Landau levels (LLs) are cornerstones of the fractional quantum Hall effect, which is a paradigm of topologically ordered phases of matter. Predicting and understanding the emergence of fractional Chern insulators in a Chern band, to a large extent, relies on judging the similarity between the Chern band and LLs. In this work, we generalize the notion of LLs to Chern bands to allow for nonuniform quantum geometries while preserving certain geometric invariants. Mathematically, generalized LLs can be understood in terms of holomorphic curves and associated moving frames in the sense of Cartan. This formalism enables a thorough analytical discussion of their associated quantum geometries. In practical terms, generalized LLs allow for a systematic discussion of the geometric stability of fractional Chern insulators and provide useful guidance in material design. Approximating Chern bands as superpositions of a few generalized LLs and employing exact diagonalization, we numerically identify a universal geometric criterion for the non-Abelian Moore-Read state to be stabilized in Chern bands, providing useful guidance for searching for such phase in moiré materials. Moreover, a double-twisted bilayer graphene model at the second magic angle is used to suggest a possible experimental realization of generalized LLs and zero-field non-Abelian phases. More broadly, our results point to generalized LLs being an interdisciplinary research direction connecting Kähler geometry, topologically ordered phases, and moiré materials, which we expect will benefit the study of the geometric aspect of correlated phases in a more general sense.

The nitrogen-vacancy (NV) center in diamond is a solid-state spin defect that has been widely adopted for quantum sensing and quantum information processing applications. Typically, experiments are performed either with a single isolated NV center or with an unresolved ensemble of many NV centers, resulting in a trade-off between measurement speed and spatial resolution or control over individual defects. In this work, we introduce an experimental platform that bypasses this trade-off by addressing multiple optically resolved NV centers in parallel. We perform charge- and spin-state manipulations selectively on multiple NV centers from within a larger set, and we manipulate and measure the electronic spin states of over 100 NV centers in parallel. We show that the high signal-to-noise ratio of the measurements enables the detection of shot-to-shot pairwise correlations between the spin states of 108 NV centers, corresponding to the simultaneous measurement of 5778 unique correlation coefficients. We discuss how our platform can be scaled to parallel experiments with thousands of individually resolved NV centers. These results enable parallelized high-throughput sensing experiments that retain the spatial resolution of single defects and will, thereby, help to unlock advances in applications such as single-molecule NMR and characterization of integrated circuits. In addition, our approach to multiplexing provides a natural platform for the application of recently developed correlated sensing techniques.

Single nitrogen vacancy (NV) centers in diamond have been used extensively for high-sensitivity nanoscale sensing, but conventional approaches use confocal microscopy to measure individual centers sequentially, limiting throughput and access to nonlocal physical properties, where simultaneous, high-fidelity measurement of multiple centers is required. Here, we design and implement a multiplexed NV sensing platform that allows us to read out many single NV centers simultaneously using a low-noise camera. Using this platform, we coherently manipulate and read out the spin states of hundreds of individual NV centers in parallel, achieving comparable magnetic field sensitivity to confocal measurements. We also implement a parallelized version of spin-to-charge-conversion readout for low NV center spin state readout noise and use it to demonstrate multiplexed covariance magnetometry, in which we measure ten two-point magnetic field correlators from five NV centers simultaneously. From these measurements, we demonstrate the quantitative reconstruction of spatially varying magnetic correlations arising from a current-carrying wire. The number of correlators we can measure is limited only by the available laser power, opening the door to massively multiplexed covariance magnetometry. In contrast to scanning probes for imaging spatially varying magnetic fields, our approach measures the temporal dynamics of the magnetic field at many precisely defined positions simultaneously, from which the local noise spectrum and nonlocal properties such as correlation functions can be computed. This high-fidelity readout platform will find immediate applications in studying condensed matter phenomena that are characterized by the noise spectrum or correlation functions, including quantum phase transitions, dynamics far from equilibrium, magnetic order, and correlated electron phenomena.

Orbital selectivity is pivotal in dictating the phase diagrams of multiorbital systems, with prominent examples including the orbital-selective Mott phase and superconductivity. The intercalation of anisotropic layers represents an effective method for enhancing orbital selectivity and thereby shaping the low-energy physics of multiorbital systems. Despite its potential, related experimental studies, especially those elucidating the correlation between orbital selectivity and magnetism, remain limited. In this work, we systematically examine the interplay between orbital selectivity and magnetism in the newly discovered anisotropic kagome ${\mathrm{TbTi}}_3{\mathrm{Bi}}_4$ single crystal, and report the coexistence of orbital-selective dual-band modulations ($q_1\sim 1/3a^{*}$, $q_2\sim 0.28b^{*}$) within the antiferromagnetic (AFM) state. By combining soft x-ray and vacuum ultraviolet angle-resolved photoemission spectroscopy measurements, neutron powder diffraction, scanning tunneling microscopy, and density-functional-theory calculations, we identify these dual-band reconstructions as manifestations of the AFM order driven by a (approximately $1/3$, 0.28, 0) nesting instability of the intercalated Tb $5d_{xz}$ orbitals. These orbital-selective modulations induce unusual momentum-dependent band folding and lead to the emergence of Dirac cones only at the ${\overline{M}}_1$ point, signaling a topological phase transition in the AFM state. Importantly, the discovery of orbital-selective (approximately $1/3$, 0.28, 0) AFM order offers crucial insights into the mechanism underlying the fractional magnetization plateau in this kagome AFM metal. Our findings not only underscore the essential role of both conducting and localized electrons in determining the magnetic orders of $\mathrm{Ln}{\mathrm{Ti}}_3{\mathrm{Bi}}_4$ ($\mathrm{Ln}=\mathrm{lanthanide}$) kagome metals but also offer a pathway for manipulating magnetism through selective control of anisotropic electronic structures.

The recently introduced “fuzzy-sphere” method has enabled accurate numerical regularizations of certain three-dimensional (3D) conformal field theories (CFTs). The regularization is provided by the noncommutative geometry of the lowest Landau level filled by electrons, such that the charge is trivially gapped due to the Pauli exclusion principle at filling factor $\nu =1$, while the electron spins encode the desired CFT. Successful applications of the fuzzy sphere to paradigmatic CFTs, such as the 3D Ising model, raise an important question: How finely tuned does the underlying electron system need to be? Here, we show that the 3D Ising CFT can also be realized at fractional electron fillings. In such cases, the CFT spectrum is intertwined with the charge-neutral spectrum of the underlying fractional quantum Hall state—a feature that is trivially absent in the previously studied $\nu =1$ case. Remarkably, we show that the mixing between the CFT spectrum and the fractional quantum Hall spectrum is strongly suppressed within the numerically accessible system sizes. Moreover, we demonstrate that the CFT critical point is unaffected by the exchange statistics of the particles and by the nature of topological order in the charge sector. Our results set the stage for the fuzzy-sphere exploration of conformal critical points between topologically ordered states.

The traditional view of the anomalous Hall effect (AHE) in ferromagnets is that it arises from the magnetization perpendicular to the measurement plane and that there is a linear dependence on the latter. Underlying such a view is the thinking that the AHE is a time-reversal symmetry breaking phenomenon and can therefore be treated in terms of a power series in the magnetic order. However, this view is squarely challenged by a number of recent experiments, urging for a thorough theoretical investigation on the fundamental level. We find that for strong magnets, it is more appropriate and fruitful to regard the AHE as a spin-group symmetry breaking phenomenon where the critical parameter is the spin-orbit interaction strength, which involves a much smaller energy scale. In collinear ferromagnets, the spin-orbit coupling breaks the $\infty 2^{\prime }$ spin rotation symmetry, and the key to characterizing such symmetry breaking is the identification of spin-orbit vectors which transform regularly under spin-group operations. Born out of our framework is a rich multipolar relationship between the anomalous Hall conductivity and the magnetization direction, with each pole being expanded progressively in powers of the spin-orbit coupling strength. For the leading order contribution, i.e., the dipole, its isotropic part corresponds to the traditional view, and its anisotropic part can lead to the in-plane AHE where the magnetization lies within the measurement plane. Beyond the dipolar structure, the octupolar structure offers the leading order source of nonlinearity and hence introduces unique anisotropy where the dipolar structure cannot. Our theory thus offers a unified explanation for the in-plane AHE recently observed in various ferromagnets, and further extends the candidate material systems. It can also be generalized to study the anomalous Hall effect in crystals with any periodic spin structure and to study the nonlinear Hall effect and the spin Hall effect. Our theory lays the ground for decoding the coupling between various transport and optical phenomena and the magnetic orders.

Spin-forbidden ($\mathrm{\Delta }S\ne 0$) multiplet excitations and their coupling to magnetic properties are of increasing importance for magneto-optical studies of correlated materials. Nonetheless, the mechanisms for optically brightening these transitions and their generality remain poorly understood. Here, we report magnetic circular dichroism (MCD) spectroscopy on the van der Waals ferromagnet (FM) ${\mathrm{CrI}}_3$. Previously unreported spin-forbidden ($\mathrm{\Delta }S=1$) ${{}^{4}A}_{2\mathrm{g}}\to {{}^{2}E}_{\mathrm{g}}/{{}^{2}T}_{1\mathrm{g}}$ ${\mathrm{Cr}}^{3+}$ $dd$ excitations are observed near the ligand-to-metal charge-transfer excitation threshold. The assignment of these excitations and their ${\mathrm{Cr}}^{3+}$ multiplet character is established through complementary Cr $L_3$-edge resonant inelastic x-ray scattering measurements along with charge-transfer multiplet calculations and chemical trends in the chromium trihalide series ($\mathrm{Cr}{X}_3$, $X=$ Cl, Br, I). We utilize the high sensitivity of MCD spectroscopy to study the thickness-dependent optical response. The spin-forbidden excitations remain robust down to the monolayer limit, and we observe a significant magnetic-field dependence of the MCD spectrum across the antiferromagnetic-to-FM transition in few-layer samples. We preliminarily attribute this behavior to changes in the metal-ligand covalency with magnetic state. Our results clarify the magneto-optical response of ${\mathrm{CrI}}_3$ and identify covalency as a central mechanism for the brightening and field tunability of spin-forbidden multiplet excitations.

The effect of decoherence on topological order (TO) has been most deeply understood for the toric code, the paragon of Abelian TOs. We show that certain non-Abelian TOs can be analyzed and understood to a similar degree, despite being significantly richer. We consider both wave-function deformations and quantum channels acting on $D_4$ TO, which has recently been realized on a quantum processor. By identifying the corresponding local statistical mechanical spin or rotor model with $D_4$ symmetry, we find a remarkable stability against proliferating non-Abelian anyons. This is shown by leveraging a reformulation in terms of the tractable O(2) loop model in the pure state case and $n$ coupled O(2) loop models for Rényi-$n$ quantities in the decoherence case—corresponding to worldlines of the proliferating anyon with quantum dimension 2. In particular, we find that the purity ($n=2$) remains deep in the $D_4$ TO for any decoherence strength, while the $n\to \infty$ limit becomes critical upon maximally decohering a particular anyon type, similar to our wave-function deformation result. The information-theoretic threshold ($n\to 1$) appears to be controlled by a disordered version of these statistical mechanical models, akin to the toric code case although significantly more robust. We furthermore use Monte Carlo simulations to explore the phase diagrams when multiple anyon types proliferate at the same time, leading to a continued stability of the $D_4$ TO in addition to critical phases with emergent U(1) symmetry. Instead of loop models, these are now described by net models corresponding to different anyon types coupled together according to fusion rules. This opens up the exploration of statistical mechanical models for decohered non-Abelian TO, which can inform optimal decoders and which in an ungauged formulation provides examples of non-Abelian strong-to-weak symmetry breaking.

We use symmetry analysis and density functional theory to show that changes in magnetic order at a surface with respect to magnetic order in the bulk can be generically determined by considering local magnetoelectric responses of the crystal. Specifically, analysis of the local atomic-site magnetoelectric responses, or, equivalently, the corresponding atomic-site magnetic multipoles, can be used to predict all surface magnetic modifications arising purely from symmetry lowering via termination of the bulk magnetic order. This analysis applies even in materials with no bulk magnetoelectric response or net surface magnetization. We then demonstrate our arguments for two example antiferromagnets, topological semimetal CuMnAs and rocksalt NiO. We find that the (010) and $(1\overline{1}0)$ surfaces of CuMnAs and NiO, respectively, exhibit a series of antiferroically, as well as roughness-sensitive, ferroically ordered, modifications of the surface magnetic dipole moments, via canting or changes in sublattice magnitude, consistent with the bulk ordering of the magnetic multipoles. Our findings demonstrate a universal bulk-boundary correspondence allowing the general prediction of minimal possible surface and interface magnetic modifications, even in materials with no net magnetoelectric response. Furthermore, it paves the way for more accurate interpretations of a wide variety of surface-sensitive measurements.

Arrays of coupled superconducting qubits are analog quantum simulators able to emulate a wide range of tight-binding models in parameter regimes that are difficult to access or adjust in natural materials. In this work, we use a superconducting qubit array to emulate a tight-binding model on the rhombic lattice, which features flat bands. Enabled by broad adjustability of the dispersion of the energy bands and of on-site disorder, we examine regimes where flat-band localization and Anderson localization compete. We observe disorder-induced localization for dispersive bands and disorder-induced delocalization for flat bands. Remarkably, we find a sudden transition between the two regimes and, in its vicinity, the semblance of quantum critical scaling.

It is known that particles with exotic properties can emerge in systems made of simple constituents such as qubits, due to long-range quantum entanglement. In this paper, we provide quantitative characterizations of entanglement necessary for emergent anyons and fermions by using the geometric entanglement measure (GEM), which quantifies the maximal overlap between a given state and any short-range-entangled states. For systems with emergent anyons, based on the braiding statistics, we show that the GEM scales linearly in the system size regardless of microscopic details. The phenomenon of emergent anyons can also be understood within the framework of quantum error correction (QEC). Specifically, we show that the GEM of any 2D stabilizer codes must be at least quadratic in the code distance. Our proof is based on a generic prescription for constructing string operators, establishing a rigorous and direct connection between emergent anyons and QEC. For systems with emergent fermions, despite that the ground state subspaces could be exponentially huge and their coding properties could be rather poor, we show that the GEM also scales linearly in the system size. Our analysis establishes an intriguing link between quantum anomaly and entanglement: A quantum state respecting anomalous 1-form symmetries must be long-range entangled and have large GEM. Our results also extend to mixed states, such as the $ZX$-dephased toric code, providing a provably nontrivial class of intrinsically mixed-state phases.

Twisted bilayer graphene (TBG) has elements in common with two paradigmatic examples of strongly correlated physics: quantum Hall physics and Hubbard physics. On one hand, TBG hosts flat topological Landau-level-like bands which exhibit the quantum anomalous Hall effects under the right conditions. On the other hand, these bands are characterized by concentrated charge density and show signs of extensive entropy usually attributed to local moments. The combination of these features leads to a question: Can decoupled moments emerge in an isolated topological band, despite the lack of exponentially localized Wannier orbitals? In this work, we answer the question affirmatively by proposing a minimal model for the flat topological bands in TBG that combines topology and charge concentration at the AA sites, leading to analytic wave functions that closely approximate those of the Bistritzer-MacDonald model with realistic parameters. Importantly, charge concentration also leads to Berry curvature concentration at $\mathrm{\Gamma }$, giving rise to a small parameter $s$ that makes the model analytically tractable. We show that, rather surprisingly, the model hosts nearly decoupled flavor moments without invoking any extra degrees of freedom. These moments are nonlocal due to topology-enforced power-law tails, yet have parametrically small overlap. We develop a systematic diagrammatic expansion in which the self-energy can be computed exactly to leading order in $s^2$ in the fluctuating moment regime and predict momentum-resolved spectral functions for future experiments to verify. Our key discovery is a charge-neutrality state we refer to as the “Mott semimetal” characterized by high flavor entropy and a Mott gap that exists throughout most of the Brillouin zone but closes at the $\mathrm{\Gamma }$ point. At $\mathrm{\Gamma }$, the spectral function contains a single Dirac cone per spin per valley and responds to perturbations in an exotic manner that is distinct from any other theoretical picture of TBG. Away from neutrality, the Mott semimetal gaps out in a spectrally imbalanced manner, with one Mott band having zero quasiparticle residue at the $\mathrm{\Gamma }$ point. The model accurately reproduces results from finite-temperature thermodynamic measurements, leads to new experimental predictions, and resolves the problem of the emergence of Hubbard physics in isolated topological bands.

Liquid crystals have proven to provide a versatile experimental and theoretical platform for studying topological objects such as vortices, skyrmions, and hopfions. In parallel, in hard condensed matter physics, the concept of topological phases and topological order has been introduced in the context of spin liquids to investigate emergent phenomena like quantum Hall effects and high-temperature superconductivity. Here, we bridge these two seemingly disparate perspectives on topology in physics. Combining experiments and simulations, we show how topological defects in liquid crystals can be used as versatile building blocks to create complex, highly degenerate topological phases, which we refer to as “combinatorial vortex lattices” (CVLs). CVLs exhibit extensive residual entropy and support locally stable quasiparticle excitations in the form of charge-conserving topological monopoles, which can act as mobile information carriers and be linked via Dirac strings. CVLs can be rewritten and reconfigured on demand, endowed with various symmetries, and modified through laser-induced topological surgery—an essential capability for information storage and retrieval. We demonstrate experimentally the realization, stability, and precise optical manipulation of CVLs, thus opening new avenues for understanding and technologically exploiting higher-hierarchy topology in liquid crystals and other ordered media.

Antiferromagnetic materials (AFMs) have been gaining lots of attention due to their great potential in spintronics devices and the recently discovered novel spin structure in the momentum space, i.e., $C$-paired spin-valley or spin-momentum locking (CSML), where spins and valleys or momenta are locked to each other due to the crystal symmetry guaranteeing zero magnetization. Here, we systematically study CSMLs and propose a general theory and algorithm using little cogroup and coset representatives, which reveals that 12 elementary kinds of CSMLs, determined by the geometric relation of spins and valleys and the essential symmetry guaranteeing zero magnetization, are sufficient to fully represent all possible CSMLs. By combining the proposed algorithm and high-throughput first-principles calculations, we predict 38 magnetic point groups and identify 142 experimentally verified AFMs that can realize CSML. Besides predicting new materials, our theory can naturally reveal underlying mechanisms of CSMLs’ responses to external fields. As an example, two qualitatively different types of piezomagnetism via occupation imbalance or spin tilting are predicted in ${\mathrm{RbV}}_2{\mathrm{Te}}_2\mathrm{O}$. The algorithm and conclusions can be directly extended to the locking between valley or momentum and any other pseudovector degree of freedom, e.g., Berry curvature, as exemplified in ${\mathrm{RbV}}_2{\mathrm{Te}}_2\mathrm{O}$ and the new proposed piezo-Hall effect, where a strain can induce a nonzero anomalous Hall conductance. In addition, the proposed concept and methodology can be straightforwardly applied to other symmetry groups, such as spin group.

High-speed, nonvolatile tunability is critical for advancing reconfigurable photonic devices used in neuromorphic information processing, sensing, and communication. Despite significant progress in developing phase-change and ferroelectric materials, achieving highly efficient, reversible, rapid switching of optical properties has remained a challenge. Recently, sliding ferroelectricity has been discovered in 2D semiconductors, which also host strong excitonic effects. Here, we demonstrate that these materials enable nanosecond ferroelectric switching in the complex refractive index, substantially modulating their linear optical responses. The maximum index modulation reaches about 4, resulting in a relative reflectance change exceeding 85%. Both on and off switching occur within 2.5 ns, with switching energy at femtojoule levels. The switching mechanism is driven by tuning the excitonic peak splitting of a rhombohedral molybdenum disulfide bilayer in an engineered Coulomb screening environment. This new switching mechanism establishes a new direction for developing high-speed, nonvolatile optical memories and highly efficient, compact reconfigurable photonic devices. Additionally, the demonstrated imaging technique offers a rapid method to characterize domains and domain walls in 2D semiconductors with rhombohedral stacking.

Atomic defects underpin the properties of van der Waals materials, and their understanding is essential for advancing quantum and energy technologies. Scanning transmission electron microscopy is a powerful tool for defect identification in atomically thin materials, and extending it to multilayer and beam-sensitive materials would accelerate their exploration. Here, we establish a comprehensive defect library in a bilayer of the magnetic quasi-1D semiconductor CrSBr by combining atomic-resolution imaging, deep learning, and ab initio calculations. We apply a custom-developed machine learning work flow to detect, classify, and average point vacancy defects. This classification enables us to uncover several distinct Cr interstitial defect complexes, combined Cr and Br vacancy defect complexes, and lines of vacancy defects that extend over many unit cells. We show that their occurrence is in agreement with our computed structures and binding energy densities, reflecting the intriguing layer interlocked crystal structure of CrSBr. Our ab initio calculations show that the interstitial defect complexes give rise to highly localized electronic states. These states are of particular interest due to the reduced electronic dimensionality and magnetic properties of CrSBr and are, furthermore, predicted to be optically active. Our results broaden the scope of defect studies in challenging materials and reveal new defect types in bilayer CrSBr that can be extrapolated to the bulk and to over 20 materials belonging to the same FeOCl structural family.

The AdS/CFT correspondence stipulates a duality between conformal field theories and certain theories of quantum gravity in one higher spatial dimension. However, probing this conjecture on contemporary classical or quantum computers is challenging. We formulate an efficiently implementable multiscale entanglement renormalization ansatz model of AdS/CFT, providing a mapping between a ($1+1$)-dimensional critical spin system and a ($2+1$)-dimensional bulk theory. Using a combination of numerics and analytics, we show that the bulk theory arising from this optimized tensor network furnishes excitations with attractive interactions. Remarkably, these excitations have one- and two-particle energies matching the predictions for matter coupled to AdS gravity at long distances, thus displaying key features of AdS physics. We show that these potentials arise as a direct consequence of entanglement renormalization and discuss how this approach can be used to efficiently simulate bulk dynamics using realistic quantum devices.

The spin-$1/2$ kagome Heisenberg antiferromagnets are believed to host exotic quantum entangled states. Recently, the reports of $1/9$ magnetization plateau and magnetic oscillations in a kagome antiferromagnet ${\mathrm{YCu}}_3{(\mathrm{OH})}_6{\mathrm{Br}}_2[{\text{Br}}_x{(\mathrm{OH})}_{1-x}]$ (YCOB) have made this material a promising candidate for experimentally realizing quantum spin liquid states. Here, we present measurements of the specific heat $C_p$ in YCOB in high magnetic fields (up to 41.5 T) down to 0.46 K, and the $1/9$ plateau feature has been confirmed. Moreover, the temperature dependence of $C_p/T$ in the vicinity of $1/9$ plateau region can be fitted by a linear in $T$ term which indicates the presence of a Dirac spectrum, together with a constant term, which indicates a finite density of states contributed by other spinon Fermi surfaces. Surprisingly, the constant term is highly anisotropic in the direction of the magnetic field. Additionally, we observe a double-peak feature near 30 T above the $1/9$ plateau which is another hallmark of fermionic excitations in the specific heat. This combination of gapless behavior and the double-peak structure strongly suggests that the $1/9$ plateau in YCOB is nontrivial and hosts fermionic quasiparticles.

Exotic quantum solids can host electronic states that spontaneously break rotational symmetry of the electronic structure, such as electronic nematic phases and unidirectional charge density waves (CDWs). When electrons couple to the lattice, uniaxial strain can be used to anchor and control this electronic directionality. Here, we reveal an unusual impact of strain on unidirectional “smectic” CDW orders in kagome superconductors ${\mathrm{AV}}_3{\mathrm{Sb}}_5$ using spectroscopic-imaging scanning tunneling microscopy. We discover local decoupling between the smectic electronic director axis and the direction of anisotropic strain. While the two can generally be aligned along the same direction in regions of a small CDW gap, the tendency for alignment decreases in regions where the CDW gap is the largest. This feature, in turn, suggests nanoscale variations in smectic susceptibility, which we attribute to a combination of local strain and electron correlation strength. Overall, we observe an unusually high decoupling rate between the smectic electronic director of the three-state Potts order and anisotropic strain, revealing weak smectoelastic coupling in the CDW phase of kagome superconductors. This finding is phenomenologically different from the extensively studied nematoelastic coupling in the Ising nematic phase of Ising nematic phase of Fe-based superconductor bulk single crystals, providing a contrasting picture of how strain can control electronic unidirectionality in different families of quantum materials.

Controlling electrically stimulated quantum light sources (QLSs) is key for developing integrated and low-scale quantum devices. The underlying mechanisms leading to electrically driven quantum emission, however, are complex, as a large number of electronic states of the system can be involved and, thus, impact the emission dynamics. Here, we use a scanning tunneling microscope to electrically excite a model QLS, namely, a single ZnPc molecule, and disentangle the interplay of charge transfer and excited state formation. The luminescence spectra reveal two lines, associated to the emission of the neutral (exciton) and positively charged (trion) ZnPc, both exhibiting single-photon source behavior. In addition, we find a correlation between the charged and neutral emission, specifically, the signature of a photon cascade in which the radiative decay of the molecular trion is followed by the formation and decay of the exciton. By adjusting the charging vs discharging rate, we show that we can control these emission statistics. This generic strategy is further established by a comprehensive rate equation model comprising a variety of states that mediate excited state formation in the electrically driven single and cascaded photon emission process, revealing the complex internal dynamics of the molecular junction.