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A recent mathematical framework for optimizing resistor networks to achieve values in the M{\Omega} through G{\Omega} levels was employed for two specific cases. Objectives here include proof of concept and identification of possible apparatus limitations for future experiments involving graphene-based quantum Hall array resistance standards. Using fractal-like, or recursive, features of the framework allows one to calculate and implement network designs with substantially lower-valued resistors. The cases of 100 M{\Omega} and 1 G{\Omega} demonstrate that, theoretically, one would not need more than 100 quantum Hall elements to achieve these high resistances.

A mathematical approach is adopted for optimizing the number of total device elements required for obtaining high effective quantized resistances in graphene-based quantum Hall array devices. This work explores an analytical extension to the use of star-mesh transformations such that fractal-like, or recursive, device designs can yield high enough resistances (like 1 E{\Omega}, arguably the highest resistance with meaningful applicability) while still being feasible to build with modern fabrication techniques. Epitaxial graphene elements are tested, whose quantized Hall resistance at the nu=2 plateau (R_H = 12906.4 {\Omega}) becomes the building block for larger effective, quantized resistances. It is demonstrated that, mathematically, one would not need more than 200 elements to achieve the highest pertinent resistances

Advances in the development of graphene-based technology have enabled improvements in DC resistance metrology. Devices made from epitaxially grown graphene have replaced the GaAs-based counterparts, leading to an easier and more accessible realization of the ohm. By optimizing the scale of the growth, it has become possible to fabricate quantized Hall array resistance standards (QHARS) with nominal values between 1 k{\Omega} and 1.29 M{\Omega}. One of these QHARS device designs accommodates a value of about 1.01 M{\Omega}, which made it an ideal candidate to pursue a proof-of-concept that graphene-based QHARS devices are suitable for forming wye-delta resistance networks. In this work, the 1.01 M{\Omega} array output nearly 20.6 M{\Omega} due to the wye-delta transformation, which itself is a special case of star-mesh transformations. These mathematical equivalence principles allow one to extend the QHR to the 100 M{\Omega} and 10 G{\Omega} resistance levels with fewer array elements than would be necessary for a single array with many more elements in series. The 1.01 M{\Omega} device shows promise that the wye-delta transformation can shorten the calibration chain, and, more importantly, provide a chain with a more direct line to the quantum SI.

The extremely low temperatures have limited the availability and accuracy of experimental thermophysical property measurements for cryogens, particularly transport properties. Traditional scaling techniques such as corresponding states theory have long been known to be inaccurate for fluids with strong quantum effects. To address this need, this paper investigates how quantum effects impact thermodynamics and momentum transfer (shear viscosity) in the fluid phases of hydrogen, deuterium, and neon. We utilize experimental viscosity measurements and reference empirical equations of state to show that conventional entropy scaling is inadequate for quantum-dominated systems. We then provide a simple empirical correction to entropy scaling based on the ratio of quantum to packing length scale that accounts for the deviations.

We demonstrate the preparation of both armchair and zigzag epitaxial graphene nanoribbons (GNRs) on 4H-SiC using a polymer-assisted, sublimation growth method. Historically, the preparation of GNRs depended on the quality, or smoothness, of the surface changes during growth. The physical phenomenon of terrace step formation introduces the risk of GNR deformation along sidewalls, but the risk is heavily mitigated by this polymer-assisted sublimation method. Two widths (100 nm and 50 nm) are examined electrically and optically for both armchair and zigzag GNRs. Our electrical results support the expected behaviors of the GNRs, while the optical signatures of variable strain reveal the subtle differences among all the GNR species measured.

Providing consistent, individualized feedback to teachers is essential for improving instruction but can be prohibitively resource intensive in most educational contexts. We develop an automated tool based on natural language processing to give teachers feedback on their uptake of student contributions, a high-leverage teaching practice that supports dialogic instruction and makes students feel heard. We conduct a randomized controlled trial as part of an online computer science course, Code in Place (n=1,136 instructors), to evaluate the effectiveness of the feedback tool. We find that the tool improves instructors' uptake of student contributions by 24% and present suggestive evidence that our tool also improves students' satisfaction with the course. These results demonstrate the promise of our tool to complement existing efforts in teachers' professional development. [The project was partially funded by the HAI Hoffman-Yee grant.]

Classroom discourse is a core medium of instruction - analyzing it can provide a window into teaching and learning as well as driving the development of new tools for improving instruction. We introduce the largest dataset of mathematics classroom transcripts available to researchers, and demonstrate how this data can help improve instruction. The dataset consists of 1,660 45-60 minute long 4th and 5th grade elementary mathematics observations collected by the National Center for Teacher Effectiveness (NCTE) between 2010-2013. The anonymized transcripts represent data from 317 teachers across 4 school districts that serve largely historically marginalized students. The transcripts come with rich metadata, including turn-level annotations for dialogic discourse moves, classroom observation scores, demographic information, survey responses and student test scores. We demonstrate that our natural language processing model, trained on our turn-level annotations, can learn to identify dialogic discourse moves and these moves are correlated with better classroom observation scores and learning outcomes. This dataset opens up several possibilities for researchers, educators and policymakers to learn about and improve K-12 instruction. The dataset can be found at https://github.com/ddemszky/classroom-transcript-analysis., Comment: 18th Workshop on Innovative Use of NLP for Building Educational Applications

In conversation, "uptake" happens when a speaker builds on the contribution of their interlocutor by, for example, acknowledging, repeating or reformulating what they have said. In education, teachers' uptake of student contributions has been linked to higher student achievement. Yet measuring and improving teachers' uptake at scale is challenging, as existing methods require expensive annotation by experts. We propose a framework for computationally measuring uptake, by (1) releasing a dataset of student-teacher exchanges extracted from US math classroom transcripts annotated for uptake by experts; (2) formalizing uptake as pointwise Jensen-Shannon Divergence (pJSD), estimated via next utterance classification; (3) conducting a linguistically-motivated comparison of different unsupervised measures and (4) correlating these measures with educational outcomes. We find that although repetition captures a significant part of uptake, pJSD outperforms repetition-based baselines, as it is capable of identifying a wider range of uptake phenomena like question answering and reformulation. We apply our uptake measure to three different educational datasets with outcome indicators. Unlike baseline measures, pJSD correlates significantly with instruction quality in all three, providing evidence for its generalizability and for its potential to serve as an automated professional development tool for teachers.

Responsive teaching is a highly effective strategy that promotes student learning. In math classrooms, teachers might "funnel" students towards a normative answer or "focus" students to reflect on their own thinking, deepening their understanding of math concepts. When teachers focus, they treat students' contributions as resources for collective sensemaking, and thereby significantly improve students' achievement and confidence in mathematics. We propose the task of computationally detecting funneling and focusing questions in classroom discourse. We do so by creating and releasing an annotated dataset of 2,348 teacher utterances labeled for funneling and focusing questions, or neither. We introduce supervised and unsupervised approaches to differentiating these questions. Our best model, a supervised RoBERTa model fine-tuned on our dataset, has a strong linear correlation of .76 with human expert labels and with positive educational outcomes, including math instruction quality and student achievement, showing the model's potential for use in automated teacher feedback tools. Our unsupervised measures show significant but weaker correlations with human labels and outcomes, and they highlight interesting linguistic patterns of funneling and focusing questions. The high performance of the supervised measure indicates its promise for supporting teachers in their instruction., Comment: 10 pages, 5 figures, North American Chapter of the Association for Computational Linguistics (NAACL) Workshop, Innovative Use of NLP for Building Educational Applications

In this work, limiting factors for developing metrologically useful arrays from epitaxial graphene on SiC are lifted with a combination of centimeter-scale, high-quality material growth and the implementation of superconducting contacts. Standard devices for metrology have been restricted to having a single quantized value output based on the $\nu$ = 2 Landau level. With the demonstrations herein of devices having multiple outputs of quantized values available simultaneously, these versatile devices can be used to disseminate the ohm globally. Such devices are designed to give access to quantized resistance values over the range of three orders of magnitude, starting as low as the standard value of approximately 12.9 k$\Omega$ and reaching as high as 1.29 M$\Omega$. Several experimental methods are used to assess the quality and versatility of the devices, including standard lock-in techniques and Raman spectroscopy.

Despite calls for more evidence regarding the effectiveness of teacher education practices, causal research in the field remains rare. One reason is that we lack designs and measurement approaches that appropriately meet the challenges of causal inference in the context of teacher education programs. This article provides a framework for how to fill this gap. We first outline the difficulties of doing causal research in teacher education. We then describe a set of replicable practices for developing measures of key teaching outcomes, and propose causal research designs suited to the needs of the field. Finally, we identify community-wide initiatives that are necessary to advance effectiveness research in teacher education at scale.

This work reports information on the transience of hole doping in epitaxial graphene devices when nitric acid is used as an adsorbent. Under vacuum conditions, desorption processes are monitored by electrical and spectroscopic means to extract the relevant timescales from the corresponding data. It is of vital importance to understand the reversible nature of hole doping because such device processing can be a suitable alternative to large-scale, metallic gating. Most measurements are performed post-exposure at room temperature, and, for some electrical transport measurements, at 1.5 K. Vacuum conditions are applied to many measurements to replicate the laboratory conditions under which devices using this doping method would be measured. The relevant timescales from transport measurements are compared with results from X-ray photoelecton spectroscopy and Fourier transform infrared spectroscopy measurements, with the latter performed at ambient conditions and accompanied by calculations of the spectra in the Reststrahlen band.

This work reports the dynamics of transient hole doping in epitaxial graphene devices by using nitric acid as an adsorbent. The timescales associated with corresponding desorption processes are extracted from the data. The understanding of reversible hole doping without gating is of crucial importance to those fabricating devices with a particular functionality. Measurements of the electrical and optical properties of several devices post-exposure were performed with transport temperatures between 300 K and 1.5 K. Ambient conditions are applied to non-transport measurements to replicate the most likely laboratory conditions for handling devices using this doping method. The relevant timescales from transport measurements are compared with results from Raman spectroscopy measurements.

The utilization of multiple current terminals on millimeter-scale graphene p-n junction devices has enabled the measurement of many atypical, fractional multiples of the quantized Hall resistance at the i=2 plateau. These fractions take the form a/b R_H and can be determined both analytically and by simulations. These experiments validate the use of either the LTspice circuit simulator or the analytical framework recently presented in similar work. Furthermore, the production of several devices with large-scale junctions substantiates the approach of using simple ultraviolet lithography to obtain junctions of sufficient sharpness.

Just a few of the promising applications of graphene Corbino pnJ devices include two-dimensional Dirac fermion microscopes, custom programmable quantized resistors, and mesoscopic valley filters. In some cases, device scalability is crucial, as seen in fields like resistance metrology, where graphene devices are required to accommodate currents of the order 100 {\mu}A to be compatible with existing infrastructure. However, fabrication of these devices still poses many difficulties. In this work, unusual quantized resistances are observed in epitaxial graphene Corbino p-n junction devices held at the i=2 plateau and agree with numerical simulations performed with the LTspice circuit simulator. The formulae describing experimental and simulated data are empirically derived for generalized placement of up to three current terminals and accurately reflects observed partial edge channel cancellation. These results support the use of ultraviolet lithography as a way to scale up graphene-based devices with suitably narrow junctions that could be applied in a variety of subfields

The use of multiple current terminals on millimeter-scale graphene $p-n$ junction devices fabricated with Corbino geometries, or quantum Hall resistance dartboards, have enabled the measurement of several fractional multiples of the quantized Hall resistance at the $\nu=2$ plateau ($R_H\approx 12906 {\Omega}$). Experimentally obtained values agreed with corresponding numerical simulations performed with the LTspice circuit simulator. More complicated designs of the quantum Hall resistance dartboard were simulated to establish the potential parameter space within which these Corbino-type devices could output resistance. Most importantly, these measurements support simpler processes of ultraviolet lithography as a more efficient means of scaling up graphene-based device sizes while maintaining sufficiently narrow junctions.

We have demonstrated the millimeter-scale fabrication of monolayer epitaxial graphene $p-n$ junction devices using simple ultraviolet photolithography, thereby significantly reducing device processing time compared to that of electron beam lithography typically used for obtaining sharp junctions. This work presents measurements yielding nonconventional, fractional multiples of the typical quantized Hall resistance at $\nu=2$ ($R_H\approx 12906 {\Omega}$) that take the form: $\frac{a}{b}R_H$. Here, $a$ and $b$ have been observed to take on values such 1, 2, 3, and 5 to form various coefficients of $R_H$. Additionally, we provide a framework for exploring future device configurations using the LTspice circuit simulator as a guide to understand the abundance of available fractions one may be able to measure. These results support the potential for drastically simplifying device processing time and may be used for many other two-dimensional materials.

An algorithm is introduced for predicting quantized resistances in graphene p-n junction devices that utilize more than a single entry and exit point for electron flow. Depending on the configuration of an arbitrary number of terminals, electrical measurements yield fractional multiples of the typical quantized Hall resistance at the $\nu=2$ plateau $R_H \approx 12906 {\Omega}$ and take the form: $\frac{a}{b}R_H$. This theoretical formulation is independent of material, and applications to other material systems that exhibit quantum Hall behaviors are to be expected. Furthermore, this formulation is supported with experimental data from graphene-based devices with multiple source and drain terminals.

Two-dimensional (2D) materials that exhibit charge density waves (CDWs) have generated many research endeavors in the hopes of employing their exotic properties for various quantum-based technologies. Early investigations surrounding CDWs were mostly focused on bulk materials. However, applications for quantum devices have since required devices to be constructed from few-layer material to fully utilize the material's properties. This field has greatly expanded over the decades, warranting a focus on the computational efforts surrounding CDWs in 2D materials. In this review, we will cover ground in the following relevant, theory-driven subtopics for TaS2 and TaSe2: summary of general computational techniques and methods, atomic structures, Raman modes, and effects of confinement and dimensionality. Through understanding how the computational methods have enabled incredible advancements in quantum materials, one may anticipate the ever-expanding directions available for continued pursuit as the field brings us through the 21st century.

The growth of transition metal dichalcogenide (TMDC) alloys provides an opportunity to experimentally access information elucidating how optical properties change with gradual substitutions in the lattice compared with their pure compositions. In this work, we performed growths of alloyed crystals with stoichiometric compositions between pure forms of NbSe2 and WSe2, followed by an optical analysis of those alloys by utilizing Raman spectroscopy and spectroscopic ellipsometry.

Monolayer epitaxial graphene is an appropriate candidate for a wide variety of electronic and optical applications. One advantage of growing graphene on the Si face of SiC is that it develops as a single crystal, as does the layer underneath, commonly referred to as the interfacial buffer layer. The properties of this supporting layer include a band gap, making it of interest to groups seeking to build devices with on-off capabilities. In this work, using density functional theory, we have calculated the bonding characteristics of the buffer layer to the SiC substrate beneath. These calculations were used to determine a periodic length between the covalent bonds acting as anchor points in this interface. Additionally, it is evident that the formation of these anchor points depends on the lattice mismatch between the graphene layer and SiC.

This brief is one in a series aimed at providing K-12 education decision makers and advocates with an evidence base to ground discussions about how to best serve students during and following the novel coronavirus pandemic. For children meeting academic benchmarks before the shutdown, slowdowns through September will not be catastrophic. However, delayed openings or shutdowns combined with weak remote learning offerings in the fall may set students' learning back significantly. In order to move students through grade-level content, schools will need to lean heavily on tiered strategies that include broad-based supports for all students and intensive intervention for students who have felt the pandemic's impacts most directly. Face-to-face instruction is particularly important for early elementary students. Targeted support strategies for families, such as take-home books, text messages, and family involvement programs, can effectively supplement in-school curriculum. Teaching grade-level content to all students in the fall, while identifying students needing special support, can help students remain on track. Scheduled time for teachers to communicate across grade-level teams and efforts to maximize instructional time can help students catch up while avoiding redundancy. Teacher looping structures that keep students and teachers together for more than one academic year seem to be beneficial, but the evidence is thin, and large-scale shifts would require teachers to learn new content across multiple grade levels. Large-scale, standardized testing is unlikely to yield results quickly enough and/or at a grain size that teachers can use to plan instruction. Remediation programs that supplant regular instruction are likely to prevent students from learning new, grade-level content.

In conversation, uptake happens when a speaker builds on the contribution of their interlocutor by, for example, acknowledging, repeating or reformulating what they have said. In education, teachers' uptake of student contributions has been linked to higher student achievement. Yet measuring and improving teachers' uptake at scale is challenging, as existing methods require expensive annotation by experts. We propose a framework for computationally measuring uptake, by (1) releasing a dataset of student-teacher exchanges extracted from US math classroom transcripts annotated for uptake by experts; (2) formalizing uptake as pointwise Jensen-Shannon Divergence (pJSD), estimated via next utterance classification; (3) conducting a linguistically-motivated comparison of different unsupervised measures and (4) correlating these measures with educational outcomes. We find that although repetition captures a significant part of uptake, pJSD outperforms repetition-based baselines, as it is capable of identifying a wider range of uptake phenomena like question answering and reformulation. We apply our uptake measure to three different educational datasets with outcome indicators. Unlike baseline measures, pJSD correlates significantly with instruction quality in all three, providing evidence for its generalizability and for its potential to serve as an automated professional development tool for teachers., Comment: ACL 2021

Tantalum diselenide (TaSe$_{2}$) is a metallic transition metal dichalcogenide whose equilibrium structure and vibrational behavior strongly depends on temperature and thickness, including the emergence of charge density wave (CDW) states at very low T. In this work, observed modes for mono- and bi-layer are described across several spectral regions and com-pared to the bulk ones. Such modes, including an experimentally observed forbidden Raman mode and low frequency CDW modes, are then matched to corresponding density functional theory (DFT) predicted vibrations, to unveil their inner working. The excellent match between experimental and computational results justifies the presented vibrational visualizations of these modes. Additional support is provided by experimental phonons seen in Raman spectra as a function of temperature and thickness. These results highlight the importance of understanding interlayer interactions and their effects on mode behaviors., Comment: arXiv admin note: substantial text overlap with arXiv:2005.11350

This paper describes and evaluates a web-based coaching program designed to support teachers in implementing Common Core-aligned math instruction. Web-based coaching programs can be operated at relatively lower costs, are scalable, and make it more feasible to pair teachers with coaches who have expertise in their content area and grade level. Results from our randomized field trial document sizable and sustained effects on both teachers' ability to analyze instruction and on their instructional practice, as measured the Mathematical Quality of Instruction (MQI) instrument and student surveys. However, these improvements in instruction did not result in corresponding increases in math test scores as measured by state standardized tests or interim assessments. We discuss several possible explanations for this pattern of results.