The unified mathematical theory of gapped and gapless edges of two-dimensional (2d) topological orders was developed by two of the authors. According to this theory, the critical point of a purely edge topological phase transition of a 2d topological order can be mathematically characterized by an enriched fusion category. In this work, we provide a physical proof of this fact in a concrete example: the 2d Z2 topological order. In particular, we construct an enriched fusion category, which describes a gappable nonchiral gapless edge of the 2d Z2 topological order.

We believe that a necessary first step in understanding the ground-state properties of the spin-12 kagome Heisenberg antiferromagnet is a better understanding of this model's very large number of low-energy singlet states. A description of the low-energy states that is both accurate and amenable for numerical work may ultimately prove to have greater value than knowing only what these properties are, in particular, when they turn on the delicate balance of many small energies.

Origami design principles are scale invariant and enable direct miniaturization of origami structures provided the sheets used for folding have equal thickness to length ratios. Recently, seminal steps have been taken to fabricate microscale origami using unidirectionally actuated sheets with nanoscale thickness. Here, we extend the full power of origami-inspired fabrication to nanoscale sheets by engineering bidirectional folding with 4 nm thick atomic layer deposition (ALD) SiNx-SiO2 bilayer films.

Recent technological advances have introduced diverse engineered nanoparticles (ENPs) into our air, water, medicine, cosmetics, clothing, and food. However, the health and environmental effects of these increasingly common ENPs are still not well understood. In particular, potential neurological effects are one of the most poorly understood areas of nanoparticle toxicology (nanotoxicology), in that low-to-moderate neurotoxicity can be subtle and difficult to measure.

Reducing the energy bandwidth of electrons in a lattice below the long-range Coulomb interaction energy promotes correlation effects. Moiré superlattices—which are created by stacking van der Waals heterostructures with a controlled twist angle1,2,3—enable the engineering of electron band structure. Exotic quantum phases can emerge in an engineered moiré flat band.

Non-Fermi liquid and unconventional quantum critical points (QCP) with strong fractionalization are two exceptional phenomena beyond the classic condensed matter doctrines, both of which could occur in strongly interacting quantum many-body systems. This work demonstrates that using a controlled method one can construct a non-Fermi liquid within a considerable energy window based on the unique physics of unconventional QCPs.

A variety of precise experiments have been carried out to establish the character of the superconducting state in Sr2RuO4. Many of these appear to imply contradictory conclusions concerning the symmetries of this state. Here we propose that these results can be reconciled if we assume that there is a near-degeneracy between a dx2−y2 (B1g in group theory nomenclature) and a gxy(x2−y2) (A2g) superconducting state.

The defining characteristic of hole-doped cuprates is d-wave high temperature superconductivity. However, intense theoretical interest is now focused on whether a pair density wave state (PDW) could coexist with cuprate superconductivity [D. F. Agterberg et al., Annu. Rev. Condens. Matter Phys. 11, 231 (2020)]. Here, we use a strong-coupling mean-field theory of cuprates, to model the atomic-scale electronic structure of an eight-unit-cell periodic, d-symmetry form factor, pair density wave (PDW) state coexisting with d-wave superconductivity (DSC).

Physics education research (PER) has long used concept inventories to investigate student learning over time and to compare performance across various student subpopulations. PER has traditionally used normalized gain to explore these questions but has begun to use established methods from other fields, including Cohen's d, multiple linear regression, and linear mixed effects models. The choice of analysis method for examining student learning gains in PER is a current subject of debate.

An amendment to this paper has been published and can be accessed via a link at the top of the paper. © 2020, The Author(s).