research community. A well-known example of such an entangled behavior is the Jahn-Teller effect, where the lifting of orbital degeneracy proceeds through lattice distortions. Here we demonstrate that a highly-symmetrical 5d1 double perovskite Ba2MgReO6, comprising a 3D array of isolated ReO6 octahedra, represents a rare example of a dynamic Jahn-Teller system in the strong spin-orbit coupling regime. Thermodynamic and resonant inelastic x-ray scattering experiments, supported by quantum chemistry calculations, undoubtedly show that the Jahn-Teller instability leads to a ground-state doublet, resolving a long-standing puzzle in this family of compounds. The dynamic state of ReO6 octahedra persists down to the lowest temperatures, where a multipolar order sets in, allowing for investigations of the interplay between a dynamic JT effect and strongly correlated electron behavior. Dynamic Jahn-Teller effect is rarely realized in condensed matter systems. Here, the authors demonstrate its occurrence in Ba2MgReO6, a 5d1 double perovskite, using resonant inelastic x-ray scattering, thermodynamic measurements and quantum chemistry calculations.

Graphene nanoribbons (GNRs) produced by means of bottom-up chemical self-assembly are considered promising candidates for the next-generation nanoelectronic devices. We address the electronic transport properties of angled two-terminal GNR junctions, which are inevitable in the interconnects in graphene-based integrated circuits. We construct a library of over 400000 distinct configurations of 60^∘ and 120^∘ junctions connecting armchair GNRs of different widths. Numerical calculations combining the tight-binding approximation and the Green's function formalism allow identifying numerous junctions with conductance close to the limit defined by the GNR leads. Further analysis reveals underlying structure-property relationships with crucial roles played by the bipartite symmetry of graphene lattice and the presence of resonant states localized at the junction. In particular, we discover and explain the phenomenon of binary conductance in 120^∘ junctions connecting metallic GNR leads that guarantees maximum possible conductance. Overall, our study defines the guidelines for engineering GNR junctions with desired electrical properties.

Real-world samples of graphene often exhibit various types of out-of-plane disorder–ripples, wrinkles and folds–introduced at the stage of growth and transfer processes. These complex out-of-plane defects resulting from the interplay between self-adhesion of graphene and its bending rigidity inevitably lead to the scattering of charge carriers thus affecting the electronic transport properties of graphene. We address the ballistic charge-carrier transmission across the models of out-of-plane defects using tight-binding and density functional calculations while fully taking into account lattice relaxation effects. The observed transmission oscillations in commensurate graphene wrinkles are attributed to the interference between intra- and interlayer transport channels, while the incommensurate wrinkles show vanishing backscattering and retain the transport properties of flat graphene. The suppression of backscattering reveals the crucial role of lattice commensuration in the electronic transmission. Our results provide guidelines to controlling the transport properties of graphene in presence of this ubiquitous type of disorder.

AbstractAlthough chromium trihalides are widely regarded as a promising class of two-dimensional magnets for next-generation devices, an accurate description of their electronic structure and magnetic interactions has proven challenging to achieve. Here, we quantify electronic excitations and spin interactions in CrX3 (X = Cl, Br, I) using embedded many-body wavefunction calculations and fully generalized spin Hamiltonians. We find that the three trihalides feature comparable d-shell excitations, consisting of a high-spin 4A2$$({t}_{2g}^{3}{e}_{g}^{0})$$ ( t 2 g 3 e g 0 ) ground state lying 1.5–1.7 eV below the first excited state 4T2 ($${t}_{2g}^{2}{e}_{g}^{1}$$ t 2 g 2 e g 1 ). CrCl3 exhibits a single-ion anisotropy Asia = − 0.02 meV, while the Cr spin-3/2 moments are ferromagnetically coupled through bilinear and biquadratic exchange interactions of J1 = − 0.97 meV and J2 = − 0.05 meV, respectively. The corresponding values for CrBr3 and CrI3 increase to Asia = −0.08 meV and Asia= − 0.12 meV for the single-ion anisotropy, J1 = −1.21 meV, J2 = −0.05 meV and J1 = −1.38 meV, J2 = −0.06 meV for the exchange couplings, respectively. We find that the overall magnetic anisotropy is defined by the interplay between Asia and Adip due to magnetic dipole–dipole interaction that favors in-plane orientation of magnetic moments in ferromagnetic monolayers and bulk layered magnets. The competition between the two contributions sets CrCl3 and CrI3 as the easy-plane (Asia + Adip >0) and easy-axis (Asia + Adip <0) ferromagnets, respectively. The differences between the magnets trace back to the atomic radii of the halogen ligands and the magnitude of spin–orbit coupling. Our findings are in excellent agreement with recent experiments, thus providing reference values for the fundamental interactions in chromium trihalides.

The moir & eacute; superlattice in twisted bilayer graphene has been proven to be a versatile platform for exploring exotic quantum phases. Extensive investigations have been invoked focusing on the zero-magnetic-field phase diagram at the magic twist angle around theta = 1.1 degrees, which has been indicated to be an exclusive regime for exhibiting a flat band with the interplay of strong electronic correlation and untrivial topology in the experiment so far. In contrast, electronic bands in non-magic-angle twisted bilayer graphene host dominant electronic kinetic energy compared to Coulomb interaction. By quenching the kinetic energy and enhancing Coulomb exchange interactions by means of an applied perpendicular magnetic field, here we unveil gapped flat Hofstadter subbands at large magnetic flux that yield correlated insulating states in minimally twisted bilayer graphene at theta = 0.41 degrees. These states appear with isospin symmetry breaking due to strong Coulomb interactions. Our work provides a platform to study the phase transition of the strongly correlated Hofstadter spectrum.

Ordinary metals contain electron liquids within well-defined ‘Fermi’ surfaces at which the electrons behave as if they were non-interacting. In the absence of transitions to entirely new phases such as insulators or superconductors, interactions between electrons induce scattering that is quadratic in the deviation of the binding energy from the Fermi level. A long-standing puzzle is that certain materials do not fit this ‘Fermi liquid’ description. A common feature is strong interactions between electrons relative to their kinetic energies. One route to this regime is special lattices to reduce the electron kinetic energies. Twisted bilayer graphene 1 – 4 is an example, and trihexagonal tiling lattices (triangular ‘kagome’), with all corner sites removed on a 2 × 2 superlattice, can also host narrow electron bands 5 for which interaction effects would be enhanced. Here we describe spectroscopy revealing non-Fermi-liquid behaviour for the ferromagnetic kagome metal Fe 3 Sn 2 (ref. 6 ). We discover three C 3 -symmetric electron pockets at the Brillouin zone centre, two of which are expected from density functional theory. The third and most sharply defined band emerges at low temperatures and binding energies by means of fractionalization of one of the other two, most likely on the account of enhanced electron–electron interactions owing to a flat band predicted to lie just above the Fermi level. Our discovery opens the topic of how such many-body physics involving flat bands 7 , 8 could differ depending on whether they arise from lattice geometry or from strongly localized atomic orbitals 9 , 10 .

Exploring and understanding topological phases in systems with strong distributed disorder requires developing fundamentally new approaches to replace traditional tools such as topological band theory. Here, we present a general real-space renormalization group (RG) approach for scattering models, which is capable of dealing with strong distributed disorder without relying on the renormalization of Hamiltonians or wave functions. Such scheme, based on a block-scattering transformation combined with a replica strategy, is applied for a comprehensive study of strongly disordered unitary scattering networks with localized bulk states, uncovering a connection between topological physics and critical behavior. Our RG scheme leads to topological flow diagrams that unveil how the microscopic competition between reflection and non-reciprocity leads to the large-scale emergence of macroscopic scattering attractors, corresponding to trivial and topological insulators. Our findings are confirmed by a scaling analysis of the localization length (LL) and critical exponents, and experimentally validated. The results not only shed light on the fundamental understanding of topological phase transitions and scaling properties in strongly disordered regimes, but also pave the way for practical applications in modern topological condensed-matter and photonics, where disorder may be seen as a useful design degree of freedom, and no longer as a hindrance.

Clarifying the underlying mechanisms that govern ordering transitions in condensed matter systems is crucial for comprehending emergent properties and phenomena. While transitions are often classified as electronically driven or lattice-driven, we present a departure from this conventional paradigm in the case of the double perovskite Ba$_2$MgReO$_6$. Leveraging resonant and non-resonant elastic x-ray scattering techniques, we unveil the simultaneous ordering of structural distortions and charge quadrupoles at a critical temperature of $T_\mathrm{q}$$\sim$33 K. Using a variety of complementary first-principles-based computational techniques, we demonstrate that while electronic interactions drive the ordering at $T_\mathrm{q}$, it is ultimately the lattice that dictates the specific ground state that emerges. Our findings highlight the crucial interplay between electronic and lattice degrees of freedom, providing a unified framework to understand and predict unconventional emergent phenomena in quantum materials.

Fractional charges are one of the wonders of the fractional quantum Hall effect. Such objects are also anticipated in two-dimensional hexagonal lattices under time reversal symmetry-emerging as bound states of a rotating bond texture called a Kekulé vortex. However, the physical mechanisms inducing such topological defects remain elusive, preventing experimental realization. Here, we report the observation of Kekulé vortices in the local density of states of graphene under time reversal symmetry. The vortices result from intervalley scattering on chemisorbed hydrogen adatoms. We uncover that their 2π winding is reminiscent of the Berry phase π of the massless Dirac electrons. We can also induce a Kekulé pattern without vortices by creating point scatterers such as divacancies, which break different point symmetries. Our local-probe study thus confirms point defects as versatile building blocks for Kekulé engineering of graphene's electronic structure.

We model interactions following the Sachdev-Ye-Kitaev (SYK) framework in disordered graphene flakes up to 300 000 atoms in size (∼100  nm in diameter) subjected to an out-of-plane magnetic field B of 5-20 Tesla within the tight-binding formalism. We investigate two sources of disorder: (i) irregularities at the system boundaries, and (ii) bulk vacancies-for a combination of which we find conditions that could be favorable for the formation of the phase with Sachdev-Ye-Kitaev features under realistic experimental conditions above the liquid helium temperature.

The interplay of topological characteristics in real space and reciprocal space can lead to the emergence of unconventional topological phases. In this Letter, we implement a novel mechanism for generating higher-Chern flat bands on the basis of twisted bilayer graphene (TBG) coupled to topological magnetic structures in the form of the skyrmion lattice. In particular, we discover a scenario for generating |C| = 2 dispersionless electronic bands when the skyrmion periodicity and the moiré periodicity match. Following the Wilczek argument, the statistics of the charge-carrying excitations in this case is bosonic, characterized by electronic charge Q = 2e, which is even in units of electron charge e. The skyrmion coupling strength triggering the topological phase transition is realistic, with its lower bound estimated as 4 meV. The Hofstadter butterfly spectrum results in an unexpected quantum Hall conductance sequence ±2e2h,±4e2h,... for TBG with the skyrmion order.

While bottom-up synthesis allows for precise control over the properties of graphene nanoribbons (GNRs), the use of certain precursor molecules can result in edge defects, such as missing benzene rings that resemble a ‘bite’. We investigate the adverse effect of the ‘bite’ defects on the electronic transport properties in three chevron-type GNRs and discover that the extent of scattering is governed by the different defect positions. Applying the concepts learned in single GNRs, we engineer defects in two nanostructures to construct prototypical components for nanoelectronics. First, we design a switch, consisting of three laterally fused fluorenyl-chevron GNRs, and place a pair of ‘bite’ defects to effectively allow the switching between four binary states corresponding to distinct current pathways. Second, we show that conscientious placement of a ‘bite’ defect pair can increase conductance between two leads in a triple chevron GNR junction. Overall, we outline how the incorporation of ‘bite’ defects affects transport properties in chevron-type nanostructures and provide a guide on how to design nanoelectronic components.

Defects in solids are unavoidable and can create complex electronic states that can significantly influence the electrical and optical properties of semiconductors. With the rapid progress in the integration of 2D semiconductors in practical devices, it is imperative to understand and characterize the influence of defects in this class of materials. Here, we examine the electrical response of defect filling and emission using deep level transient spectroscopy (DLTS) and reveal defect states and their hybridization in a monolayer MOCVD-grown material deposited on CMOS-compatible substrates. Supported by aberration-corrected STEM imaging and theoretical calculations, we find that neighboring sulfur vacancy pairs introduce additional shallow trap states via hybridization of individual vacancy levels. Even though such vacancy pairs only represent ~10% of the total defect concentration, they can have a substantial influence on the off currents and switching slopes of field-effect transistors based on 2D semiconductors. Our technique, which can quantify the energy states of different defects and their interactions, allows rapid and nondestructive electrical characterization of defect states important for the defect engineering of 2D semiconductors.

We formulate the chiral decomposition rules that govern the electronic structure of a broad family of twisted N + M multilayer graphene configurations that combine arbitrary stacking order and a mutual twist. We show that at the magic angle in the chiral limit the low-energy bands of such systems are composed of chiral pseudospin doublets that are energetically entangled with two flat bands per valley induced by the moiré superlattice potential. The analytic construction is supported by explicit numerical calculations based on realistic parametrization. We further show that vertical displacement fields can open energy gaps between the pseudospin doublets and the two flat bands, such that the flat bands may carry nonzero valley Chern numbers. These results provide guidelines for the rational design of topological and correlated states in generic twisted graphene multilayers.

In the recent paper [1], a new method based on measuring a temperature correction to a quantum-oscillation frequency was proposed to study an energy-band dispersion of charge carriers in small Fermi surface (FS) pockets of crystals. To illustrate their approach, Guo et al. [1] applied it to a number of materials and, in particular, to the multiband metal LaRhIn$_5$ which, apart from high-frequency oscillations associated with a large FS, also exhibits the oscillations with the low frequency $F\approx 7$ T. Although the method of Ref. [1] really detects charge carriers with a linear dispersion, it does not distinguish between the carriers near a Dirac point and near a nodal line, since all such quasiparticles disperse linearly. Here we ask what is the nature of the carriers associated with the frequency $F$ in LaRhIn$_5$ and call attention to the puzzling origin of this frequency.