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The Eremenko-Lyubich class consists of transcendental entire functions with bounded singular set and the Speiser class is made up of functions with a finite singular set. In an earlier paper "Models for the Eremenko-Lyubich class" I gave a method for constructing Eremenko-Lyubich functions that approximate certain simpler functions called models. In this paper, I show that all such models can be approximated in a weaker sense by Speiser class functions, and that the stronger approximation possible using Eemenko-Lyubich functions can fail for the Speiser class. In particular, I give geometric restrictions on the geometry of a Speiser class function that need not be satisfied by general Eremenko-Lyubich functions., Comment: 49 pages, 17 figures

If $f$ is in the Eremenko-Lyubich class (transcendental entire functions with bounded singular set) then $\Omega= \{ z: |f(z)| > R\}$ and $f|_\Omega$ must satisfy certain simple topological conditions when $R$ is sufficiently large. A model $(\Omega, F)$ is an open set $\Omega$ and a holomorphic function $F$ on $\Omega$ that satisfy these same conditions. We show that any model can be approximated by an Eremenko-Lyubich function in a precise sense. In many cases, this allows the construction of functions in the Eremenko-Lyubich with a desired property to be reduced to the construction of a model with that property, and this is often much easier to do., Comment: 28 pages, 6 figures

Since its first description in 1948, the Casimir effect has been studied extensively. Standard arguments for its existence hinge on the elimination of certain modes of the electromagnetic field because of the boundary conditions in the Casimir cavity. As such, it has been suggested that the ground state energy of the vacuum within the cavity may be reduced compared to the value outside. Could this have an effect on physical phenomena within the cavity? We study this Casimir energy and probe whether the critical temperature $T_c$ of a superconductor is altered when it is placed in the cavity. We do not detect any change in $T_c$ larger than 12 microKelvin, but theoretically expect a change on the order of 0.025 microKelvin, roughly 1000 times lower than our achieved sensitivity., Comment: arXiv admin note: text overlap with arXiv:2004.13771

A rational lemniscate is a level set of $|r|$ where $r: \hat{\mathbb{C}} \rightarrow \hat{\mathbb{C}}$ is rational. We prove that any planar Euler graph can be approximated, in a strong sense, by a homeomorphic rational lemniscate. This generalizes Hilbert's lemniscate theorem; he proved that any Jordan curve can be approximated (in the same strong sense) by a polynomial lemniscate that is also a Jordan curve. As consequences, we obtain a sharp quantitative version of the classical Runge's theorem on rational approximation, and we give a new result on the approximation of planar continua by Julia sets of rational maps.

Weakly interacting massive particles (WIMPs) may interact with a virtual pion that is exchanged between nucleons. This interaction channel is important to consider in models where the spin-independent isoscalar channel is suppressed. Using data from the first science run of the LUX-ZEPLIN dark matter experiment, containing 60 live days of data in a 5.5~tonne fiducial mass of liquid xenon, we report the results on a search for WIMP-pion interactions. We observe no significant excess and set an upper limit of $1.5\times10^{-46}$~cm$^2$ at a 90\% confidence level for a WIMP mass of 33~GeV/c$^2$ for this interaction.

The quasi-two-dimensional magnetic topological insulator MnBi$_2$Se$_4$, stabilized via non-equilibrium molecular beam epitaxy, is investigated by resonant soft x-ray scattering. Kiessig fringes are observed, confirming a high sample quality and a thin film thickness of 10 septuple layers ($\sim$13 nm). An antiferromagnetic Bragg peak is observed at the structurally forbidden reflection, whose magnetic nature is validated by studying its temperature, energy, and polarization dependence. Through a detailed analysis, an A-type antiferromagetic order with in-plane moments is implied. This alternative spin structure in MnBi$_2$Se$_4$, in contrast to the Ising antiferromagnetic states in other magnetic topological insulators, might be relevant for hosting new topological states.

The first science run of the LUX-ZEPLIN (LZ) experiment, a dual-phase xenon time project chamber operating in the Sanford Underground Research Facility in South Dakota, USA, has reported leading limits on spin-independent WIMP-nucleon interactions and interactions described from a non-relativistic effective field theory (NREFT). Using the same 5.5~t fiducial mass and 60 live days of exposure we report on the results of a relativistic extension to the NREFT. We present constraints on couplings from covariant interactions arising from the coupling of vector, axial currents, and electric dipole moments of the nucleon to the magnetic and electric dipole moments of the WIMP which cannot be described by recasting previous results described by an NREFT. Using a profile-likelihood ratio analysis, in an energy region between 0~keV$_\text{nr}$ to 270~keV$_\text{nr}$, we report 90% confidence level exclusion limits on the coupling strength of five interactions in both the isoscalar and isovector bases., Comment: 7 pages, 4 figures

Building a modular architecture with superconducting quantum computing chips is one of the means to achieve qubit scalability, allowing the screening, selection, replacement, and integration of individual qubit modules into large quantum systems. However, the nondestructive replacement of modules within a compact architecture remains a challenge. Liquid metals, specifically gallium alloys, can be alternatives to solid-state galvanic interconnects. This is motivated by their self-healing, self-aligning, and other desirable fluidic properties, potentially enabling the nondestructive replacement of modules at room temperatures, even after operating the entire system at millikelvin regimes. In this study, we present coplanar waveguide resonators (CPWRs) interconnected by gallium alloy droplets, achieving high internal quality factors up to nearly one million and demonstrating performance on par with the continuous solid-state CPWRs. Leveraging the desirable fluidic properties of gallium alloys at room temperature and their compact design, we envision a modular quantum system enabled by liquid metals.

We present the coupled oscillator: a new mechanism for signal amplification with widespread application in metrology. We introduce the mechanical theory of this framework, and support it by way of simulations. We present a particular implementation of coupled oscillators: a microelectromechanical system (MEMS) that uses one large (~100mm) N52 magnet coupled magnetically to a small (~0.25mm), oscillating N52 magnet, providing a force resolution of 200zN measured over 1s in a noiseless environment. We show that the same system is able to resolve magnetic gradients of 130aT/cm at a single point (within 500um). This technology therefore has the potential to revolutionize force and magnetic gradient sensing, including high-impact areas such cardiac and brain imaging., Comment: 13 pages, 17 figures

Heterostructures of two-dimensional (2D) van der Waals (vdW) magnets and topological insulators (TI) are of substantial interest as candidate materials for efficient spin-torque switching, quantum anomalous Hall effect, and chiral spin textures. However, since many of the vdW magnets have Curie temperatures below room temperature, we want to understand how materials can be modified to stabilize their magnetic ordering to higher temperatures. In this work, we utilize molecular beam epitaxy to systematically tune the Curie temperature ($T_C$) in thin film Fe$_3$GeTe$_2$/Bi$_2$Te$_3$ from bulk-like values ($\sim$220 K) to above room temperature by increasing the growth temperature from 300 $^\circ$C to 375 $^\circ$C. For samples grown at 375 $^\circ$C, cross-sectional scanning transmission electron microscopy (STEM) reveals the spontaneous formation of different Fe$_m$Ge$_n$Te$_2$ compositions (e.g. Fe$_5$Ge$_2$Te$_2$ and Fe$_7$Ge$_6$Te$_2$) as well as intercalation in the vdW gaps, which are possible origins of the enhanced Curie temperature. This observation paves the way for developing various Fe$_m$Ge$_n$Te$_2$/TI heterostructures with novel properties., Comment: 8 pages, 4 figures

Systems with flat bands are ideal for studying strongly correlated electronic states and related phenomena. Among them, kagome-structured metals such as CoSn have been recognized as promising candidates due to the proximity between the flat bands and the Fermi level. A key next step will be to realize epitaxial kagome thin films with flat bands to enable tuning of the flat bands across the Fermi level via electrostatic gating or strain. Here we report the band structures of epitaxial CoSn thin films grown directly on insulating substrates. Flat bands are observed using synchrotron-based angle-resolved photoemission spectroscopy (ARPES). The band structure is consistent with density functional theory (DFT) calculations, and the transport properties are quantitatively explained by the band structure and semiclassical transport theory. Our work paves the way to realize flat band-induced phenomena through fine-tuning of flat bands in kagome materials., Comment: 30 pages, 12 figures

Introducing magnetism to the surface state of topological insulators, such as Bi2Te3, can lead to a variety of interesting phenomena. We use scanning tunneling microscopy (STM) to study a single quintuple layer (QL) of the van der Waals magnet Fe3GeTe2 (FGT) that is grown on Bi2Te3 via molecular beam epitaxy. STM topographic images show that the FGT grows as free-standing islands on Bi2Te3 and outwards from Bi2Te3 steps. Atomic resolution imaging shows atomic lattices of 390 +- 10 pm for FGT and 430 +- 10 pm for Bi2Te3, consistent with the respective bulk crystals. A moir\'e pattern is observed on FGT regions with a periodicity of 4.3 +- 0.4 nm that can be attributed solely to this lattice mismatch and thus indicates zero rotational misalignments. While most of the surface is covered by a single QL of the FGT, there are small double QL regions, as well as regions with distinct chemical terminations due to an incomplete QL. The most common partial QL surface termination is the FeGe layer, in which the top two atomic layers are missing. This termination has a distinctive electronic structure and a (sqrt3 x sqrt3)R30 reconstruction overlaid on the moir\'e pattern in STM images. Magnetic circular dichroism (MCD) measurements confirm these thin FGT films are ferromagnetic with TC ~190 K., Comment: 12 pages, 5 figures

We strengthen the classical approximation theorems of Weierstrass, Runge and Mergelyan by showing the polynomial and rational approximants can be taken to have a simple geometric structure. In particular, when approximating a function $f$ on a compact set $K$, the critical points of our approximants may be taken to lie in any given domain containing $K$, and all the critical values in any given neighborhood of the polynomially convex hull of $f(K)$.

The chemical activity of ionized hydrogen describes the potency of protons in solution and is used to define the pH with wide-ranging applications in biological and materials sciences. Measuring pH with graphene field-effect transistors (FETs) has been described in the past but has yet to be characterized with a monolayer hexagonal boron nitride (hBN) capping layer. hBN capping is hypothesized to lower the chemical affinity of protons to oxidized defects in the graphene crystal and lower the standard deviation of pH measurement via screening charge density. First, the electronic properties of commercial, monolayer graphene and monolayer hBN/graphene, both on four-inch 90 nm SiO2/p-type Si, were contrasted as a function of solutal pH in 10 mM phosphate buffered solution. The two-dimensional (2D) FETs were fabricated with photoresistless metallization followed by microcentrifuge tube-masking and reactive ion etching to define a quasi-pure 2D sensing mesa for pH sensing. Thereafter, the devices were exposed to phosphate buffer of varying pH and the resistance and liquid-transfer characteristics measured. The hBN/graphene/SiO2 FETs had higher linearity, and both lower standard deviation and range of Dirac voltage shifting than monolayer graphene/SiO2. Then, before microcentrifuge tube-masking, freshly metallized devices were coated with 9 nm of Al2O3 by electron beam deposition. The Al2O3/graphene/SiO2 and Al2O3/hBN/graphene/SiO2 devices showed an altered response to the pH of the phosphate buffered solutions before and after basic etching of the Al2O3 with NaOH (pH = 12). This prompted studying the pH-dependencies of the 2D devices as a function of the thickness of Al2O3 via atomic layer deposition. These results show that modifying the surface of monolayer graphene with nanoscale dielectrics enables tuning of the pH-dependent electronic properties of graphene pH sensors.

Electrical detection of messenger ribonucleic acid (mRNA) is a promising approach to enhancing transcriptomics and disease diagnostics because of its sensitivity, rapidity, and modularity. Reported here is a fast SARS-CoV-2 mRNA biosensor (<1 minute) with a limit of detection of 1 aM, and dynamic range of 4 orders of magnitude and a linear sensitivity of 22 mV per molar decade. These figures of merit were obtained on photoresistlessly patterned monolayer graphene field-effect transistors (FETs) derived from commercial four-inch graphene on 90 nm of silicon dioxide on p-type silicon. Then, to facilitate mRNA hybridization, graphene sensing mesa were coated with an ultrathin sub-percolation threshold gold film for bonding 3'-thiolated single-stranded deoxyribonucleic acid (ssDNA) probes complementary to SARS-CoV-2 nucleocapsid phosphoprotein (N) gene. Sub-percolated gold was used to minimize the distance between the graphene material and surface hybridization events. The liquid-transfer characteristics of the graphene FETs repeatedly shows correlation between the Dirac voltage and the copy number of polynucleotide. Ultrathin percolated gold films on graphene FETs facilitate two-dimensional electron gas (2DEG) mRNA biosensors for transcriptomic profiling., Comment: 15 pages, 6 figures Keywords: transcriptome, virus, monolayer graphene, percolated gold, 2DEG, field-effect transistor

Magnetic materials with kagome crystal structure exhibit rich physics such as frustrated magnetism, skyrmion formation, topological flat bands, and Dirac/Weyl points. Until recently, most studies on kagome magnets have been performed on bulk crystals or polycrystalline films. Here we report the atomic layer molecular beam epitaxy synthesis of high-quality thin films of topological kagome magnet Fe${_3}$Sn${_2}$. Structural and magnetic characterization of Fe${_3}$Sn${_2}$ on epitaxial Pt(111) identifies highly ordered films with c-plane orientation and an in-plane magnetic easy axis. Studies of the local magnetic structure by anomalous Nernst effect imaging reveals in-plane oriented micrometer size domains. Superlattice structures consisting of Fe${_3}$Sn${_2}$ and Fe${_3}$Sn are also synthesized by atomic layer molecular beam epitaxy, demonstrating the ability to modulate the sample structure at the atomic level. The realization of high-quality films by atomic layer molecular beam epitaxy opens the door to explore the rich physics of this system and investigate novel spintronic phenomena by interfacing Fe${_3}$Sn${_2}$ with other materials., Comment: 8 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:2105.12203

We demonstrate that kinetics play an important role in the epitaxial growth of Fe$_3$GeTe$_2$ (FGT) van der Waals (vdW) ferromagnetic films by molecular beam epitaxy. By varying the deposition rate, we control the formation or suppression of an initial tellurium-deficient non-van der Waals phase (Fe$_3$Ge$_2$) prior to realizing epitaxial growth of the vdW FGT phase. Using cross-sectional scanning transmission electron microscopy and scanning tunneling microscopy, we optimize the FGT films to have atomically smooth surfaces and abrupt interfaces with the Ge(111) substrate. The magnetic properties of our high quality material are confirmed through magneto-optic, magnetotransport, and spin-polarized STM studies. Importantly, this demonstrates how the interplay of energetics and kinetics can help tune the re-evaporation rate of chalcogen atoms and interdiffusion from the underlayer, which paves the way for future studies of van der Waals epitaxy., Comment: 18 pages, 4 figures

We show that any dynamics on any planar set $S$ discrete in some domain $D$ can be realized by the postcritical dynamics of a function holomorphic in $D$, up to a small perturbation. A key step in the proof, and a result of independent interest, is that any planar domain $D$ can be equilaterally triangulated with triangles whose diameters $\rightarrow0$ (at any prescribed rate) near $\partial D$.

Catheter ablation is currently the only curative treatment for scar-related ventricular tachycardias (VTs). However, not only are ablation procedures long, with relatively high risk, but success rates are punitively low, with frequent VT recurrence. Personalized in-silico approaches have the opportunity to address these limitations. However, state-of-the-art reaction diffusion (R-D) simulations of VT induction and subsequent circuits used for in-silico ablation target identification require long execution times, along with vast computational resources, which are incompatible with the clinical workflow. Here, we present the Virtual Induction and Treatment of Arrhythmias (VITA), a novel, rapid and fully automated computational approach that uses reaction-Eikonal methodology to induce VT and identify subsequent ablation targets. The rationale for VITA is based on finding isosurfaces associated with an activation wavefront that splits in the ventricles due to the presence of an isolated isthmus of conduction within the scar; once identified, each isthmus may be assessed for their vulnerability to sustain a reentrant circuit, and the corresponding exit site automatically identified for potential ablation targeting. VITA was tested on a virtual cohort of 7 post-infarcted porcine hearts and the results compared to R-D simulations. Using only a standard desktop machine, VITA could detect all scar-related VTs, simulating activation time maps and ECGs (for clinical comparison) as well as computing ablation targets in 48 minutes. The comparable VTs probed by the R-D simulations took 68.5 hours on 256 cores of high-performance computing infrastructure. The set of lesions computed by VITA was shown to render the ventricular model VT-free. VITA could be used in near real-time as a complementary modality aiding in clinical decision-making in the treatment of post-infarction VTs.