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Hofstadter's butterfly, the predicted energy spectrum for non-interacting electrons confined to a two-dimensional lattice in a magnetic field, is one of the most remarkable fractal structures in nature. At rational ratios of magnetic flux quanta per lattice unit cell, this spectrum shows self-similar distributions of energy levels that reflect its recursive construction. For most materials, Hofstadter's butterfly is predicted under experimental conditions that are unachievable using laboratory-scale magnetic fields. More recently, electrical transport studies have provided evidence for Hofstadter's butterfly in materials engineered to have artificially large lattice constants, such as those with moir\'e superlattices. Yet to-date, direct spectroscopy of the fractal energy spectrum predicted by Hofstadter nearly 50 years ago has remained out of reach. Here we use high-resolution scanning tunneling microscopy / spectroscopy (STM / STS) to probe the flat electronic bands in twisted bilayer graphene near the predicted second magic angle, an ideal setting for spectroscopic studies of Hofstadter's spectrum. Our study shows the fractionalization of flat moir\'e bands into discrete Hofstadter subbands and discerns experimental signatures of self-similarity of this spectrum. Moreover, our measurements uncover a spectrum that evolves dynamically with electron density, displaying phenomena beyond that of Hofstadter's original model due to the combined effects of strong correlations, Coulomb interactions, and the quantum degeneracy of electrons in twisted bilayer graphene., Comment: 20 pages, 5 figures

Individuals who identify as sexual and gender minorities, including lesbian, gay, bisexual, transgender, queer, and others (LGBTQ+) are more likely to experience poorer health than their heterosexual and cisgender counterparts. One primary source that drives these health disparities is minority stress (i.e., chronic and social stressors unique to LGBTQ+ communities' experiences adapting to the dominant culture). This stress is frequently expressed in LGBTQ+ users' posts on social media platforms. However, these expressions are not just straightforward manifestations of minority stress. They involve linguistic complexity (e.g., idiom or lexical diversity), rendering them challenging for many traditional natural language processing methods to detect. In this work, we designed a hybrid model using Graph Neural Networks (GNN) and Bidirectional Encoder Representations from Transformers (BERT), a pre-trained deep language model to improve the classification performance of minority stress detection. We experimented with our model on a benchmark social media dataset for minority stress detection (LGBTQ+ MiSSoM+). The dataset is comprised of 5,789 human-annotated Reddit posts from LGBTQ+ subreddits. Our approach enables the extraction of hidden linguistic nuances through pretraining on a vast amount of raw data, while also engaging in transductive learning to jointly develop representations for both labeled training data and unlabeled test data. The RoBERTa-GCN model achieved an accuracy of 0.86 and an F1 score of 0.86, surpassing the performance of other baseline models in predicting LGBTQ+ minority stress. Improved prediction of minority stress expressions on social media could lead to digital health interventions to improve the wellbeing of LGBTQ+ people-a community with high rates of stress-sensitive health problems., Comment: This paper is accepted in 2024 IEEE 11th International Conference on Data Science and Advanced Analytics (DSAA)

Flat bands and nontrivial topological physics are two important topics of condensed matter physics. With a unique stacking configuration analogous to the Su-Schrieffer-Heeger (SSH) model, rhombohedral graphite (RG) is a potential candidate for realizing both flat bands and nontrivial topological physics. Here we report experimental evidence of topological flat bands (TFBs) on the surface of bulk RG, which are topologically protected by bulk helical Dirac nodal lines via the bulk-boundary correspondence. Moreover, upon {\it in situ} electron doping, the surface TFBs show a splitting with exotic doping evolution, with an order-of-magnitude increase in the bandwidth of the lower split band, and pinning of the upper band near the Fermi level. These experimental observations together with Hartree-Fock calculations suggest that correlation effects are important in this system. Our results demonstrate RG as a new platform for investigating the rich interplay between nontrivial band topology, correlation effects, and interaction-driven symmetry-broken states., Comment: 15 pages, 5 figures

A Josephson diode is a superconducting circuit element that enables non-reciprocal transport, allowing a dissipationless supercurrent to preferentially flow in a single direction. Existing methods for achieving the required symmetry breaking mostly rely on specifically-designed materials or carefully-engineered circuits composed of multiple Josephson junctions. Here, we demonstrate that applying a biharmonic drive to a conventional superconducting tunnel-junction induces a diode effect through harmonic mixing processes that shift the supercurrent region. We show that, in a conventional tunnel junction, unity efficiency is achievable while maintaining a large supercurrent. Moreover, the relative phase between the two driving tones determines the directionality of the diode, which can be tuned in situ., Comment: 6 pages, 3 figures

We introduce a semidefinite relaxation method called Hamiltonian bootstrap which finds lower bounds to the ground state energy of a quantum Hamiltonian subject to Hermitian linear constraints, along with approximations of the corresponding ground state correlation functions. We show that symmetry can be used to significantly reduce both the memory and time requirements, and we include unitary, antiunitary, discrete, and continuous symmetries in our analysis. We demonstrate Hamiltonian bootstrap using the 1D Hubbard model and find quantitative agreement with both exact diagonalization and the Bethe ansatz., Comment: 8 pages, 2 figures

We explore self-induced parametric coupling, also called internal resonances (IRs), in a membrane nanoelectromechanical system. Specifically, we focus on the formation of a limit cycle manifesting as a phononic frequency comb. Utilizing a pump-noisy-probe technique and theoretical modeling, we reveal the behavior of mechanical excitations revealing themselves as sidebands of the stationary IR response. We find that when the energy-absorbing excitation of a lower mode is parametrically-upconverted to hybridize with a higher mode, significant squeezing and bimodality in the upper mode occurs. Instead, when the upconverted absorbing excitation hybridizes with an emitting sideband of the higher mode, a Hopf bifurcation occurs and a limit cycle forms, manifesting as a frequency comb. We thus reveal a unique mechanism to obtain frequency combs in parametrically-coupled modes. We furthermore demonstrate a rich variety of IR effects, the origin of which significantly extends beyond standard linear parametric coupling phenomena. Our findings enhance the understanding of energy transfer mechanisms with implications for advanced sensing technologies and novel phononic metamaterials.

Sub-angstrom spatial resolution of electron density coupled with sub-femtosecond temporal resolution is required to directly observe the dynamics of the electronic structure of a molecule after photoinitiation or some other ultrafast perturbation. Meeting this challenge, pushing the field of quantum crystallography to attosecond timescales, would bring insights into how the electronic and nuclear degrees of freedom couple, enable the study of quantum coherences involved in molecular dynamics, and ultimately enable these dynamics to be controlled. Here we propose to reach this realm by employing convergent-beam X-ray crystallography with high-power attosecond pulses from a hard-X-ray free-electron laser. We show that with dispersive optics, such as multilayer Laue lenses of high numerical aperture, it becomes possible to encode time into the resulting diffraction pattern with deep sub-femtosecond precision. Each snapshot diffraction pattern consists of Bragg streaks that can be mapped back to arrival times and positions of X-rays on the face of a crystal. This can span tens of femtoseconds, and can be finely sampled as we demonstrate experimentally. The approach brings several other advantages, such as an increase of the number of observable reflections in a snapshot diffraction pattern, all fully integrated, to improve the speed and accuracy of serial crystallography -- especially for crystals of small molecules., Comment: 18 pages, 7 figures

The Blatter radical has been suggested as a building block in future molecular spintronic devices due to its radical character and expected long-spin lifetime. However, whether and how the radical character manifests itself in the charge transport and magnetotransport properties seems to depend on the environment or has not yet been studied. Here, we investigate single-molecule junctions of the Blatter radical molecule in a mechanically controlled break junction device at low temperature. Differential conductance spectroscopy on individual junctions shows two types of zero-bias anomalies attributed to Kondo resonances revealing the ability to retain the open-shell nature of the radical molecule in a two-terminal device. Additionally, a high negative magnetoresistance is also observed in junctions without showing a zero-bias peak. We posit that the high negative magnetoresistance is due to the effect of a singlet-triplet Kondo effect under magnetic field originating from a double-quantum-dot system consisting of a Blatter radical molecule with a strong correlation to a second side-coupled molecule. Our findings not only provide the possibility of using the Blatter radical in a two-terminal system under cryogenic conditions but also reveal the magnetotransport properties emerging from different configurations of the molecule inside a junction., Comment: 17 pages, 5 figures

The Berry phase is a fundamental concept in quantum mechanics with profound implications for understanding topological properties of quantum systems. This tutorial provides a comprehensive introduction to the Berry phase, beginning with the essential mathematical framework required to grasp its significance. We explore the intrinsic link between the emergence of a non-trivial Berry phase and the presence of topological characteristics in quantum systems, showing the connection between the Berry phase and the band structure as well as the phase's gauge-invariant nature during cyclic evolutions. The tutorial delves into various topological effects arising from the Berry phase, such as the quantum, anomalous, and spin Hall effects, which exemplify how these quantum phases manifest in observable phenomena. We then extend our discussion to cover the transport properties of topological insulators, elucidating their unique behaviour rooted in Berry phase physics. This tutorial aims at equipping its readers with a robust understanding of the basic theory around the Berry phase and its pivotal role in the realm of topological quantum phenomena., Comment: 24 pages, 11 figures

In the field of superconducting electronics, the on-chip generation of AC radiation is essential for further advancements. Although a Josephson junction can emit AC radiation from a purely DC voltage bias, the coherence of this radiation is significantly limited by Johnson-Nyquist noise. We relate this limitation to the thermodynamic uncertainty relation (TUR) in the field of stochastic thermodynamics. Recent findings indicate that the thermodynamic uncertainty relation can be broken by a classical pendulum clock. We demonstrate how the violation of the TUR can be used as a design principle for radiation sources by showing that a superconducting clock circuit emits coherent AC radiation from a DC bias., Comment: 19 pages, 5 figures, Submission to SciPost

Integration of 2D materials in nanoelectromechanical systems (NEMS) marries the robustness of silicon-based materials with exceptional electrical controllability in 2D materials, drastically enhancing system performance which now is the key for many advanced applications in nanotechnology. Here, we experimentally demonstrate and theoretically analyze a powerful on-chip graphene integrated NEMS device consisting of a hybrid graphene/silicon-nitride membrane with metallic leads that enables an extremely large static and dynamic parameter regulation. When a static voltage is applied to the leads, the force induced by the thermal expansion difference between the leads and the membrane results in ultra-wide frequency tuning, deformation (post-buckling transition) and regulation of mechanical properties. Moreover, by injecting an alternating voltage to the leads, we can excite the resonator vibrating even far beyond its linear regime without a complex and space consuming actuation system. Our results prove that the device is a compact integrated system possessing mechanical robustness, high controllability, and fast response. It not only expands the limit of the application range of NEMS devices but also pushes multidimensional nanomechanical resonators into working in the nonlinear regime.

Logic circuits consist of devices that can be controlled between two distinct states. The recent demonstration that a superconducting current flowing in a constriction can be controlled via a gate voltage ($V_G$) - can lead to superconducting logic with better performance than existing logics. However, before such logic is developed, high reproducibility in the functioning of GCS devices and optimization of their performance must be achieved. Here, we report an investigation of gated Nb devices showing GCS with unprecedently-high reproducibility. Based on the investigation of a statistically-significant number of devices, we demonstrate that the GCS is independent of the constriction width, in contrast with previous reports, and confirm a strong correlation between the GCS and the leakage current ($I_{leak}$) induced by $V_G$. We also achieve a voltage output in our devices larger than the typical values reported to date by at least one order of magnitude, which is relevant for the future interconnection of devices, and show that $I_{leak}$ can be used as a tool to modulate the operational $V_G$ of devices on a $SiO_2$ substrates. These results altogether represent an important step forward towards the optimization of reproducibility and performance of GCS devices, and the future development of a GCS-based logic., Comment: 31 pages, 14 figures, 1 table

Materials with strongly correlated electrons exhibit physical properties that are often difficult to predict as they result from the interactions of large numbers of electrons combined with several quantum degrees of freedom. The layered oxide perovskite Sr$_2$RuO$_4$ is a strongly correlated electron material that has been intensively investigated since its discovery due to its unusual physical properties. Whilst recent experiments have reopened the debate on the exact symmetry of the superconducting state in Sr$_2$RuO$_4$, a deeper understanding of the Sr$_2$RuO$_4$ normal state appears crucial as this is the background in which electron pairing occurs. Here, by using low-energy muon spin spectroscopy we discover the existence of magnetism at the surface of Sr$_2$RuO$_4$ in its normal state. We detect static weak dipolar fields yet manifesting below a relatively high onset temperature larger than 50 K, which reveals the unconventional nature of the observed magnetism. We relate the origin of this phase breaking time reversal symmetry to electronic ordering in the form of orbital loop currents that originate at the reconstructed Sr$_2$RuO$_4$ surface. Our observations set a reference for the discovery of the same magnetic phase in other materials and unveil an electronic ordering mechanism that can influence unconventional electron pairing with broken time reversal symmetry in those materials where the observed magnetic phase coexists with superconductivity., Comment: 20 pages, 5 figures

The application of a gate voltage to control the superconducting current flowing through a nanoscale superconducting constriction, named as gate-controlled supercurrent (GCS), has raised great interest for fundamental and technological reasons. To gain a deeper understanding of this effect and develop superconducting technologies based on it, the material and physical parameters crucial for GCS must be identified. Top-down fabrication protocols should be also optimized to increase device scalability, although studies suggest that top-down fabricated devices are more resilient to show GCS. Here, we investigate gated superconducting nanobridges made with a top-down fabrication process from thin films of the non-centrosymmetric superconductor NbRe. Unlike other devices previously reported, our NbRe devices systematically exhibit GCS, when made in specific conditions, which paves the way for higher device scalability. Our results also suggest that surface properties of NbRe nanobridges and their modification during fabrication are key for GCS., Comment: 14 pages, 4 figures

Here we demonstrate superconducting Dayem-bridge weak-links made of different stoichiometric compositions of NbRe. Our devices possess a relatively high critical temperature, normal-state resistance, and kinetic inductance. In particular, the high kinetic inductance makes this material a good alternative to more conventional niobium-based superconductors (e.g., NbN or NbTiN) for the realization of superinductors and high-quality factor resonators, whereas the high normal-state resistance yields a large output voltage in superconducting switches and logic elements realized upon this compound. Moreover, out-of-plane critical magnetic fields exceeding 2 T ensure that possible applications requiring high magnetic fields can also be envisaged. Altogether, these features make this material appealing for a number of applications in the framework of quantum technologies., Comment: 10 pages, 4 figures