Ground state degeneracy of the Ising cage-net model

The Ising cage-net model, first proposed in Phys. Rev. X 9, 021010 (2019), is a representative type I fracton model with nontrivial non-abelian features. In this paper, we calculate the ground state degeneracy of this model and find that, even though it follows a similar coupled layer structure as the X-cube model, the Ising cage-net model cannot be "foliated" in the same sense as X-cube as defined in Phys. Rev. X 8, 031051 (2018). A more generalized notion of "foliation'' is hence needed to understand the renormalization group transformation of the Ising cage-net model. The calculation is done using an operator algebra approach that we develop in this paper, and we demonstrate its validity through a series of examples

Gapped interfaces in fracton models and foliated fields

Abstract This work investigates the gapped interfaces of 3+1d fracton phases of matter using foliated gauge theories and lattice models. We analyze the gapped boundaries and gapped interfaces in X cube model, and the gapped interfaces between the X-cube model and the toric code. The gapped interfaces are either “undecorated” or “decorated”, where the “decorated” interfaces have additional Chern-Simons like actions for foliated gauge fields. We discover many new gapped boundaries and interfaces, such as (1) a gapped boundary for X-cube model where the electric lineons orthogonal to the interface become the magnetic lineons, the latter are the composite of magnetic planons; (2) a Kramers-Wannier-duality type gapped interface between the X-cube model and the toric code model from gauging planar subsystem one-form symmetry; and (3) an electromagnetic duality interface in the X-cube model that exchanges the electric and magnetic lineons

Distortion of DNA Origami on Graphene Imaged with Advanced TEM Techniques

While graphene may appear to be the ultimate support membrane for transmission electron microscopy (TEM) imaging of DNA nanostructures, very little is known if it poses an advantage over conventional carbon supports in terms of resolution and contrast. Microscopic investigations are carried out on DNA origami nanoplates that are supported onto freestanding graphene, using advanced TEM techniques, including a new dark-field technique that is recently developed in our lab. TEM images of stained and unstained DNA origami are presented with high contrast on both graphene and amorphous carbon membranes. On graphene, the images of the origami plates show severe unwanted distortions, where the rectangular shape of the nanoplates is significantly distorted. From a number of comparative control experiments, it is demonstrated that neither staining agents, nor screening ions, nor the level of electron-beam irradiation cause this distortion. Instead, it is suggested that origami nanoplates are distorted due to hydrophobic interaction of the DNA bases with graphene upon adsorption of the DNA origami nanoplates.BN/Cees Dekker LabBN/Technici en AnalistenQN/AfdelingsbureauQN/Zandbergen La