Showing 1–42 of 42 results for author: Rigosi, A

Nonlocal Transport in Cr-doped (Bi,Sb)2Te3: Absence of Nonchiral Edge States

Authors: Valery Ortiz Jimenez, Paul M. Haney, Farzad Mahfouzi, Ngoch Thanh Mai Tran, Albert F. Rigosi, Curt A. Richter

Abstract: The quantum anomalous Hall effect shows great promise for realization of the ohm without the need for an external magnetic field. The most mature material platform is magnetically doped topological insulators. In these materials, precise quantization is limited to low temperatures, with the activation energy for dissipative transport typically in the range of 1 K. One potential source of dissipati… ▽ More The quantum anomalous Hall effect shows great promise for realization of the ohm without the need for an external magnetic field. The most mature material platform is magnetically doped topological insulators. In these materials, precise quantization is limited to low temperatures, with the activation energy for dissipative transport typically in the range of 1 K. One potential source of dissipative transport is non-chiral edge states. These states are expected to be present in sufficiently thick samples. In this work, we perform extensive Hall and non-local resistance measurements in a Hall bar geometry at 2 K. By comparing 15 independent transport measurements to different transport models, we find that the system behavior is well-described by a simple continuum Ohm's law model. The addition of non-chiral edge states into the model does not significantly improve the fitting, and we conclude that there is not strong evidence for these states. We discuss the implications of our results for the prospect of high temperature quantized anomalous Hall effect in these materials. △ Less

Submitted 19 November, 2025; originally announced November 2025.

From Wye-Delta to Cross-Square Recursion Configurations in Graphene-Based Quantum Hall Arrays

Authors: Ngoc Thanh Mai Tran, Marta Musso, Dominick S. Scaletta, Wei-Chen Lin, Valery Ortiz Jimenez, Dean G. Jarrett, Massimo Ortolano, Curt A. Richter, Chi-Te Liang, David B. Newell, Albert F. Rigosi

Abstract: In electrical metrology, the quantum Hall effect is accessed at the Landau level filling factor ν = 2 plateau to define and disseminate the unit of electrical resistance (ohm). The robustness of the plateau is only exhibited at this Landau level filling factor and thus places a constraint on the quantized resistances that are accessible when constructing quantized Hall array resistance standards (… ▽ More In electrical metrology, the quantum Hall effect is accessed at the Landau level filling factor ν = 2 plateau to define and disseminate the unit of electrical resistance (ohm). The robustness of the plateau is only exhibited at this Landau level filling factor and thus places a constraint on the quantized resistances that are accessible when constructing quantized Hall array resistance standards (QHARS) using epitaxial graphene on SiC. To overcome devices constrained by using Hall elements in series or in parallel, this work approaches the fabrication of a cross-square network configuration, which is similar to but departs slightly from conventional wye-delta designs and achieves significantly higher effective quantized resistance outputs. Furthermore, the use of pseudofractal-like recursion amplifies the ability to reach high resistances. QHARS devices designed as the ones here are shown to achieve an effective resistance of 55.81 M$Ω$ in one configuration and 27.61 G$Ω$ in another, with a hypothetically projected 317.95 T$Ω$ that could be accessed with more specialized equipment. Teraohmmeter measurements reveal the limits of conventional wet cryogenic systems due to resistance leakage. Ultimately, this work builds on the capability of realizing exceptionally high-value quantum resistance standards. △ Less

Submitted 5 August, 2025; originally announced August 2025.

Influences of the Minkowski-Bouligand Dimension on Graphene-Based Quantum Hall Array Designs

Authors: Dominick S. Scaletta, Ngoc Thanh Mai Tran, Marta Musso, Valery Ortiz Jimenez, Heather M. Hill, Dean G. Jarrett, Massimo Ortolano, Curt A. Richter, David B. Newell, Albert F. Rigosi

Abstract: This work elaborates on how one may develop high-resistance quantized Hall array resistance standards (QHARS) by using star-mesh transformations for element count minimization. Refinements are made on a recently developed mathematical framework optimizing QHARS device designs based on full, symmetric recursion by reconciling approximate device values with exact effective quantized resistances foun… ▽ More This work elaborates on how one may develop high-resistance quantized Hall array resistance standards (QHARS) by using star-mesh transformations for element count minimization. Refinements are made on a recently developed mathematical framework optimizing QHARS device designs based on full, symmetric recursion by reconciling approximate device values with exact effective quantized resistances found by simulation and measurement. Furthermore, this work explores the concept of fractal dimension, clarifying the benefits of both full and partial recursions in QHARS devices. Three distinct partial recursion cases are visited for a near-1 Gigaohm QHARS device. These partial recursions, analyzed in the context of their fractal dimensions, offer increased flexibility in accessing desired resistance values within a specific neighborhood compared to full recursion methods, though at the cost of the number of required devices. △ Less

Submitted 31 July, 2025; originally announced July 2025.

Implementing Pseudofractal Designs in Graphene-Based Quantum Hall Arrays using Minkowski-Bouligand Algorithms

Authors: Dominick S. Scaletta, Ngoc Thanh Mai Tran, Marta Musso, Dean G. Jarrett, Heather M. Hill, Massimo Ortolano, David B. Newell, Albert F. Rigosi

Abstract: This work introduces a pseudofractal analysis for optimizing high-resistance graphene-based quantized Hall array resistance standards (QHARS). The development of resistance standard device designs through star-mesh transformations is detailed, aimed at minimizing element count. Building on a recent mathematical framework, the approach presented herein refines QHARS device concepts by considering d… ▽ More This work introduces a pseudofractal analysis for optimizing high-resistance graphene-based quantized Hall array resistance standards (QHARS). The development of resistance standard device designs through star-mesh transformations is detailed, aimed at minimizing element count. Building on a recent mathematical framework, the approach presented herein refines QHARS device concepts by considering designs incorporating pseudofractals (which may be expressed as star-mesh transformations). To understand how future QHARS pseudofractal designs enable varying sizes of neighborhoods of available quantized resistance, Minkowski-Bouligand algorithms are used to analyze fractal dimensions of the device design topologies. Three distinct partial recursion cases are explored in addition to the original full recursion design, and expressions for their total element counts are derived. These partial recursions, assessed through their fractal dimensions, offer enhanced flexibility in achieving specific resistance values within a desired neighborhood compared to full recursion methods, albeit with an increased number of required elements. The formalisms presented are material-independent, making them broadly applicable to other quantum Hall systems and artifact standards. △ Less

Submitted 31 July, 2025; originally announced July 2025.

Auxiliary Calculations for Graphene-Based Quantum Hall Arrays Using Partially Recursive Star-Mesh Transformations

Authors: Dominick S. Scaletta, Albert F. Rigosi

Abstract: A previous mathematical approach adopted for optimizing the number of total device elements required for obtaining high effective quantized resistances in graphene-based quantum Hall array devices (QHARS) has been further explored with partial recursion patterns. Designs would assume the use of epitaxial graphene elements, whose quantized Hall resistance at the ν=2 plateau (R_H \approx 12906.4 \Oh… ▽ More A previous mathematical approach adopted for optimizing the number of total device elements required for obtaining high effective quantized resistances in graphene-based quantum Hall array devices (QHARS) has been further explored with partial recursion patterns. Designs would assume the use of epitaxial graphene elements, whose quantized Hall resistance at the ν=2 plateau (R_H \approx 12906.4 \Ohm) becomes the building block for larger effective, quantized resistances. Auxiliary calculations suggest the importance of applying full recursions at least once to maximize the reduction of total QHARS elements needed for high resistances. △ Less

Submitted 22 February, 2024; originally announced February 2024.

Constructing 100 MΩ and 1 GΩ Resistance Standards via Star-Mesh Transformations

Authors: Dean G. Jarrett, Albert F. Rigosi, Dominick S. Scaletta, Ngoc Thanh Mai Tran, Heather M. Hill, Alireza R. Panna, Cheng Hsueh Yang, Yanfei Yang, Randolph E. Elmquist, David B. Newell

Abstract: A recent mathematical framework for optimizing resistor networks to achieve values in the MΩ through GΩ 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 on… ▽ More A recent mathematical framework for optimizing resistor networks to achieve values in the MΩ through GΩ 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 MΩ and 1 GΩ demonstrate that, theoretically, one would not need more than 100 quantum Hall elements to achieve these high resistances. △ Less

Submitted 2 February, 2024; originally announced February 2024.

Fractal-like star-mesh transformations using graphene quantum Hall arrays

Authors: Dominick S. Scaletta, Swapnil M. Mhatre, Ngoc Thanh Mai Tran, Cheng-Hsueh Yang, Heather M. Hill, Yanfei Yang, Linli Meng, Alireza R. Panna, Shamith U. Payagala, Randolph E. Elmquist, Dean G. Jarrett, David B. Newell, Albert F. Rigosi

Abstract: 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 EΩ, arguably the highest resis… ▽ More 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 EΩ, 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 Ω) 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 △ Less

Submitted 27 September, 2023; originally announced September 2023.

A unified realization of electrical quantities from the quantum International System of Units

Authors: Linsey K. Rodenbach, Jason M. Underwood, Ngoc Thanh Mai Tran, Alireza R. Panna, Molly P. Andersen, Zachary S. Barcikowski, Shamith U. Payagala, Peng Zhang, Lixuan Tai, Kang L. Wang, Dean G. Jarrett, Randolph E. Elmquist, David B. Newell, Albert F. Rigosi, David Goldhaber-Gordon

Abstract: In the revised International System of Units (SI), the ohm and the volt are realized from the von Klitzing constant and the Josephson constant, and a practical realization of the ampere is possible by applying Ohm's law directly to the quantum Hall and Josephson effects. As a result, it is possible to create an instrument capable of realizing all three primary electrical units, but the development… ▽ More In the revised International System of Units (SI), the ohm and the volt are realized from the von Klitzing constant and the Josephson constant, and a practical realization of the ampere is possible by applying Ohm's law directly to the quantum Hall and Josephson effects. As a result, it is possible to create an instrument capable of realizing all three primary electrical units, but the development of such a system remains challenging. Here we report a unified realization of the volt, ohm, and ampere by integrating a quantum anomalous Hall resistor (QAHR) and a programmable Josephson voltage standard (PJVS) in a single cryostat. Our system has a quantum voltage output that ranges from 0.24 mV to 6.5 mV with combined relative uncertainties down to 3 $μ$V/V. The QAHR provides a realization of the ohm at zero magnetic field with uncertainties near 1 $μΩ$/$Ω$. We use the QAHR to convert a longitudinal current to a quantized Hall voltage and then directly compare that against the PJVS to realize the ampere. We determine currents in the range of 9.33 nA to 252 nA, and our lowest uncertainty is 4.3 $μ$A/A at 83.9 nA. For other current values, a systematic error that ranges from -10 $μ$A/A to -30 $μ$A/A is present due to the imperfect isolation of the PJVS microwave bias. △ Less

Submitted 12 August, 2025; v1 submitted 31 July, 2023; originally announced August 2023.

Comments: 16 pages, 4 figures, 15 pages of supplemental information

Variable Electrical Responses in Epitaxial Graphene Nanoribbons

Authors: C. -C. Yeh, S. M. Mhatre, N. T. M. Tran, H. M. Hill, H. Jin, P. -C. Liao, D. K. Patel, R. E. Elmquist, C. -T. Liang, A. F. Rigosi

Abstract: We have demonstrated the fabrication of both armchair and zigzag epitaxial graphene nanoribbon (GNR) devices on 4H-SiC using a polymer-assisted sublimation growth method. The phenomenon of terrace step formation has traditionally introduced the risk of GNR deformation along sidewalls, but a polymer-assisted sublimation method helps mitigate this risk. Each type of 50 nm wide GNR is examined electr… ▽ More We have demonstrated the fabrication of both armchair and zigzag epitaxial graphene nanoribbon (GNR) devices on 4H-SiC using a polymer-assisted sublimation growth method. The phenomenon of terrace step formation has traditionally introduced the risk of GNR deformation along sidewalls, but a polymer-assisted sublimation method helps mitigate this risk. Each type of 50 nm wide GNR is examined electrically and optically (armchair and zigzag), with the latter method being a check on the quality of the GNR devices and the former using alternating current to investigate resistance attenuation from frequencies above 100 Hz. Rates of attenuation are determined for each type of GNR device, revealing subtle suggested differences between armchair and zigzag GNRs. △ Less

Submitted 25 April, 2023; originally announced April 2023.

Star-Mesh Quantized Hall Array Resistance Devices

Authors: Dean G. Jarrett, Ching-Chen Yeh, Shamith U. Payagala, Alireza R. Panna, Yanfei Yang, Linli Meng, Swapnil M. Mhatre, Ngoc Thanh Mai Tran, Heather M. Hill, Dipanjan Saha, Randolph E. Elmquist, David B. Newell, Albert F. Rigosi

Abstract: 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 nomina… ▽ More 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 kΩ and 1.29 MΩ. One of these QHARS device designs accommodates a value of about 1.01 MΩ, 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 MΩ array output nearly 20.6 MΩ 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 MΩ and 10 GΩ resistance levels with fewer array elements than would be necessary for a single array with many more elements in series. The 1.01 MΩ 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. △ Less

Submitted 21 April, 2023; originally announced April 2023.

Quantum Entropic Effects in the Liquid Viscosities of Hydrogen, Deuterium, and Neon

Authors: Ian Bell, Jacob W. Leachman, Albert F. Rigosi, Heather M. Hill

Abstract: 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 thermo… ▽ More 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. △ Less

Submitted 9 March, 2023; originally announced March 2023.

Optical Signatures of Strain Differences in Epitaxial Graphene Nanoribbons

Authors: Heather M. Hill, Ching-Chen Yeh, Swapnil M. Mhatre, Ngoc Thanh Mai Tran, Hanbyul Jin, Adam J. Biacchi, Chi-Te Liang, Angela R. Hight Walker, Albert F. Rigosi

Abstract: 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 he… ▽ More 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. △ Less

Submitted 28 February, 2023; originally announced February 2023.

Fabrication of uniformly doped graphene quantum Hall arrays with multiple quantized resistance outputs

Authors: Swapnil M. Mhatre, Ngoc Thanh Mai Tran, Heather M. Hill, Ching-Chen Yeh, Dipanjan Saha, David B. Newell, Angela R. Hight Walker, Chi-Te Liang, Randolph E. Elmquist, Albert F. Rigosi

Abstract: 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 $ν$ = 2 Landau level. With the demonstrations herein of… ▽ More 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 $ν$ = 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$Ω$ and reaching as high as 1.29 M$Ω$. Several experimental methods are used to assess the quality and versatility of the devices, including standard lock-in techniques and Raman spectroscopy. △ Less

Submitted 10 June, 2022; originally announced June 2022.

Spectroscopic assessment of short-term nitric acid doping of epitaxial graphene

Authors: Ngoc Thanh Mai Tran, Swapnil M. Mhatre, Cristiane N. Santos, Adam J. Biacchi, Mathew L. Kelley, Heather M. Hill, Dipanjan Saha, Chi-Te Liang, Randolph E. Elmquist, David B. Newell, Benoit Hackens, Christina A. Hacker, Albert F. Rigosi

Abstract: 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 proces… ▽ More 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. △ Less

Submitted 15 April, 2022; originally announced April 2022.

Timescales for Nitric Acid Desorption in Epitaxial Graphene Devices

Authors: Swapnil M. Mhatre, Ngoc Thanh Mai Tran, Heather M. Hill, Dipanjan Saha, Angela R. Hight Walker, Chi-Te Liang, Randolph E. Elmquist, David B. Newell, Albert F. Rigosi

Abstract: 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… ▽ More 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. △ Less

Submitted 15 April, 2022; originally announced April 2022.

Large-scale five- and seven-junction epitaxial graphene devices

Authors: Dinesh Patel, Martina Marzano, Chieh-I Liu, Heather M. Hill, Mattias Kruskopf, Hanbyul Jin, Jiuning Hu, David B. Newell, Chi-Te Liang, Randolph Elmquist, Albert F. Rigosi

Abstract: 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 anal… ▽ More 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. △ Less

Submitted 26 March, 2022; v1 submitted 12 March, 2022; originally announced March 2022.

Algorithms for determining resistances in quantum Hall annuli with p-n junctions

Authors: Chieh-I Liu, Dominick S. Scaletta, Dinesh K. Patel, Mattias Kruskopf, Antonio Levy, Heather M. Hill, Albert F. Rigosi

Abstract: 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 μA to be compatible with existing in… ▽ More 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 μA 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 △ Less

Submitted 12 March, 2022; originally announced March 2022.

Fabrication of quantum Hall p-n junction checkerboards

Authors: Dinesh K. Patel, Martina Marzano, Chieh-I Liu, Mattias Kruskopf, Randolph E. Elmquist, Chi-Te Liang, Albert F. Rigosi

Abstract: Measurements of fractional multiples of the ν=2 plateau quantized Hall resistance (R_H {\approx} 12906 Ω) were enabled by the utilization of multiple current terminals on millimetre-scale graphene p-n junction devices fabricated with interfaces along both lateral directions. These quantum Hall resistance checkerboard devices have been demonstrated to match quantized resistance outputs numerically… ▽ More Measurements of fractional multiples of the ν=2 plateau quantized Hall resistance (R_H {\approx} 12906 Ω) were enabled by the utilization of multiple current terminals on millimetre-scale graphene p-n junction devices fabricated with interfaces along both lateral directions. These quantum Hall resistance checkerboard devices have been demonstrated to match quantized resistance outputs numerically calculated with the LTspice circuit simulator. From the devices' functionality, more complex embodiments of the quantum Hall resistance checkerboard were simulated to highlight the parameter space within which these devices could operate. Moreover, these measurements suggest that the scalability of p-n junction fabrication on millimetre or centimetre scales is feasible with regards to graphene device manufacturing by using the far more efficient process of standard ultraviolet lithography. △ Less

Submitted 12 March, 2022; originally announced March 2022.

Expansion of Graphene-Based Device Technology for Resistance Metrology

Authors: Albert F. Rigosi

Abstract: The field of Quantum Hall metrology had a strong start with the implemntation of GaAs-based devices, given that 2D materials systems provided access to interesting quantum phenomena, including the infrastructure associated with making relevant measurements. With the technology laid out, further improvements in both infrastructure and standards were achieved in the previous two decades as EG-based… ▽ More The field of Quantum Hall metrology had a strong start with the implemntation of GaAs-based devices, given that 2D materials systems provided access to interesting quantum phenomena, including the infrastructure associated with making relevant measurements. With the technology laid out, further improvements in both infrastructure and standards were achieved in the previous two decades as EG-based quantized Hall resistance (QHR) devices became established as national standards. Since the metrology community has reached some understanding that a comparison against GaAs-based QHR devices had been accomplished, the next steps became clearer as far as how the EG-based QHR with a single Hall bar could be further developed. Since the early 90s, it has been of modest interest that QHR devices have a means of interconnecting several single Hall bar elements and has since been a subject of research. NMIs are now presently at a juncture where consideration must be granted beyond just simplicity of operation. A natural direction for resistance standards would be to increase the total accessible parameter space. This means using EG-based QHR devices to output more than the single value at the $ν= 2$ plateau (about 12.9 k$Ω$). A first natural question is whether one may use the $ν= 6$ plateau or $ν= 10$ plateau, and though some work has been done with these Landau levels in graphene, they simply do not offer the same level of precision as the $ν= 2$ plateau. △ Less

Submitted 11 February, 2022; originally announced February 2022.

Marking the Graphene Era in Disseminating the Redefined SI

Authors: Albert F. Rigosi

Abstract: The history of quantum Hall standards stretches several decades and mostly begins with the use of GaAs given that 2D electron systems exhibit interesting quantum phenomena. At the end 2000s, research in 2D materials like graphene became prevalent. The QHE was observed and quickly became accessible to metrologists. QHR devices were becoming graphene-based, with fabrications performed by chemical va… ▽ More The history of quantum Hall standards stretches several decades and mostly begins with the use of GaAs given that 2D electron systems exhibit interesting quantum phenomena. At the end 2000s, research in 2D materials like graphene became prevalent. The QHE was observed and quickly became accessible to metrologists. QHR devices were becoming graphene-based, with fabrications performed by chemical vapor deposition (CVD), epitaxial growth, and the exfoliation of graphite. Given the many methods of available graphene synthesis, efforts to find an optimal synthesis method for metrological purposes were underway. Exfoliated graphene was widely known to exhibit the highest mobilities due to its pristine crystallinity. It was a primary initial candidate as far as metrological testing was concerned. △ Less

Submitted 11 February, 2022; originally announced February 2022.

Historical Context and Outlook of Quantum Hall Research for the Redefined SI

Authors: Albert F. Rigosi

Abstract: To fully appreciate the impacts that the discovery of the quantum Hall effect had on electrical metrology, it may benefit the reader to cultivate a general understanding of the phenomenon. Two-dimensional electron systems can exhibit many interesting quantum phenomena. The QHE may be exhibited by a 2D electron system when placed under a strong magnetic field perpendicular to the plane of the syste… ▽ More To fully appreciate the impacts that the discovery of the quantum Hall effect had on electrical metrology, it may benefit the reader to cultivate a general understanding of the phenomenon. Two-dimensional electron systems can exhibit many interesting quantum phenomena. The QHE may be exhibited by a 2D electron system when placed under a strong magnetic field perpendicular to the plane of the system. These conditions allow for Landau quantization, or the discretization of available energies of the electrons affected by the magnetic field. These energy values, determined by solving the Schrödinger equation, are known as Landau levels. During the course of a QHE measurement, one defines the Hall resistance Rxy as the measured voltage, perpendicular to the direction of the applied current, divided by that same current. The characteristic longitudinal resistivity \r{ho}xx goes to zero as Rxy approaches a quantized value (nominally called a plateau). △ Less

Submitted 11 February, 2022; originally announced February 2022.

Quantum Hall $p-n$ Junction Dartboards Using Graphene Annuli

Authors: Chieh-I Liu, Dinesh K. Patel, Martina Marzano, Mattias Kruskopf, Heather M. Hill, Albert F. Rigosi

Abstract: 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 $ν=2$ plateau ($R_H\approx 12906 Ω$). Experimentally obtained values agreed with corresponding numerical simulations performed with th… ▽ More 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 $ν=2$ plateau ($R_H\approx 12906 Ω$). 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. △ Less

Submitted 24 January, 2022; originally announced January 2022.

Nonconventional Quantized Hall Resistances Obtained with $ν= 2$ Equilibration in Epitaxial Graphene $p-n$ Junctions

Authors: Albert F. Rigosi, Dinesh Patel, Martina Marzano, Mattias Kruskopf, Heather M. Hill, Hanbyul Jin, Jiuning Hu, Angela R. Hight Walker, Massimo Ortolano, Luca Callegaro, Chi-Te Liang, David B. Newell

Abstract: 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 quantize… ▽ More 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 $ν=2$ ($R_H\approx 12906 Ω$) 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. △ Less

Submitted 24 January, 2022; originally announced January 2022.

Algorithm for constructing customized quantized resistances in graphene $p-n$ junctions

Authors: Albert F. Rigosi, Martina Marzano, Antonio Levy, Heather M. Hill, Dinesh K. Patel, Mattias Kruskopf, Hanbyul Jin, Randolph E. Elmquist, David B. Newell

Abstract: 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 $ν=2$ plateau $R_H \approx 12906 Ω$ and take the form:… ▽ More 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 $ν=2$ plateau $R_H \approx 12906 Ω$ 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. △ Less

Submitted 20 January, 2022; originally announced January 2022.

Review of Theoretical and Computational Methods for 2D Materials Exhibiting Charge Density Waves

Authors: Sugata Chowdhury, Heather M. Hill, Albert F. Rigosi, Patrick M. Vora, Angela R. Hight Walker, Francesca Tavazza

Abstract: 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 u… ▽ More 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. △ Less

Submitted 17 January, 2022; originally announced January 2022.

Designs for programmable quantum resistance standards based on epitaxial graphene p-n junctions

Authors: Jiuning Hu, Albert F. Rigosi, Mattias Kruskopf, Yanfei Yang, Bi-Yi Wu, Jifa Tian, Alireza R. Panna, Hsin-Yen Lee, Shamith U. Payagala, George R. Jones, Marlin E. Kraft, Dean G. Jarrett, Kenji Watanabe, Takashi Taniguchi, Randolph E. Elmquist, David B. Newell

Abstract: We report the fabrication and measurement of top gated epitaxial graphene p-n junctions where exfoliated hexagonal boron nitride (h-BN) is used as the gate dielectric. The four-terminal longitudinal resistance across a single junction is well quantized at the von Klitzing constant R_K with a relative uncertainty of 10-7. After the exploration of numerous parameter spaces, we summarize the conditio… ▽ More We report the fabrication and measurement of top gated epitaxial graphene p-n junctions where exfoliated hexagonal boron nitride (h-BN) is used as the gate dielectric. The four-terminal longitudinal resistance across a single junction is well quantized at the von Klitzing constant R_K with a relative uncertainty of 10-7. After the exploration of numerous parameter spaces, we summarize the conditions upon which these devices could function as potential resistance standards. Furthermore, we offer designs of programmable electrical resistance standards over six orders of magnitude by using external gating. △ Less

Submitted 10 January, 2022; originally announced January 2022.

Geometric interference in a high-mobility graphene annulus p-n junction device

Authors: Son T. Le, Albert F. Rigosi, Joseph A. Hagmann, Christopher Gutierrez, Ji Ung Lee, Curt A. Richter

Abstract: The emergence of interference is observed in the resistance of a graphene annulus pn junction device as a result of applying two separate gate voltages. The observed resistance patterns are carefully inspected, and it is determined that the position of the peaks resulting from those patterns are independent of temperature and magnetic field. Furthermore, these patterns are not attributable to Ahar… ▽ More The emergence of interference is observed in the resistance of a graphene annulus pn junction device as a result of applying two separate gate voltages. The observed resistance patterns are carefully inspected, and it is determined that the position of the peaks resulting from those patterns are independent of temperature and magnetic field. Furthermore, these patterns are not attributable to Aharonov-Bohm oscillations, Fabry Perot interference at the junction, or moiré potentials. The device data are compared with those of another device fabricated with a traditional Hall bar geometry, as well as with quantum transport simulation data. Since the two devices are of different topological classes, the subtle differences observed in the corresponding measured data indicate that the most likely source of the observed geometric interference patterns is quantum scarring. △ Less

Submitted 29 December, 2021; originally announced December 2021.

Analysis of Raman and Ellipsometric Responses of Nb$_{x}$W$_{1-x}$Se$_{2}$ alloys

Authors: Albert F. Rigosi, Heather M. Hill, Sergiy Krylyuk, Nhan V. Nguyen, Angela R. Hight Walker, Albert V. Davydov, David B. Newell

Abstract: 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 analysi… ▽ More 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. △ Less

Submitted 24 December, 2021; originally announced December 2021.

Bonding characteristics of the interfacial buffer layer in epitaxial graphene via density functional theory

Authors: Alana Okullo, Heather M. Hill, Albert F. Rigosi, Angela R. Hight Walker, Francesca Tavazza, Sugata Chowdhury

Abstract: 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… ▽ More 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. △ Less

Submitted 7 December, 2021; originally announced December 2021.

Crystalline Formations of NbN/4H-SiC Heterostructure Interfaces

Authors: Michael B. Katz, Chieh-I Liu, Albert F. Rigosi, Mattias Kruskopf, Angela Hight Walker, Randolph E. Elmquist, Albert V. Davydov

Abstract: Given the importance of incorporating various superconducting materials to device fabrication or substrate development, studying the interface for possible interactions is warranted. In this work, NbN films sputter-deposited on 4H-SiC were heat-treated at 1400 C and 1870 C and were examined with transmission electron microscopy to assess whether the interfacial interactions undergo temperature-dep… ▽ More Given the importance of incorporating various superconducting materials to device fabrication or substrate development, studying the interface for possible interactions is warranted. In this work, NbN films sputter-deposited on 4H-SiC were heat-treated at 1400 C and 1870 C and were examined with transmission electron microscopy to assess whether the interfacial interactions undergo temperature-dependent behavior. We report the diffusion of NbN into the SiC substrate and the formation of NbN nanocrystallites therein during the 1400 C treatment. After the 1870 C treatment, tiered porosity and the formation of voids are observed, likely due to catalytic reactions between the two materials and accelerated by the stresses induced by the differences in the materials' coefficients of thermal expansion. Lastly, Raman spectroscopy is employed to gain an understanding of the interface lattices' optical responses. △ Less

Submitted 16 November, 2021; originally announced November 2021.

Quantum Simulation of an Extended Fermi-Hubbard Model Using a 2D Lattice of Dopant-based Quantum Dots

Authors: Xiqiao Wang, Ehsan Khatami, Fan Fei, Jonathan Wyrick, Pradeep Namboodiri, Ranjit Kashid, Albert F. Rigosi, Garnett Bryant, Richard Silver

Abstract: The Hubbard model is one of the primary models for understanding the essential many-body physics in condensed matter systems such as Mott insulators and cuprate high-Tc superconductors. Recent advances in atomically precise fabrication in silicon using scanning tunneling microscopy (STM) have made possible atom-by-atom fabrication of single and few-dopant quantum dots and atomic-scale control of t… ▽ More The Hubbard model is one of the primary models for understanding the essential many-body physics in condensed matter systems such as Mott insulators and cuprate high-Tc superconductors. Recent advances in atomically precise fabrication in silicon using scanning tunneling microscopy (STM) have made possible atom-by-atom fabrication of single and few-dopant quantum dots and atomic-scale control of tunneling in dopant-based devices. However, the complex fabrication requirements of multi-component devices have meant that emulating two-dimensional (2D) Fermi-Hubbard physics using these systems has not been demonstrated. Here, we overcome these challenges by integrating the latest developments in atomic fabrication and demonstrate the analog quantum simulation of a 2D extended Fermi-Hubbard Hamiltonian using STM-fabricated 3x3 arrays of single/few-dopant quantum dots. We demonstrate low-temperature quantum transport and tuning of the electron ensemble using in-plane gates as efficient probes to characterize the many-body properties, such as charge addition, tunnel coupling, and the impact of disorder within the array. By controlling the array lattice constants with sub-nm precision, we demonstrate tuning of the hopping amplitude and long-range interactions and observe the finite-size analogue of a transition from Mott insulating to metallic behavior in the array. By increasing the measurement temperature, we simulate the effect of thermally activated hopping and Hubbard band formation in transport spectroscopy. We compare the analog quantum simulations with numerically simulated results to help understand the energy spectrum and resonant tunneling within the array. The results demonstrated in this study serve as a launching point for a new class of engineered artificial lattices to simulate the extended Fermi-Hubbard model of strongly correlated materials. △ Less

Submitted 17 October, 2021; originally announced October 2021.

A Non-Topological Approach to Understanding Weyl Semimetals

Authors: Antonio Levy, Albert F. Rigosi, Francois Joint, Gregory S. Jenkins

Abstract: In this work, chiral anomalies and Drude enhancement in Weyl semimetals are separately discussed from a semi-classical and quantum perspective, clarifying the physics behind Weyl semimetals while avoiding explicit use of topological concepts. The intent is to provide a bridge to these modern ideas for educators, students, and scientists not in the field using the familiar language of traditional s… ▽ More In this work, chiral anomalies and Drude enhancement in Weyl semimetals are separately discussed from a semi-classical and quantum perspective, clarifying the physics behind Weyl semimetals while avoiding explicit use of topological concepts. The intent is to provide a bridge to these modern ideas for educators, students, and scientists not in the field using the familiar language of traditional solid-state physics at the graduate or advanced undergraduate physics level. △ Less

Submitted 31 January, 2021; originally announced February 2021.

Examining Experimental Raman Mode Behavior in Mono- and Bi-layer 2H-TaSe$_{2}$ via Density Functional Theory

Authors: Sugata Chowdhury, Heather M. Hill, Albert F. Rigosi, Andrew Briggs, Helmuth Berger, David B. Newell, Angela R. Hight Walker, Francesca Tavazza

Abstract: 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, incl… ▽ More 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. △ Less

Submitted 5 December, 2020; originally announced December 2020.

Comments: arXiv admin note: substantial text overlap with arXiv:2005.11350

Influence of Dimensionality on the Charge Density Wave Phase of 2H-TaSe$_{2}$

Authors: Sugata Chowdhury, Albert F. Rigosi, Heather M. Hill, Andrew Briggs, David B. Newell, Helmuth Berger, Angela R. Hight Walker, Francesca Tavazza

Abstract: Metallic transition metal dichalcogenides like tantalum diselenide (TaSe$_{2}$) exhibit exciting behaviors at low temperatures, including the emergence of charge density wave (CDW) states. In this work, density functional theory (DFT) is used to investigate how structural, electronic, and Raman spectral properties of the CDW configuration change as a function of thickness. Such findings highlight… ▽ More Metallic transition metal dichalcogenides like tantalum diselenide (TaSe$_{2}$) exhibit exciting behaviors at low temperatures, including the emergence of charge density wave (CDW) states. In this work, density functional theory (DFT) is used to investigate how structural, electronic, and Raman spectral properties of the CDW configuration change as a function of thickness. Such findings highlight the influence of dimensionality change (from 2D to 3D) and van der Waals (vdW) interactions on the system properties. The vdW effect is most strongly present in bulk TaSe$_{2}$ in the spectral range 165 cm$^{-1}$ to 215 cm$^{-1}$. The phonons seen in the experimental Raman spectra are compared with the results calculated from the DFT models as a function of temperature and layer number. The matching of data and calculations substantiates the model's description of the CDW structural formation as a function of thickness, which is shown in depth for 1L through 6L systems. These results highlight the importance of understanding interlayer interactions, which are pervasive in many quantum phenomena involving two-dimensional confinement. △ Less

Submitted 20 August, 2021; v1 submitted 22 May, 2020; originally announced May 2020.

Comments: 6 figures, 28 pages

Confocal laser scanning microscopy: A tool for rapid optical characterization of 2D materials

Authors: Vishal Panchal, Yanfei Yang, Guangjun Cheng, Jiuning Hu, Mattias Kruskopf, Chieh-I Liu, Albert F. Rigosi, Christos Melios, Angela R. Hight Walker, David B. Newell, Olga Kazakova, Randolph E. Elmquist

Abstract: Confocal laser scanning microscopy (CLSM) is a non-destructive, highly-efficient optical characterization method for large-area analysis of graphene on different substrates, which can be applied in ambient air, does not require additional sample preparation, and is insusceptible to surface charging and surface contamination. CLSM leverages optical properties of graphene and provides greatly enhanc… ▽ More Confocal laser scanning microscopy (CLSM) is a non-destructive, highly-efficient optical characterization method for large-area analysis of graphene on different substrates, which can be applied in ambient air, does not require additional sample preparation, and is insusceptible to surface charging and surface contamination. CLSM leverages optical properties of graphene and provides greatly enhanced optical contrast and mapping of thickness down to a single layer. We demonstrate the effectiveness of CLSM by measuring mechanically exfoliated and chemical vapor deposition graphene on Si/SiO2, and epitaxial graphene on SiC. In the case of graphene on Si/SiO2, both CLSM intensity and height mapping is powerful for analysis of 1-5 layers of graphene. For epitaxial graphene on SiC substrates, the CLSM intensity allows us to distinguish features such as dense, parallel 150 nm wide ribbons of graphene (associated with the early stages of the growth process) and large regions covered by the interfacial layer and 1-3 layers of graphene. In both cases, CLSM data shows excellent correlation with conventional optical microscopy, atomic force microscopy, Kelvin probe force microscopy, conductive atomic force microscopy, scanning electron microscopy and Raman mapping, with a greatly reduced acquisition time. We demonstrate that CLSM is an indispensable tool for rapid analysis of mass-produced graphene and is equally relevant to other 2D materials. △ Less

Submitted 12 April, 2018; originally announced April 2018.

Comments: 4 Figures

Rapid characterization of wafer-scale 2D material: Epitaxial graphene and graphene nanoribbons on SiC

Authors: Vishal Panchal, Yanfei Yang, Guangjun Cheng, Jiuning Hu, Chieh-I Liu, Albert F. Rigosi, Christos Melios, Olga Kazakova, Angela R. Hight Walker, David B. Newell, Randolph E. Elmquist

Abstract: We demonstrate that the confocal laser scanning microscopy (CLSM) provides a non-destructive, highly-efficient characterization method for large-area epitaxial graphene and graphene nanostructures on SiC substrates, which can be applied in ambient air without sample preparation and is insusceptible to surface charging or surface contamination. Based on the variation of reflected intensity from reg… ▽ More We demonstrate that the confocal laser scanning microscopy (CLSM) provides a non-destructive, highly-efficient characterization method for large-area epitaxial graphene and graphene nanostructures on SiC substrates, which can be applied in ambient air without sample preparation and is insusceptible to surface charging or surface contamination. Based on the variation of reflected intensity from regions covered by interfacial layer, single layer, bilayer, or few layer graphene, and through the correlation to the results from Raman spectroscopy and SPM, CLSM images with a high resolution (around 150 nm) reveal that the intensity contrast has distinct feature for undergrown graphene (mixing of dense, parallel graphene nanoribbons and interfacial layer), continuous graphene, and overgrown graphene. Moreover, CLSM has a real acquisition time hundreds of times faster per unit area than the supplementary characterization methods. We believe that the confocal laser scanning microscope will be an indispensable tool for mass-produced epitaxial graphene or applicable 2D materials. △ Less

Submitted 9 November, 2017; originally announced November 2017.

Coulomb engineering of the bandgap in 2D semiconductors

Authors: Archana Raja, Andrey Chaves, Jaeeun Yu, Ghidewon Arefe, Heather M. Hill, Albert F. Rigosi, Timothy C. Berkelbach, Philipp Nagler, Christian Schüller, Tobias Korn, Colin Nuckolls, James Hone, Louis E. Brus, Tony F. Heinz, David R. Reichman, Alexey Chernikov

Abstract: The ability to control the size of the electronic bandgap is an integral part of solid-state technology. Atomically-thin two-dimensional crystals offer a new approach for tuning the energies of the electronic states based on the interplay between the environmental sensitivity and unusual strength of the Coulomb interaction in these materials. By engineering the surrounding dielectric environment,… ▽ More The ability to control the size of the electronic bandgap is an integral part of solid-state technology. Atomically-thin two-dimensional crystals offer a new approach for tuning the energies of the electronic states based on the interplay between the environmental sensitivity and unusual strength of the Coulomb interaction in these materials. By engineering the surrounding dielectric environment, we are able to tune the electronic bandgap in monolayers of WS2 and WSe2 by hundreds of meV. We exploit this behavior to present an in-plane dielectric heterostructure with a spatially dependent bandgap, illustrating the feasibility of our approach for the creation of lateral junctions with nanoscale resolution. This successful demonstration of bandgap engineering based on the non-invasive modification of the Coulomb interaction should enable the design of a new class of atomically thin devices to advance the limits of size and functionality for solid-state technologies. △ Less

Submitted 7 February, 2017; v1 submitted 3 February, 2017; originally announced February 2017.

Measurement of the optical dielectric function of transition metal dichalcogenide monolayers: MoS2, MoSe2, WS2 and WSe2

Authors: Yilei Li, Alexey Chernikov, Xian Zhang, Albert Rigosi, Heather M. Hill, Arend M. van der Zande, Daniel A. Chenet, En-Min Shih, James Hone, Tony F. Heinz

Abstract: We report a determination of the complex in-plane dielectric function of monolayers of four transition metal dichalcogenides: MoS2, MoSe2, WS2 and WSe2, for photon energies from 1.5 - 3 eV. The results were obtained from reflection spectra using a Kramers-Kronig constrained variational analysis. From the dielectric functions, we obtain the absolute absorbance of the monolayers. We also provide a c… ▽ More We report a determination of the complex in-plane dielectric function of monolayers of four transition metal dichalcogenides: MoS2, MoSe2, WS2 and WSe2, for photon energies from 1.5 - 3 eV. The results were obtained from reflection spectra using a Kramers-Kronig constrained variational analysis. From the dielectric functions, we obtain the absolute absorbance of the monolayers. We also provide a comparison of the dielectric function for the monolayers with the corresponding bulk materials. △ Less

Submitted 14 October, 2016; originally announced October 2016.

Journal ref: Phys. Rev. B 90, 205422 (2014)

Valley Splitting and Polarization by the Zeeman Effect in Monolayer MoSe2

Authors: Yilei Li, Jonathan Ludwig, Tony Low, Alexey Chernikov, Xu Cui, Ghidewon Arefe, Young Duck Kim, Arend M. van der Zande, Albert Rigosi, Heather M. Hill, Suk Hyun Kim, James Hone, Zhiqiang Li, Dmitry Smirnov, Tony F. Heinz

Abstract: We have measured circularly polarized photoluminescence in monolayer MoSe2 under perpendicular magnetic fields up to 10 T. At low doping densities, the neutral and charged excitons shift linearly with field strength at a rate of $\mp$ 0.12 meV/T for emission arising, respectively, from the K and K' valleys. The opposite sign for emission from different valleys demonstrates lifting of the valley de… ▽ More We have measured circularly polarized photoluminescence in monolayer MoSe2 under perpendicular magnetic fields up to 10 T. At low doping densities, the neutral and charged excitons shift linearly with field strength at a rate of $\mp$ 0.12 meV/T for emission arising, respectively, from the K and K' valleys. The opposite sign for emission from different valleys demonstrates lifting of the valley degeneracy. The magnitude of the Zeeman shift agrees with predicted magnetic moments for carriers in the conduction and valence bands. The relative intensity of neutral and charged exciton emission is modified by the magnetic field, reflecting the creation of field-induced valley polarization. At high doping levels, the Zeeman shift of the charged exciton increases to $\mp$ 0.18 meV/T. This enhancement is attributed to many-body effects on the binding energy of the charged excitons. △ Less

Submitted 30 September, 2014; originally announced September 2014.

Journal ref: Phys. Rev. Lett. 113, 266804 (2014)

Exciton Binding Energy and Nonhydrogenic Rydberg Series in Monolayer WS2

Authors: Alexey Chernikov, Timothy C. Berkelbach, Heather M. Hill, Albert Rigosi, Yilei Li, Ozgur B. Aslan, David R. Reichman, Mark S. Hybertsen, Tony F. Heinz

Abstract: We have experimentally determined the energies of the ground and first four excited excitonic states of the fundamental optical transition in monolayer WS2, a model system for the growing class of atomically thin two-dimensional semiconductor crystals. From the spectra, we establish a large exciton binding energy of 0.32 eV and a pronounced deviation from the usual hydrogenic Rydberg series of ene… ▽ More We have experimentally determined the energies of the ground and first four excited excitonic states of the fundamental optical transition in monolayer WS2, a model system for the growing class of atomically thin two-dimensional semiconductor crystals. From the spectra, we establish a large exciton binding energy of 0.32 eV and a pronounced deviation from the usual hydrogenic Rydberg series of energy levels of the excitonic states. We explain both of these results using a microscopic theory in which the non-local nature of the effective dielectric screening modifies the functional form of the Coulomb interaction. These strong but unconventional electron-hole interactions are expected to be ubiquitous in atomically thin materials. △ Less

Submitted 2 September, 2014; v1 submitted 17 March, 2014; originally announced March 2014.

Comments: published version

Journal ref: Phys. Rev. Lett. 113, 076802 (2014)

Molecular beam growth of graphene nanocrystals on dielectric substrates

Authors: Ulrich Wurstbauer, Theanne Schiros, Cherno Jaye, Annette S. Plaut, Rui He, Albert Rigosi, Christopher Gutiérrez, Daniel Fischer, Loren N. Pfeiffer, Abhay N. Pasupathy, Aron Pinczuk, Jorge M. García

Abstract: We demonstrate the growth of graphene nanocrystals by molecular beam methods that employ a solid carbon source, and that can be used on a diverse class of large area dielectric substrates. Characterization by Raman and Near Edge X-ray Absorption Fine Structure spectroscopies reveal a sp2 hybridized hexagonal carbon lattice in the nanocrystals. Lower growth rates favor the formation of higher quali… ▽ More We demonstrate the growth of graphene nanocrystals by molecular beam methods that employ a solid carbon source, and that can be used on a diverse class of large area dielectric substrates. Characterization by Raman and Near Edge X-ray Absorption Fine Structure spectroscopies reveal a sp2 hybridized hexagonal carbon lattice in the nanocrystals. Lower growth rates favor the formation of higher quality, larger size multi-layer graphene crystallites on all investigated substrates. The surface morphology is determined by the roughness of the underlying substrate and graphitic monolayer steps are observed by ambient scanning tunneling microscopy. △ Less

Submitted 18 June, 2012; v1 submitted 13 February, 2012; originally announced February 2012.

Comments: Accepted in Carbon; Discussion section added; 20 pages, 6 figures (1 updated)

Observation of non-conventional spin waves in composite fermion ferromagnets

Authors: U. Wurstbauer, S. S. Mandal, D. Majumder, I. Dujovne, T. D. Rhone, B. S. Dennis, A. F. Rigosi, J. K. Jain, A. Pinczuk, K. W. West, L. N. Pfeiffer

Abstract: We find unexpected low energy excitations of fully spin-polarized composite-fermion ferromagnets in the fractional quantum Hall liquid, resulting from a complex interplay between a topological order manifesting through new energy levels and a magnetic order due to spin polarization. The lowest energy modes, which involve spin reversal, are remarkable in displaying unconventional negative dispersio… ▽ More We find unexpected low energy excitations of fully spin-polarized composite-fermion ferromagnets in the fractional quantum Hall liquid, resulting from a complex interplay between a topological order manifesting through new energy levels and a magnetic order due to spin polarization. The lowest energy modes, which involve spin reversal, are remarkable in displaying unconventional negative dispersion at small momenta followed by a deep roton minimum at larger momenta. This behavior results from a nontrivial mixing of spin-wave and spin-flip modes creating a spin-flip excitonic state of composite-fermion particle-hole pairs. The striking properties of spin-flip excitons imply highly tunable mode couplings that enable fine control of topological states of itinerant two-dimensional ferromagnets. △ Less

Submitted 14 August, 2011; originally announced August 2011.

Comments: 4 pages, 4 figures

Journal ref: Phys.Rev.Lett.107:066804,2011