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At least 91 records · Page 5

An approach for fast and accurate simulation of phase change material based thermal energy storage in buildings

Latent heat thermal energy storage (LHTES) has significant potential for mitigating peak electricity demand and enabling load shifting in buildings. Phase Change Material embedded heat exchangers (PCM-HX) can significantly improve energy demand management due to high storage capacity. However, PCM-HX evaluation typically depends on computationally expensive fully transient simulations, posing significant challenges for scalable system- and building-level energy assessments across different climates and system architectures. This paper presents a generalized, accurate, and computationally efficient methodology for simulating building energy systems integrated with LHTES. The PCM-HX transient performance is represented by performance maps generated using a Generalized Resistance-Capacitance Model (GRCM) that enables accurate predictions of arbitrary PCM-HXs at low computational cost. The feasibility of the proposed approach was verified using a case study considering a dual-mode heat pump-thermal energy storage (HP-TES) system simulated in Modelica with Spawn of EnergyPlus™ for a DOE prototype small office building in two locations: Tampa, FL, and International Falls, MN. The PCM-HX performance maps provided accurate predictions of PCM-HX transient behavior, with mean absolute percentage deviations within 2–4% compared to GRCM while also achieving at least 1800× reduction in computational time. Moreover, the HP-TES system achieved energy savings of up to 17.4% in Tampa, FL, and 62.2% in International Falls, MN, demonstrating the broader applicability of the proposed methodology across different climate zones. This work highlights the importance of robust PCM-HX models in enabling accurate and computationally efficient building-level simulations and enabling future research opportunities for investigating optimized HP-TES designs and advanced control strategies for grid-interactive buildings.

Modelica↗

Scalar and Tensor Charmonium Resonances in Coupled-Channel Scattering from Lattice QCD

We determine J P C = 0 + + and 2 + + hadron-hadron scattering amplitudes in the charmonium energy region up to 4100 MeV using lattice QCD, a first-principles approach to QCD. Working at m π ≈ 391 MeV , more than 200 finite-volume energy levels are computed and these are used in extensions of the Lüscher formalism to determine infinite-volume coupled-channel scattering amplitudes. We find that this energy region contains a single χ c 0 and a single χ c 2 resonance. Both are found as pole singularities on the closest unphysical Riemann sheet, just below 4000 MeV with widths around 70 MeV. The largest couplings are to kinematically closed D * D ¯ * channels in S -wave, and couplings to several decay channels consisting of pairs of open-charm mesons are found to be large and significant in both cases. Above the ground state χ c 0 , no other scalar bound states or near- D D ¯ threshold resonances are found, in contrast to several theoretical and experimental studies. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Stable cycling of high-mass loaded MnO 2 electrodes for sodium-ion batteries

Achieving cost-effective, sustainable solutions for large-scale energy storage are critical for advancing the global clean energy transition. In view of the challenges posed by limited lithium reserves, low-cost sodium-ion batteries (SIBs) have emerged as a promising direction, especially for grid-level energy storage. Among the various battery electrode materials, manganese dioxide (MnO 2 ) stands out as a favorable choice for such large-scale applications due to its earth abundance, cost-effectiveness, and non-toxic nature. Although MnO 2 is known as a pseudocapacitive material with superior cycling stability in aqueous electrolytes, its dissolution in non-aqueous electrolytes has restricted its use in long-lifetime batteries. In this study, we address two issues which have limited the use of MnO 2 electrodes in non-aqueous electrolytes. First, using electrochemical quartz crystal microbalance measurements in combination with other electrochemical methods, we demonstrate that diglyme (bis(2-methoxyethyl) ether) electrolyte can achieve stable cycling of electrodeposited ε-MnO 2 . These results enable us to tackle a second objective, that is increasing the mass loading of the MnO 2 electrode, since achieving high areal energy density is a significant factor in reducing manufacturing costs. Using 3D printed graphene aerogel (GA) as a scaffold, our studies show that the electrodeposited MnO 2 /GA electrodes possess scalable properties with mass loadings from 20 to 80 mg cm −2 . The resulting electrodes exhibit areal energy densities as high as 4.4 mA h cm −2 at a current density of 10 mA cm −2 . The high mass loaded MnO 2 electrodes were incorporated as a cathode in a SIB which used TiO 2 as the anode. The SIB device exhibited excellent performance with power densities in excess of 70 mW cm −2 . These studies highlight the promise of MnO 2 electrodes for use in a low-cost technology for large-scale energy storage.

25 ENERGY STORAGE↗

District heating utilizing waste heat of a data center: High-temperature heat pumps

Data centers are energy-intensive facilities with substantial low-grade waste heat. High-temperature heat pumps can be critical in boosting the data center’s waste heat for district heating, improving the system-level energy efficiency of data centers, and reducing CO 2 emissions in district heating. This study built thermodynamic models to assess high-temperature heat pumps with six configurations using low global warming potential refrigerants to supply heat up to 120 °C. The heat pump configurations include single-stage or two-stage cycles with advanced components, such as internal heat exchanger, economizer, flash tank, or parallel compressor. The refrigerants include R1234ze(Z), R1233ed(E), R1224yd(Z), R600, and R600a, and R245fa is used as a reference. A case study was carried out to recover the waste heat from the Frontier high-performance computing data center and provide hot water for district heating at the US Department of Energy’s Oak Ridge National Laboratory campus. The optimized performance of high-temperature heat pumps is characterized with various effectiveness of internal heat exchangers, and the operating parameters of economizer or flash tank, as well as their combination. The results show that the configurations of two-stage cycles with internal heat exchanger + flash tank and internal heat exchanger + economizer/parallel-compressor provide the highest coefficient of performance under scenarios of the maximum allowable value and a fixed value (0.3) of the internal heat exchangers’ effectiveness, respectively. R1234ze(Z) and R600a are the most promising refrigerants, considering trade-offs between the coefficient of performance and the volumetric heating capacity. The single-stage cycle with internal heat exchanger + economizer/parallel-compressor using R1234ze(Z) is recommended for utilizing Fronter’s waste heat in district heating. A one mega-watt high-temperature heat pump will reduce 33,100–33,200 metric tons of CO2 emission annually, corresponding to 85.4 %–85.6 % of equivalent CO2 emissions from natural gas boilers. Here, this study provides good guidelines for designing and deploying high-temperature heat pumps to support sustainable data centers and decarbonize district heating in the US.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Microtron Data Log

The Microtron at Los Alamos National Laboratory (LANL) is a versatile electron accelerator originally designed for medical therapy. Since 2001, it has been used for non-destructive radiographic imaging and research and development applications. Operating at four different energy levels—6, 10, 15, and 20 MeV—the Microtron produces dose rates of approximately 780, 1800, 2700, and 2800 R/min at a distance of one meter from the source, respectively. This high-energy X-ray source enables detailed internal examination of dense and thick objects without causing damage, making it invaluable for various scientific and industrial applications. For instance, LANL’s Microtron has been utilized to study the performance of large-panel cerium-doped lutetium yttrium silicon oxide (LYSO) scintillators, which are essential components in advanced imaging systems.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Mobility Energy Productivity (MEP) Metric: Partnerships, Applications, and Key Enhancements

The Mobility Energy Productivity (MEP) metric is a holistic measure of transportation systems performance that quantifies the ability of individuals to reach destinations in a cost-efficient and energy-efficient manner. This presentation highlights recent partnerships that have advanced the adoption of MEP as a decision-support tool by various agencies, stakeholders, and researchers. Applications include evaluating multimodal accessibility, comparing system-level energy impacts, and informing infrastructure investment strategies. Key enhancements to the metric - such as expanded regional applications and incorporation of emerging technologies - are also discussed. Together, these efforts highlight the potential of MEP to inform data-driven decisions that shape future transportation systems.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Design Principles in Engineering of Multigrain Nanocatalysts via Multiscale Electronic Structure Characterization

Engineering grain boundary (GB) strain provides a promising pathway to tune the catalytic properties of nanocrystals. However, structural heterogeneity from random grain orientation and geometry has limited clear structure–property correlations. Here, we utilize a multigrain Co3O4/Mn3O4 core/shell nanocrystal platform as a model system to systematically investigate how geometric misfit strain at GBs serves as catalytically active sites for the oxygen reduction reaction. Through precise subnanometer-level control over grain morphology and by integrating multiscale electronic structure characterization, we identify the electronic structural signature of GB defects and establish a direct correlation between localized strain fields and modified electronic states. Strain modulation at GBs alters the eg orbital energy levels, with elongation along the z-axis combined with shear strain stabilizing the eg states, in contrast to the destabilization observed under pure shear strain. This stabilization mechanism enhances the electrocatalytic activity and selectivity of strained GBs compared with strain-relaxed grain surfaces. Furthermore, we reveal that GBs exhibit a radial strain gradient, producing a spatial energy shift that further modulates local electronic structures, as resolved through the classification of electron energy loss spectroscopy data. Together, these findings demonstrate that geometric misfit strain enables precise tuning of grain geometry and the resulting electronic structures, offering a robust strategy for engineering next-generation nanocatalysts.

Cho, Min Gee↗

Excited-state uncertainties in lattice-QCD calculations of multi-hadron systems

Excited-state effects lead to hard-to-quantify systematic uncertainties in lattice quantum chromodynamics (LQCD) spectroscopy calculations when computationally accessible imaginary times are smaller than inverse excitation gaps, as often arises for multi-hadron systems with signal-to-noise problems. Lanczos residual bounds address this by providing two-sided constraints on energies that do not require assumptions beyond Hermiticity, but often give very conservative systematic uncertainty estimates. Here, a more-constraining set of gap bounds is introduced for hadron spectroscopy. These bounds provide tighter constraints whose validity requires an explicit assumption about an energy gap. Exactly solvable lattice field theory correlators are used to test the utility of residual and gap bounds at finite and infinite statistics. Two-sided bounds and other analysis methods are then applied to a high-statistics LQCD calculation of nucleon-nucleon scattering at $m_π\sim 800$ MeV. Generalized eigenvalue problem (GEVP) and Lanczos energy estimators are compatible when applied to the same correlator data, but analyses including different interpolating operators show statistically significant inconsistencies. However, two-sided bounds from all operators are consistent. Under the assumption that the number of energy levels below $NΔ$ and $ΔΔ$ thresholds is the same as for non-interacting nucleons, gap bounds are sufficient to constrain nucleon-nucleon scattering amplitudes at phenomenologically relevant precision. Lanczos methods further reveal that energy-eigenstate estimates from previously studied asymmetric correlators have not converged over accessible imaginary times. Nevertheless, data-driven examples demonstrate why assumptions are required to draw conclusions about the natures of two-nucleon ground states at these masses.

Detmold, William [MIT, Cambridge, CTP]↗

DUNE – Simulation Validation of Fermilab Detector Reconstruction

DUNE (Deep Underground Neutrino Experiment) is Fermilab’s flagship international experiment designed to study neutrinos by sending an intense beam from Illinois to detectors located 1,300 kilometers away at the Sanford Underground Research Facility (SURF) in South Dakota. To prepare for such a large-scale experiment, physicists develop detailed simulations to produce mock data sets which are analyzed by the CAFAna framework. During my internship, I developed software using the CAFAna framework to analyze simulated detector data and generated plots to make data trends easier to interpret and identify patterns. My analysis has uncovered inconsistencies in reconstructed neutrino tracks, duplicated reconstructed tracks causing sporadic spikes in the data, and unnatural differences in energy levels between interaction types. These analyses help verify that the improvements to detector simulations do not introduce unintended resolution errors and ensure proper reconstruction performance, supporting DUNE’s goal of making precise neutrino measurements and advancing the Department of Energy’s mission of fundamental scientific discovery.

Vershaw, Andre [Unlisted, US, IL; Fermilab] (ORCID↗

A limit to strong shock behavior in the dynamic response of matter at pressure

Solids under high pressures experience a series of regimes, where their microstructure adapts to the applied compression and these key transitions are discussed in this paper. As strain increases, new forces emerge at extreme pressures. A previous study introduced the concept of the weak shock limit (WSL), at which the ambient theoretical shear strength is overcome. Above the WSL, further deformation under strong shock conditions results in electrons occupying higher energy levels as strain increases. As pressure rises further, shock melting occurs in the material and at around three times this melting pressure, the strong shock limit is reached where the driving physics under pressure switches, with electrons forced into higher energy states. This leads to significant reduction in their compressibility due to changes in electronic structure and developing electron degeneracy pressures. A derivation for conditions at this state is presented, which indicates that a dependence of the threshold pressure on the free electron number density defines the limit observed. This correlation suggests that ambient material moduli govern material compression up to nearly 50% strain. These observations show that models should account for different behaviors as dominant physics changes in each regime accessed as shock pressure increases.

36 MATERIALS SCIENCE↗

Carbon-Based Quantum Information Science with Symmetry Protected Topological States (Final Report, DOE-BES award DE-SC0023105)

This research program established the scientific foundation for the rational, bottom-up design, synthesis, isolation, and investigation of symmetry-protected topological (SPT) electron spin qubits embedded in graphene nanoribbons (GNRs). The work focused on integrating atomically precise low-dimensional carbon nanostructures with emerging quantum logic architectures, providing a pathway toward scalable quantum materials for next-generation computing and sensing technologies. A central component of the program was the elucidation of fundamental relationships between real-space molecular architecture, local spin density distributions, electronic band dispersion, and energy level alignment in atomically precise GNR systems. These correlations define key operational parameters of SPT qubits and were systematically investigated to establish quantitative benchmarks against established molecular and solid-state spin qubit platforms. Attention was given to properties critical for quantum device performance, e.g. decoherence times, spectral sharpness of energy transitions, and tunable exchange interactions between spin states. The research demonstrated that these parameters can be engineered with atomic precision through scalable bottom-up synthetic strategies. Theory-guided design played a central role in identifying candidate structures hosting topologically protected spin states. Experimental validation was performed using both ensemble measurements and single-molecule characterization. In addition to advances in quantum materials synthesis, the program developed and applied spin-sensitive scanning probe microscopy techniques capable of directly probing quantum states and dynamic processes with atomic-scale spatial resolution. These capabilities enabled direct observation and characterization of quantum structures at the single-atom level. While the research activities were primarily hypothesis-driven fundamental investigations, the program adopted a comprehensive materials-by-design framework aimed at translating scientific discoveries into technological concepts compatible with scalable and intelligent manufacturing approaches.

36 MATERIALS SCIENCE↗

Second harmonic generation in topological insulators under quantizing magnetic fields

We theoretically investigate the second harmonic generation (SHG) of topological insulator surface states in a perpendicular magnetic field. Our theory is based on the microscopic expression of the second-order magneto-optical conductivity developed from the density matrix formalism, taking into account hexagonal warping effects on the surface states' band structure. Using numerically exact Landau-level energies and wave functions including hexagonal warping, we calculate the spectrum of SHG conductivities under normal incidence for different values of magnetic field and chemical potential. The imaginary parts of the SHG conductivities show prominent resonant peaks corresponding to one-photon and two-photon inter-Landau-level transitions. Treating the hexagonal warping term perturbatively, these transitions are clarified analytically within a perturbation theory from which approximate selection rules for the allowable optical transitions for SHG are determined. Furthermore, our results show extremely high SHG susceptibility that is easily tunable by magnetic field and doping level for topological surface states in the far-infrared regime, exceeding that of many conventional nonlinear materials. This work highlights the key role of hexagonal warping effects in generating second-order optical responses and provides insights into the nonlinear magneto-optical properties of the topological insulators.

Landau levels↗

Novel Organosulfur-Based Electrolytes for Safe Operation of High Voltage Li-ion Batteries over a Wide Operating Temperature

This project addresses the failure of conventional electrolytes and enables high-voltage operation of lithium-ion batteries (LIBs) by developing a novel organosulfur-based electrolyte system. To achieve this goal, we first designed and synthesized new organosulfur solvents that functionalized with strong electron-withdrawing groups such as fluoroalkyl and cyano substituents. Through regio-specific molecular engineering, supported by theoretical calculations, we lowered the highest occupied molecular orbital (HOMO) energy levels of these molecules to increase their anodic stability for high-voltage operation. We then optimized the formulation of the organosulfur-based electrolyte with additives, co-solvents and salts tailored to the newly synthesized solvent molecules. In parallel, we utilized advanced spectroscopic techniques—including in situ FTIR, EIS, and DEMS—to thoroughly elucidate the mechanisms of interaction between the electrolyte and electrode materials. Finally, we evaluated 2 Ah pouch cells under both normal and extreme conditions. Pouch cells with the newly developed electrolyte system demonstrated >90% capacity retention after 500 cycles under 4.5 V operating voltage, >80% capacity retention after 1000 cycles in coin cell level. In addition, the cells exhibited high safety and reliable operation capability over a wide temperature range from −30 °C to +45 °C.

25 ENERGY STORAGE↗

Demonstration of the rodeo algorithm on a quantum computer

The rodeo algorithm is an efficient algorithm for eigenstate preparation and eigenvalue estimation for any observable on a quantum computer. This makes it a promising tool for studying the spectrum and structure of atomic nuclei as well as other fields of quantum many-body physics. The only requirement is that the initial state has sufficient overlap probability with the desired eigenstate. While it is exponentially faster than well-known algorithms such as phase estimation and adiabatic evolution for eigenstate preparation, it has yet to be implemented on an actual quantum device. In this work, we apply the rodeo algorithm to determine the energy levels of a random one-qubit Hamiltonian, resulting in a relative error of 0.08% using mid-circuit measurements on the IBM Q device Casablanca. This surpasses the accuracy of directly-prepared eigenvector expectation values using the same quantum device. We take advantage of the high-accuracy energy determination and use the Hellmann-Feynman theorem to compute eigenvector expectation values for a different random one-qubit observable. For the Hellmann-Feynman calculations, we find a relative error of 0.7%. Here, we conclude by discussing possible future applications of the rodeo algorithm for multi-qubit Hamiltonians.

algorithm↗

Energy density driven ultrafast electronic excitations in a cuprate superconductor

Controlling nonequilibrium dynamics in quantum materials requires ultrafast probes with spectral selectivity. We report femtosecond reflectivity measurements on the cuprate superconductor Bi 2⁢ Sr 2⁢ CaCu 2 ⁢O 8+𝛿 using free-electron laser extreme-ultraviolet (23.5–177 eV) and near-infrared (1.5 eV) pump pulses. EUV pulses access deep electronic states, while NIR light excites valence-band transitions. Despite these distinct channels, both schemes produce nearly identical dynamics: above 𝑇 𝑐 , excitations relax through fast (100–300 fs) and slower (1–5 ps) channels; below 𝑇 𝑐 , a delayed component signals quasiparticle recombination and condensate recovery. We find that when electronic excitations are involved, the ultrafast response is governed mainly by absorbed energy rather than by the microscopic nature of the excitation. In contrast, bosonic driving in the THz or midinfrared produces qualitatively different dynamics. By demonstrating that EUV excitation of a correlated superconductor yields macroscopic dynamics converging with those from optical pumping, this work defines a new experimental paradigm: FEL pulses at core-level energies provide a powerful means to probe and control nonequilibrium electronic states in quantum materials on their intrinsic femtosecond timescales. This establishes FEL-based EUV pumping as a new capability for ultrafast materials science, opening routes toward soft x-ray and attosecond studies of correlated dynamics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Halogenated Dibenzo[ f , h ]quinoxaline Units Constructed 2D‐Conjugated Guest Acceptors for 19% Efficiency Organic Solar Cells

Abstract Halogenation of Y‐series small‐molecule acceptors (Y‐SMAs) is identified as an effective strategy to optimize photoelectric properties for achieving improved power‐conversion‐efficiencies (PCEs) in binary organic solar cells (OSCs). However, the effect of different halogenation in the 2D‐structured large π‐fused core of guest Y‐SMAs on ternary OSCs has not yet been systematically studied. Herein, four 2D‐conjugated Y‐SMAs (X‐QTP‐4F, including halogen‐free H‐QTP‐4F, chlorinated Cl‐QTP‐4F, brominated Br‐QTP‐4F, and iodinated I‐QTP‐4F) by attaching different halogens into 2D‐conjugation extended dibenzo[ f , h ]quinoxaline core are developed. Among these X‐QTP‐4F, Cl‐QTP‐4F has a higher absorption coefficient, optimized molecular crystallinity and packing, suitable cascade energy levels, and complementary absorption with PM6:L8‐BO host. Moreover, among ternary PM6:L8‐BO:X‐QTP‐4F blends, PM6:L8‐BO:Cl‐QTP‐4F obtains a more uniform and size‐suitable fibrillary network morphology, improved molecular crystallinity and packing, as well as optimized vertical phase distribution, thus boosting charge generation, transport, extraction, and suppressing energy loss of OSCs. Consequently, the PM6:L8‐BO:Cl‐QTP‐4F‐based OSCs achieve a 19.0% efficiency, which is among the state‐of‐the‐art OSCs based on 2D‐conjugated Y‐SMAs and superior to these devices based on PM6:L8‐BO host (17.70%) and with guests of H‐QTP‐4F (18.23%), Br‐QTP‐4F (18.39%), and I‐QTP‐4F (17.62%). The work indicates that halogenation in 2D‐structured dibenzo[ f , h ]quinoxaline core of Y‐SMAs guests is a promising strategy to gain efficient ternary OSCs.

14 SOLAR ENERGY↗

Dosimetric and biological impact of activity extravasation of radiopharmaceuticals in PET imaging

The increasing use of nuclear medicine and PET imaging has intensified scrutiny of radiotracer extravasation. To our knowledge, this topic is understudied but holds great potential for enhancing our understanding of extravasation in clinical PET imaging. This work aims to (1) quantify the absorbed doses from radiotracer extravasation in PET imaging, both locally at the site of extravasation and with the extravasation location as a source of exposure to bodily organs and (2) assess the biological ramifications within the injection site at the cellular level. A radiation dosimetry simulation was performed using a whole-body 4D Extended Cardiac-Torso (XCAT) phantom embedded in the GATE Monte Carlo platform. A 10-mCi dose of 18 F-FDG was chosen to simulate a typical clinical PET scan scenario, with 10% of the activity extravasated in the antecubital fossa of the right arm of the phantom. The extravasation volume was modeled as a 5.5 mL rectangle in the hypodermal layer of skin. Absorbed dose contributions were calculated for the first two half-lives, assuming biological clearance thereafter. Dose calculations were performed as absorbed doses at the organ and skin levels. Energy deposition was simulated both at the local extravasation site and in multiple organs of interest and converted to absorbed doses based on their respective masses. Each simulation was repeated ten times to estimate Monte Carlo uncertainties. Biological impacts on cells within the extravasated volume were evaluated by randomizing cells and exposing them to a uniform radiation source of 18 F and 68 Ga. Particle types, their energies, and direction cosines were recorded in phase space files using a separate Geant4 simulation to characterize their entry into the nucleus of the cellular volume. Subsequently, the phase space files were imported into the TOPAS-nBio simulation to assess the extent of DNA damage, including double-strand breaks (DSBs) and single-strand breaks (SSBs). Organ-level dosimetric estimations are presented for 18 F and 68 Ga radionuclides in various organs of interest. With 10% extravasation, the hypodermal layer of the skin received the highest absorbed dose of 1.32 ± 0.01 Gy for 18 F and 0.99 ± 0.01 Gy for 68 Ga. The epidermal and dermal layers received absorbed doses of 0.07 ± 0.01 Gy and 0.13 ± 0.01 Gy for 18 F, and 0.14 ± 0.01 Gy and 0.29 ± 0.01 Gy for 68 Ga, respectively. In the extravasated volume, 18 F caused an average absorbed dose per nucleus of 0.17 ± 0.01 Gy, estimated to result in 10.58 ± 0.50 DSBs and 268.11 ± 12.43 SSBs per nucleus. For 68 Ga, the absorbed dose per nucleus was 0.11 ± 0.01 Gy, leading to an estimated 6.49 ± 0.34 DSBs and 161.24 ± 8.12 SSBs per nucleus. Absorbed doses in other organs were on the order of micro-gray (µGy). The likelihood of epidermal erythema resulting from extravasation during PET imaging is low, as the simulated absorbed doses to the epidermis remain below the thresholds that trigger such effects. Moreover, the organ-level absorbed doses were found to be clinically insignificant across various simulated organs. The minimal DNA damage at the extravasation site suggests that long-term harm, such as radiation-induced carcinogenesis, is highly unlikely.

DNA strand breaks↗

Spectroscopy of the fractal Hofstadter energy spectrum

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 moiré superlattices. Yet, so far, direct spectroscopy of the fractal energy spectrum predicted by Hofstadter nearly 50 years ago has remained out of reach. Here, in this work, we use high-resolution scanning tunnelling microscopy/spectroscopy (STM/STS) to investigate the flat electronic bands in twisted bilayer graphene (TBG) near the predicted second magic angle, an ideal setting for spectroscopic studies of Hofstadter’s spectrum. Our study shows the fractionalization of flat moiré 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, showing phenomena beyond that of Hofstadter’s original model owing to the combined effects of strong correlations, Coulomb interactions and the quantum degeneracy of electrons in TBG.

electronic properties and materials↗