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At least 973 records · Page 54

Twists and turns: stacking and structure-dependent optical response in MoS 2 nanoscrolls

Transition metal dichalcogenide (TMD) nanoscrolls (NSs), specifically MoS 2 NSs, present unique structural and optical properties, exhibiting prominent photoluminescence (PL) signals despite their multilayer nature. Here, this study investigates the structural and spectroscopic characteristics of MoS 2 NSs, correlating them to show the effects of reduced interlayer interactions on excitons of MoS 2 NSs. The reduction in interlayer interaction arises from two main factors: (1) symmetry-broken mixed stacking due to misalignment between layers and (2) a highly inhomogeneous strain profile generated by the Archimedean spiral geometry with positive eccentricity. Transmission electron microscopy, field emission scanning electron microscopy, atomic force microscopy, Raman spectroscopy, and second harmonic generation measurements confirm these findings. Low-temperature PL spectroscopy explores the impact of reduced interlayer interactions on exciton properties such as exciton–phonon coupling and oscillator strength. This study provides crucial insights into the structure, stacking and unique optical properties of TMD NSs, advancing the understanding of interlayer interactions and their impacts in complex quasi-one-dimensional nanostructures.

25 ENERGY STORAGE

First on-line commissioning experiments at the St. Benedict facility

Nuclear beta decays provide an excellent probe of fundamental symmetries due to their mediation by the weak interaction. In particular, precise measurements of these decays provide constraints on the unitarity of the Cabbibo-Kobayashi-Maskawa (CKM) quark-mixing matrix. While superallowed pure Fermi decays currently set the most precise limits, the alternative suite of superallowed mixed mirror decays has been ill-studied. These nuclei can provide an important consistency check of calculation and measurement methods employed for the pure Fermi decays, more critically needed now in the wake of a 2.4σ deviation from unitarity of the CKM matrix. In order to remedy the gap in data for mirror decays, the Superallowed Transition Beta-Neutrino Decay Ion Coincidence Trap (St. Benedict) facility is being commissioned at the University of Notre Dame’s Nuclear Science Laboratory (NSL). In this paper, we present first results of the commissioning of the St. Benedict facility on-line at the TwinSol radioactive beam facility. The results of initial commissioning experiments involving the St. Benedict gas catcher, RF carpet, RFQ ion guide and RFQ cooler-buncher will be presented.

beta decay

Role of the isovector spin-orbit potential in mitigating the CREX-PREX dilemma

Pioneering electroweak measurements of the neutron skin thickness in lead-208 and calcium-48 are challenging our understanding of nuclear dynamics. Many theoretical models suggest that the slope of the symmetry energy controls the development of a neutron skin in neutron-rich nuclei. This led to the expectation that if lead-208 exhibits a large neutron skin, calcium-48 should as well. Given that the PREX Collaboration reported a relatively thick neutron skin in lead, we anticipated that calcium would also have a significant neutron skin. Instead, the CREX Collaboration reported a thin neutron skin in calcium. Although many suggestions have been proposed, the “CREX-PREX dilemma” remains unsolved. Recently, an intriguing scenario has emerged, suggesting that an enhanced isovector spin-orbit interaction could simultaneously account for both results. Following this approach, we performed relativistic mean-field calculations with an increased isovector spin-orbit potential. Our findings indicate that, while this modification significantly affects the structure of calcium-48, it has only a marginal impact on lead-208, thereby bringing the results into better agreement with experiment. Furthermore, the strong enhancement required to mitigate the CREX-PREX dilemma destroys the agreement with a successful spin-orbit phenomenology, primarily by modifying the well-known ordering of spin-orbit partners.

Neutron skin thickness

Quantitative Nonlinear Optical Polarimetry with High Spatial Resolution

Nonlinear optical microscopy such as in the optical second-harmonic generation (SHG) modality has become a popular tool today for probing materials in the physical and biological sciences. While imaging and spectroscopy are widely used in the microscopy mode, nonlinear polarimetry, which can shed light on materials’ symmetry and microstructure, is relatively underdeveloped. This is partly because quantitative analytical modeling of the optical SHG response for anisotropic crystals and films largely assumes low-numerical aperture (NA) focusing of light, where the plane-wave approximation is sufficient. Tight focusing provides unique benefits in revealing out-of-plane polarization responses, which cannot be detected by near-plane-wave illumination at normal incidence. Here, we outline a method for quantitatively analyzing SHG polarimetry measurements obtained under high-NA focusing within a microscope geometry. Experiments and simulations of a variety of standard samples, from single crystals to thin films, are in good agreement, including measured and simulated spatial SHG maps of ferroelectric domains. A solution to the inverse problem is demonstrated, where the spatial distribution of an SHG tensor with unknown tensor coefficient magnitudes is determined by experimentally measured polarimetry. The ability to extract the out-of-plane component of the nonlinear polarization in normal incidence is demonstrated, which can be valuable for high-resolution polarimetry of 2D materials, thin films, heterostructures, and uniaxial crystals with a strong out-of-plane response.

36 MATERIALS SCIENCE

Oscillatory redox behavior in oxides: Cyclic surface reconstruction and reactivity modulation via the Mars–van Krevelen mechanism

The breaking of translational symmetry at oxide surfaces gives rise to coordinatively unsaturated cations/anions and surface restructuring—key factors that govern surface reactivity. Using direct in situ environmental transmission electron microscopy (TEM) observations along with atomistic modeling, we report oscillatory redox behavior in CuO under H 2 , where cyclic surface reconstruction and reactivity modulation occur via the Mars–van Krevelen (MvK) mechanism. We observe self-switching between oxygen-rich and oxygen-deficient surface reconstructions, alternately activating and deactivating the surface for H 2 O formation. During periods of chemical inactivity, the oxygen-deficient surface undergoes slow reoxidation via lattice oxygen diffusing from subsurface and bulk reservoirs, restoring the active oxygen-rich surface termination. The inherent disparity in chemical activity among undercoordinated surface ions, along with sluggish subsurface-to-surface oxygen replenishment, drives this oscillatory redox cycle, modulating H2-induced loss of lattice oxygen at the surface and its delayed replenishment from the subsurface. This creates spatiotemporally separated redox steps at the oxide surface. The phenomena and atomistic insights presented here have significant implications for manipulating the surface reactivity of oxides by tuning the separation of these redox steps.

36 MATERIALS SCIENCE

Optical cycling on thorium monoxide for an improved test of fundamental symmetries

Optical cycling refers to repeated excitation and spontaneous emission on an electronic transition in an atom or molecule. Optical cycling in molecules can enable a wide range of quantum control and readout techniques, but unfortunately it has only been demonstrated on a small class of alkalilike or alkaline-earth-like molecules. Thorium monoxide (ThO), a molecule used in one of the most precise permanent electron electric dipole moment (eEDM) searches (ACME†) [Andreev et al., Nature (London) 562, 355 (2018)], does not fall into this category. In this work, we demonstrate the first optical cycling on this nonconventional class over a range of experimental parameter space, including laser intensity, polarization switching rate, and interaction time. We show that both the 𝐽 = 1 and 𝐽 = 2 rotational levels of ThO molecule are capable of cycling an average of 11(2) photons with a single laser, at scattering rates of 1.9⁢(6) × 10 6 and 2.3⁢(7) × 10 6 s −1 , respectively, before population is lost to other vibronic levels. We outline a scheme to apply this demonstrated optical cycling in an ACME-style eEDM measurement, improving the detection efficiency by over fourfold compared to noncycling fluorescence detection. This would lead to over a twofold enhancement in the statistical sensitivity of the eEDM search. This optical-cycling scheme can be further extended to scatter ∼100 photons, which would enable a wider range of quantum control and sensing using ThO molecules.

Atomic & molecular processes in external fields

Multiscale analysis of large twist ferroelectricity and swirling dislocations in bilayer hexagonal boron nitride

With its atomically thin structure and intrinsic ferroelectric properties, heterodeformed bilayer hexagonal boron nitride (hBN) has gained prominence in next-generation non-volatile memory applications. However, studies to date have focused almost exclusively on small-twist bilayer hBN, leaving the question of whether ferroelectricity can persist under small heterostrain and large heterodeformation entirely unexplored. In this work, we establish the crystallographic origin of ferroelectricity in bilayer hBN configurations heterodeformed relative to high-symmetry configurations such as AA-stacking and 21.786789° twisted configurations (Σ7), using Smith normal form bicrystallography. We then demonstrate out-of-plane ferroelectricity in bilayer hBN across configurations vicinal to both the AA and Σ7 stackings. Atomistic simulations reveal that AA-vicinal systems support ferroelectricity under both small twist and small strain, with polarization switching in the latter governed by the deformation of swirling dislocations rather than the straight interface dislocations seen in the former. For Σ7-vicinal systems, where existing interatomic potentials underperform particularly under extreme out-of-plane compression, we develop a density-functional-theory-informed continuum framework—the bicrystallography-informed frame-invariant multiscale (BFIM) model, which captures out-of-plane ferroelectricity in heterodeformed configurations vicinal to Σ7 stacking. Interface dislocations in these large heterodeformed bilayer configurations exhibit markedly smaller Burgers vectors compared to interface dislocations in small-twist and small-strain bilayer hBN. The BFIM model reproduces experimental results and provides a powerful, computationally efficient framework for predicting ferroelectricity in large-unit-cell heterostructures where atomistic simulations are prohibitively expensive.

Ahmed, Md Tusher [Univ. of Illinois at Urbana-Cham

Impact of Tiny Fermi Pockets with Extremely High Mobility on the Hall Anomaly in the Kagome Metal CsV 3 ⁢Sb 5

The kagome metal CsV 3 ⁢Sb 5 exhibits an unusual charge-density-wave (CDW) order, where the emergence of loop current order that breaks time-reversal symmetry (TRS) has been proposed. A key feature of this CDW phase is a nonmonotonic Hall effect at low fields, often attributed to TRS breaking. However, its origin remains unclear. Here, we conduct comprehensive magnetotransport measurements on CsV 3 ⁢Sb 5 and, through mobility spectrum analysis, identify the formation of tiny Fermi pockets with extremely high mobility below the CDW transition. Furthermore, electron irradiation experiments reveal that the nonmonotonic Hall effect is significantly suppressed in samples with reduced mobility, despite no substantial change in the electronic structure. In conclusion, these results indicate that the nonmonotonic Hall effect originates from these tiny Fermi pockets with high mobility carriers rather than anomalous Hall mechanisms, providing new insights into understanding the Hall anomaly in this kagome system.

36 MATERIALS SCIENCE

Disorder-induced magnetoelastic behaviors of MnTexSbyBi1-x-y alloys

This dataset contains input and output files from density functional theory (DFT) simulations used to study the disorder-induced magnetoelastic behaviors of MnTexSbyBi1-x-y (0 ≤ x + y ≤ 1) alloys and their binary end members MnTe, MnSb, and MnBi. The alloys adopt the hexagonal NiAs-type (nickeline) structure and span ternary (MnTexSb1-x, MnTexBi1-x, MnBixSb1-x), and quaternary compositions across the full MnTe–MnSb–MnBi composition triangle. For each alloy composition, the dataset provides DFT calculations in three magnetic configurations: A-type antiferromagnetic (AFM), C-type AFM, and ferromagnetic (FM). Every magnetic configuration folder contains the fully relaxed crystal structure (CONTCAR), VASP input parameters (INCAR), and the main VASP output file (OUTCAR), from which total electronic energies, Mn magnetic moments, lattice parameters, and percent volume changes between magnetic states are extracted. These data are used to construct compositional phase diagrams, evaluate thermodynamic stability (formability), and map magnetoelastic responses across the alloy space. For A-type AFM and FM configurations, additional data are provided as follows: (i) FORCE_CONSTANTS and thermal_properties.yaml files at the top level of A-type_AFM/ and FM/ folders — present only for compositions marked with an asterisk (*) in Table I of the main text. These are derived from Phonopy finite-displacement calculations on full disordered 128-atom supercells and provide vibrational free energy, entropy (Svib)contribution from explicit disorder calculations. (Table I of the associated main manuscript) (ii) A VCA/ subfolder within A-type_AFM/ and FM/, containing FORCE_CONSTANTS and thermal_properties.yaml from Virtual Crystal Approximation phonon calculations (without spin-orbit coupling). VCA data are available for all compositions and are used to estimate vibrational contributions to the Gibbs free energy across the full composition space. (iii) A SOC/ subfolder containing CONTCAR, INCAR, and OUTCAR from spin-orbit coupling calculations, providing relativistic corrections to electronic energies and lattice parameters (Tables S2–S3 of the SM, and Table I of the main manuscript). (iv) A SOC/VCA/ subfolder containing FORCE_CONSTANTS and thermal_properties.yaml from VCA phonon calculations performed within the SOC framework, combining relativistic and vibrational thermodynamic corrections. The computed properties are used to map the AFM–FM magnetic crossover near MnTe0.75Sb0.25, demonstrate disorder- and spin-induced phonon broadening, identify a semiconductor-to-metal crossover, and quantify the pronounced magnetoelastic volume response near the magnetic phase boundary.

36 MATERIALS SCIENCE

Exotic phases in finite-density ℤ 3 theories

Lattice ℤ 3 theories with complex actions share many key features with finite- density QCD including a sign problem and $\mathcal{CK}$ symmetry. Complex ℤ 3 spin and gauge models exhibit a generalized Kramers-Wannier duality mapping them onto chiral ℤ 3 spin and gauge models, which are simulatable with standard lattice methods in large regions of parameter space. The Migdal-Kadanoff real-space renormalization group (RG) preserves this duality, and we use it to compute the approximate phase diagram of both spin and gauge ℤ 3 models in dimensions one through four. Chiral ℤ 3 spin models are known to exhibit a Devil’s Flower phase structure, with inhomogeneous phases that can be thought of as ℤ 3 analogues of chiral spirals. Out of the large class of models we study, we find that only chiral spin models and their duals have a Devil’s Flower structure with an infinite set of inhomogeneous phases, a result we attribute to Elitzur’s theorem. We also find that different forms of the Migdal-Kadanoff RG produce different numbers of phases, a violation of the expectation for universal behavior from a real-space RG. We discuss extensions of our work to ℤ N models, SU(N) models and nonzero temperature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Kinetic Understanding of Field-Induced Phase Transition from Tetragonal to Ferroelectric Orthorhombic Phase in Ferroelectric CeO 2 –HfO 2 –ZrO 2 Films

The ferroelectric properties and structural phase transition behaviors of fluorite-type CeO 2 −HfO 2 −ZrO 2 films were investigated. The epitaxial films on indium tin oxide (ITO) (111)/yttria-stabilized zirconia (YSZ) (111) substrates were grown through pulsed laser deposition at room temperature and subsequently heat-treated at 1000 °C under a N 2 gas flow. The crystalline phases and Curie temperatures of the films were investigated by X-ray diffraction. An increase in the Ce or Zr content in the films led to a higher crystallographic symmetry, such as orthorhombic or tetragonal. In addition, electrical characterization revealed that the orthorhombic films and some of the tetragonal films displayed ferroelectricity. This was due to the field-induced phase transition from the tetragonal to ferroelectric orthorhombic phase in the films, where the Curie temperatures were relatively low. The tetragonal metastable phase was kinetically frozen and could not change into the stable orthorhombic phase at such a low temperature. The critical electric field where the field-induced phase transition occurred was below 0.8 MV/cm, which was sufficiently small compared to the coercive field. These results evidence the kinetic driving force that causes a field-induced phase transition from the paraelectric tetragonal phase to the ferroelectric orthorhombic phase in HfO 2 -based ferroelectrics. They also enhance our understanding of the thermodynamic phase stabilities of HfO 2 -based material polymorphs.

36 MATERIALS SCIENCE

Polarization transmission in the Hadron Storage Ring of the Electron-Ion Collider

The successful operation of the future Electron-Ion Collider is contingent on maintaining high hadron beam polarization up to 275 GeV. The Hadron Storage Ring lattice, however, features a symmetry-breaking interaction region that excites strong, nonsystematic spin resonances, posing a significant threat to polarization preservation. This paper systematically investigates two complementary strategies to ensure high polarization transmission. The first method involves optimizing the vertical betatron phase advance between Siberian snakes to orchestrate a cancellation of depolarizing kicks across the ring. We demonstrate through simulations that both dynamic and fixed-optics solutions based on this principle can successfully preserve polarization through the strongest resonances. The second, more powerful approach involves optimizing the snake rotation axes to suppress resonance driving terms at their source. We revisit established symmetric configurations, such as the Lee-Courant schemes, and introduce a novel, highly symmetric “Doubly Lee-Courant” (DLC) scheme, which enforces a local 𝜋 spin phase advance across every consecutive pair of snakes. Our analysis reveals a clear performance hierarchy, with the DLC configuration providing an exceptionally robust and energy-insensitive baseline for polarization preservation. We conclude that a hybrid strategy, using a DLC snake scheme as a symmetric foundation and betatron phase tuning for fine corrections, offers the most effective path forward for the EIC and future high-energy polarized-beam facilities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Ligand Hole Driven Metal–Insulator Transition Exemplified in a Layered Transition Metal Oxide

The interplay of cooperative Jahn–Teller (JT) distortions and charge-disproportionation (CD) with a strong electronic correlation in transition metal oxides leads to structural symmetry breaking. Both JT and CD often manifest in the form of significant modifications in electronic and structural properties such as band splitting, metal–insulator transitions (MIT), and enhanced electron lattice interactions. Notably, the charge-disproportionation is a key electronic feature that drives the MIT. Here, we demonstrate and quantify it using first-principles calculations combining density-functional theory, dynamical mean-field theory, and spin–lattice Monte Carlo simulations. Taking Ca 2 FeMnO 6 as a prototypical example of a correlated oxide, our ab initio study shows that MIT in Ca 2 FeMnO 6 arises from the partial localization of oxygen ligand holes at alternate Fe sites that control both charge and magnetic ordering. Interestingly, the band gap was found to be fundamentally controlled by the strength of the charge-transfer energy and not by the Mott–Hubbard interactions. The novel physics and insights presented in this work reveal promising routes for tuning the electronic functionality in transition-metal oxides.

36 MATERIALS SCIENCE

Competition between Hydrogen and Chalcogen Bonding in Homodimers of Chalcogen Hydrides (H 2 X) 2 , X = O, S, Se, Te

The structural and chemical bonding motifs manifested by the competition between hydrogen and chalcogen bonding in the homodimers of chalcogen hydrides (H 2 X) 2 , where X = O, S, Se, Te have been characterized using high-level electronic structure calculations and analysis of the electron density based on Quasi-atomic orbital (QUAO) and the Symmetry-adapted perturbation theory (SAPT) methods. The QUAO analysis clearly identifies a three-center interaction responsible for either hydrogen or chalcogen bonds: in the former, the σ-bond connecting the donor and hydrogen atom participating in the hydrogen bond interacts with the lone pair on the nucleophile acceptor via the hydrogen atom, while in the latter this same σ-bond interacts with the nucleophile lone pair via the donor chalcogen. The number of minimum energy structures increase dramatically from one for (H 2 O) 2 , three for (H 2 S) 2 , four for (H 2 Se) 2 , and finally six for (H 2 Te) 2 . Furthermore, the emergence of the chalcogen-bonded arrangements appears for (H 2 S) 2 with their subsequent energetic stabilization over the hydrogen-bonded minima manifesting in (H 2 Se) 2 and (H 2 Te) 2 . In particular, one of the (H 2 S) 2 , two of the (H 2 Se) 2 , and three of the (H 2 Te) 2 dimers are chalcogen bonded. Induction plays a small but important role in stabilizing hydrogen over chalcogen-bonded structures, while dispersion is more important for chalcogen bonds.

Chemical structure

Tuning the magnetic properties of the spin-split antiferromagnet MnTe through pressure

The hexagonal antiferromagnet MnTe has attracted enormous interest as a prototypical example of a spin-compensated magnet in which the combination of crystal and spin symmetries lifts the spin degeneracy of the electron bands without the need for spin-orbit coupling, a phenomenon called nonrelativistic spin splitting (NRSS). Subgroups of NRSS are determined by the specific spin-interconverting symmetry that connects the two opposite-spin sublattices. In MnTe, this symmetry is rotation, leading to the subgroup with spin splitting away from the Brillouin zone center, often called altermagnetism. MnTe also has the largest spontaneous magnetovolume effect of any known antiferromagnet, implying strong coupling between the magnetic moment and volume. This magnetostructural coupling offers a potential knob for tuning the spin-splitting properties of MnTe. Here, we use neutron diffraction with in situ applied pressure to determine the effects of pressure on the magnetic properties of MnTe and further explore this magnetostructural coupling. We find that applying pressure significantly increases the Néel temperature, but decreases the ordered magnetic moment. We explain this as a consequence of strengthened magnetic exchange interactions under pressure, resulting in higher 𝑇 N , with a simultaneous reduction of the local moment of individual Mn atoms, described here via density functional theory. This reflects the increased orbital hybridization and electron delocalization with pressure. In conclusion, these results shed light on the competition between magnetic exchange interactions and the strength of individual magnetic moments and show that the magnetic properties of MnTe can be controlled by pressure, opening the door to improved properties for spintronic applications through tuning via physical or chemical pressure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Extending quantum-mechanical benchmark accuracy to biological ligand-pocket interactions

Predicting the binding affinity of ligands to protein pockets is key in the drug design pipeline. The flexibility of ligand-pocket motifs arises from a range of attractive and repulsive electronic interactions during binding. Accurately accounting for all interactions requires robust quantum-mechanical (QM) benchmarks, which are scarce for ligand-pocket systems. Additionally, disagreement between “gold standard” Coupled Cluster (CC) and Quantum Monte Carlo (QMC) methods casts doubt on many benchmarks for larger non-covalent systems. We introduce the “QUantum Interacting Dimer” (QUID) benchmark framework containing 170 non-covalent (non-)equilibrium systems modeling chemically and structurally diverse ligand-pocket motifs. Symmetry-adapted perturbation theory shows that QUID broadly covers non-covalent binding motifs and energetic contributions. Robust binding energies are obtained using complementary CC and QMC methods, achieving agreement of 0.5 kcal/mol. The benchmark data analysis reveals that several dispersion-inclusive density functional approximations provide accurate energy predictions, though their atomic van der Waals forces differ in magnitude and orientation. Contrarily, semiempirical methods and empirical force fields require improvements in capturing non-covalent interactions (NCIs) for out-of-equilibrium geometries. The wide span of NCIs, highly accurate interaction energies, and analysis of molecular properties take QUID beyond the “gold standard” for QM benchmarks of ligand-protein systems.

Puleva, Mirela [University of Luxembourg, Luxembou

Investigation of magnetic fluctuations in L-H and H-L transition dynamics on DIII-D

The dynamics of the L-H transition is not fully understood, with many parameters changing the threshold power to enter H-mode and the self-regulation between zonal flows and turbulence in the plasma edge. This paper is primarily a presentation of experimental results for DIII-D L-H and H-L transitions and speculation on the observations made. Power threshold analysis and measurements of pedestal temperatures for these transitions are presented. A comparison is made between an L-H transition and H-L transition of comparable Psep exhibiting oscillatory behaviour, showing symmetry between forward and backward transition dynamics. This paper shows the first observations of magnetic fluctuations during L-H and H-L transitions on DIII-D, and shows that L-H and H-L transitions have similar magnetic fluctuation dynamics. Information geometry analysis has been performed on measurements of plasma density fluctuations, perpendicular plasma velocity fluctuations, and magnetic field fluctuations to investigate the self-regulation and evolution of these variables during the transitions. Perpendicular flow evolution is shown to dominate the transition dynamics in both directions, but self-regulation behaviour is observed between all three variables. A strong correlation between magnetic fluctuation information rate and density fluctuation information rate for these two shots shows the strong influence of magnetic behaviour on both the L-H and H-L transition, and that these transition dynamics necessarily include electromagnetic effects.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Nonperturbative and perturbative dynamics of a light QCD axion: Dark matter and the strong 𝐶⁢𝑃 problem

Considerable theoretical efforts have gone into expanding the reach of the quantum chromodynamics (QCD) axion beyond its canonical mass–decay-constant relation. The 𝑍 𝒩 QCD axion model reduces the QCD axion mass naturally, by invoking a discrete 𝑍 𝒩 symmetry through which the axion field is coupled to 𝒩 copies of the Standard Model. Before the QCD phase transition at temperature 𝑇 QCD , the 𝑍 𝒩 potential has a minimum at misalignment angle 𝜃 = 𝜋. At 𝑇 QCD , 𝜃 = 𝜋 becomes a maximum; the axion potential becomes exponentially suppressed and develops 𝒩 minima—only one of which actually solves the strong 𝐶⁢𝑃 problem. Before 𝑇 QCD , 𝜃 relaxes toward 𝜋. After 𝑇 QCD , the axion field starts from around the hilltop and may have sufficient kinetic energy to overcome the newly suppressed potential barriers. Such a field evolution leads to nonperturbative effects via the self-interactions near the hilltop, which can cause the exponential growth of fluctuations and backreaction on the coherent motion. This behavior can influence the relic density of the field and the minimum in which it settles. We conduct the first lattice simulations of the 𝑍 𝒩 QCD axion using 𝒞osmoℒattice to accurately calculate dark matter abundances and find nonperturbative dynamics reduce the abundance by up to a factor of two. We furthermore find that the probability of solving the strong 𝐶⁢𝑃 problem tends to diverge considerably from the naïve expectation of 1/𝒩.

Axions