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Seismological Stress Drops for Confined Ruptures Are Invariant to Normal Stress
Seismic moment and rupture length can be combined to infer stress drop, a key parameter for assessing earthquakes. In natural earthquakes, stress drops are largely depth-independent, which is surprising given the expected dependence of frictional stress on normal stresses and hence overburden. We have developed a transparent experimental fault that allows direct observation of thousands of slip events, with ruptures that are fully contained within the fault. Surprisingly, the observed stress drops are largely independent of both the magnitude of normal stress and its heterogeneity, capturing the independence seen in nature. However, we observe larger, normal stress-dependent stress drops when the fault area is reduced, which allows slip events to frequently reach the edge of the interface. We conclude that confined ruptures have normal stress independent stress drops, and thus the depth-independent stress drops of tectonic earthquakes may be a consequence of their confined nature.
The scaled-invariant Planckian metal and quantum criticality in Ce1−xNdxCoIn5
Abstract The mysterious Planckian metal state, showing perfect T -linear resistivity associated with universal scattering rate, 1/ τ = α k B T /ℏ with α ~ 1, has been observed in the normal state of various strongly correlated superconductors close to a quantum critical point. However, its microscopic origin and link to quantum criticality remains an outstanding open problem. Here, we observe quantum-critical T / B -scaling of the Planckian metal state in resistivity and heat capacity of heavy-electron superconductor Ce 1− x Nd x CoIn 5 in magnetic fields near the edge of antiferromagnetism at the critical doping x c ~ 0.03. We present clear experimental evidences of Kondo hybridization being quantum critical at x c . We provide a generic microscopic mechanism to qualitatively account for this quantum critical Planckian state within the quasi-two dimensional Kondo-Heisenberg lattice model near Kondo breakdown transition. We find α is a non-universal constant and depends inversely on the square of Kondo hybridization strength.
Defect detection in atomic-resolution images via unsupervised learning with translational invariance
Abstract Crystallographic defects can now be routinely imaged at atomic resolution with aberration-corrected scanning transmission electron microscopy (STEM) at high speed, with the potential for vast volumes of data to be acquired in relatively short times or through autonomous experiments that can continue over very long periods. Automatic detection and classification of defects in the STEM images are needed in order to handle the data in an efficient way. However, like many other tasks related to object detection and identification in artificial intelligence, it is challenging to detect and identify defects from STEM images. Furthermore, it is difficult to deal with crystal structures that have many atoms and low symmetries. Previous methods used for defect detection and classification were based on supervised learning, which requires human-labeled data. In this work, we develop an approach for defect detection with unsupervised machine learning based on a one-class support vector machine (OCSVM). We introduce two schemes of image segmentation and data preprocessing, both of which involve taking the Patterson function of each segment as inputs. We demonstrate that this method can be applied to various defects, such as point and line defects in 2D materials and twin boundaries in 3D nanocrystals.
Optimal invariant sets for atomistic machine learning
The representation of atomic configurations for machine learning models has led to numerous sets of descriptors. However, many descriptor sets are incomplete and/or functionally dependent. Incomplete sets cannot faithfully represent atomic environments. Yet complete constructions often suffer from a high degree of functional dependence, where some descriptors are functions of others. These redundant descriptors do not improve discrimination between atomic environments. We employ pattern recognition techniques to remove dependent descriptors to produce the smallest possible set that satisfies completeness. We apply this in two ways: First, we refine an existing description, the atomic cluster expansion. Second, we augment an incomplete construction, yielding a new message-passing neural network architecture that can recognize up to 5-body patterns. This architecture shows strong accuracy on state-of-the-art benchmarks while retaining low computational cost. Our results demonstrate the utility of this strategy to optimize descriptor sets across a range of descriptors and application datasets.
Sodium site occupancy and phosphate speciation in natrophosphate are invariant to changes in NaF and Na 3 PO 4 concentration
Analysis of multimodal characterization of Natrophosphate suggests that the crystalline structure is preserved across a range of synthesis conditions.
Particle-based hematite crystallization is invariant to initial particle morphology
Significance Many crystallization processes occurring in nature produce highly ordered hierarchical architectures. Their formation cannot be explained using classical models of monomer-by-monomer growth. One of the possible pathways involves crystallization through the attachment of oriented nanocrystals. Thus, it requires detailed understanding of the mechanism of particle dynamics that leads to their precise crystallographic alignment along specific faces. In this study, we discover a particle-morphology–independent oriented attachment mechanism for hematite nanocrystals. Independent of crystal morphology, particles always align along the [001] direction driven by aligning interactions between (001) faces and repulsive interactions between other pairs of hematite faces. These results highlight that strong face specificity along one crystallographic direction can render oriented attachment to be independent of initial particle morphology.
Restoring permutational invariance in the Jordan–Wigner transformation
The Jordan–Wigner transformation is a powerful tool for converting systems of spins into systems of fermions, or vice versa. While this mapping is exact, the transformation itself depends on the labelling of the spins. One consequence of this dependence is that approximate solutions of a Jordan–Wigner-transformed Hamiltonian may depend on the (physically inconsequential) labelling of the spins. In this work, we turn to an extended Jordan–Wigner transformation which remedies this problem and which may also introduce some correlation atop the Hartree–Fock solution of a transformed spin Hamiltonian. We demonstrate that this extended Jordan–Wigner transformation can be thought of as arising from a unitary version of the Lie algebraic similarity transformation (LAST) theory. Here, we show how these ideas, particularly in combination with the standard (non-unitary) version of LAST, can provide a potentially powerful tool for the treatment of the XXZ and J 1 –J 2 Heisenberg Hamiltonians.
Design of double-bend and multibend achromat lattices with large dynamic aperture and approximate invariants
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Time-reversal invariant and fully gapped unconventional superconducting state in the bulk of the topological compound Nb 0.25 Bi 2 Se 3
Recently, the niobium (Nb) doped topological insulator Bi 2 Se 3 , in which the finite magnetic moments of the Nb atoms are intercalated in the van der Waals gap between the Bi 2 Se 3 layers, has been shown to exhibit both superconductivity with $T_c$ ≃ 3 K and topological surface states. Here we report on muon spin rotation experiments probing the temperature and field dependence of effective magnetic penetration depth $λ_{\text{eff}}(T)$ in the layered topological superconductor candidate Nb 0.25 Bi 2 Se 3 . In this work the exponential temperature dependence of $λ^{–2}_{\text{eff}}(T)$ at low temperatures suggests a fully gapped superconducting state in the bulk with the superconducting transition temperature $T_c$ = 2.9 K and the gap to $T_c$ ratio 2Δ /$k_BT_c$ = 3.95(19). We also reveal that the ratio Tc/λ–2eff is comparable to those of unconventional superconductors, which hints at an unconventional pairing mechanism. Furthermore, time-reversal symmetry breaking was excluded in the superconducting state with sensitive zero-field μSR experiments. We hope the present results will stimulate theoretical investigations to obtain a microscopic understanding of the relation between superconductivity and the topologically nontrivial electronic structure of Nb 0.25 Bi 2 Se 3 .
Local invariants identify topology in metals and gapless systems
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Accuracy of ghost-rotationally-invariant slave-boson theory for multiorbital Hubbard models and realistic materials
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Time-reversal invariant topological moiré flat band: A platform for the fractional quantum spin Hall effect
Motivated by recent observation of the quantum spin Hall effect in monolayer germanene and twisted bilayer transition-metal-dichalcogenides (TMDs), we study the topological phases of moir twisted bilayers with time-reversal symmetry and spin sz conservation. By using a continuum model description which can be applied to both germanene and TMD bilayers, we show that at small twist angles the emergent moir flat bands can be topologically nontrivial due to inversion symmetry breaking. Each of these flat bands admits a lowest-Landau-level description for each spin projection in the chiral limit and at magic twist angle. Furthermore, this allows for the construction of a many-body Laughlin state with time-reversal symmetry which can be stabilized by a short-range pseudopotential, and therefore serves as an ideal platform for realizing the so-far elusive fractional quantum spin Hall effect with emergent spin-1/2 U(1) symmetry.
Normal-ordering approximations and translational (non)invariance
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Ab initio translationally invariant nucleon-nucleus optical potentials
We combine the ab initio symmetry-adapted no-core shell model (SA-NCSM) with the single-particle Green's function approach to construct optical potentials rooted in first principles. Specifically, we show that total cross sections and phase shifts for neutron elastic scattering from a 4 He target with projectile energies between 0.5 and 10 MeV closely reproduce the experiment. In addition, we discuss an important new development that resolves a long-standing issue with spurious center-of-mass motion in the Green's function formalism for many-body approaches. Furthermore, the new development opens a path for first-principle predictions of cross sections for elastic scattering of single-nucleon projectiles, nucleon capture, and deuteron breakup reactions, feasible for a broad range of open-shell spherical and deformed nuclei in the SA-NCSM approach.
Gauge-invariant observables in gravity and electromagnetism: Black hole backgrounds and null dressings
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