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At least 253 records · Page 14

NASA Tech Briefs, October 2005

Topics covered include: Insect-Inspired Optical-Flow Navigation Sensors; Chemical Sensors Based on Optical Ring Resonators; A Broad-Band Phase-Contrast Wave-Front Sensor; Progress in Insect-Inspired Optical Navigation Sensors; Portable Airborne Laser System Measures Forest-Canopy Height; Deployable Wide-Aperture Array Antennas; Faster Evolution of More Multifunctional Logic Circuits; Video-Camera-Based Position-Measuring System; N-Type delta Doping of High-Purity Silicon Imaging Arrays; Avionics System Architecture Tool; Updated Chemical Kinetics and Sensitivity Analysis Code; Predicting Flutter and Forced Response in Turbomachinery; Upgrades of Two Computer Codes for Analysis of Turbomachinery; Program Facilitates CMMI Appraisals; Grid Visualization Tool; Program Computes Sound Pressures at Rocket Launches; Solar-System Ephemeris Toolbox; Data-Acquisition Software for PSP/TSP Wind-Tunnel Cameras; Corrosion-Prevention Capabilities of a Water-Borne, Silicone-Based, Primerless Coating; Sol-Gel Process for Making Pt-Ru Fuel-Cell Catalysts; Making Activated Carbon for Storing Gas; System Regulates the Water Contents of Fuel-Cell Streams; Five-Axis, Three-Magnetic-Bearing Dynamic Spin Rig; Modifications of Fabrication of Vibratory Microgyroscopes; Chamber for Growing and Observing Fungi; Electroporation System for Sterilizing Water; Thermoelectric Air/Soil Energy-Harvesting Device; Flexible Metal-Fabric Radiators; Actuated Hybrid Mirror Telescope; Optical Design of an Optical Communications Terminal; Algorithm for Identifying Erroneous Rain-Gauge Readings; Condition Assessment and End-of-Life Prediction System for Electric Machines and Their Loads; Lightweight Thermal Insulation for a Liquid-Oxygen Tank; Stellar Gyroscope for Determining Attitude of a Spacecraft; and Lifting Mechanism for the Mars Explorer Rover.

Source record↗

Apparatus and method for creating a photonic densely-accumulated ray-point

An optical apparatus includes an optical diffraction device configured for diffracting a predetermined wavelength of incident light onto adjacent optical focal points, and a photon detector for detecting a spectral characteristic of the predetermined wavelength. One of the optical focal points is a constructive interference point and the other optical focal point is a destructive interference point. The diffraction device, which may be a micro-zone plate (MZP) of micro-ring gratings or an optical lens, generates a constructive ray point using phase-contrasting of the destructive interference point. The ray point is located between adjacent optical focal points. A method of generating a densely-accumulated ray point includes directing incident light onto the optical diffraction device, diffracting the selected wavelength onto the constructive interference focal point and the destructive interference focal point, and generating the densely-accumulated ray point in a narrow region.

Park, Yeonjoon↗

Phytoplankton Assemblage Patterns in the Southern Mid-Atlantic Bight

As part of the Wallops Coastal Oceans Observing Laboratory (Wa-COOL) Project, we sampled a time-series transect in the southern Mid-Atlantic Bight (MAB) biweekly. Our 2-year time-series data included physical parameters, nutrient concentrations, and chlorophyll a concentrations. A detailed phytoplankton assemblage structure was examined in the second year. During the 2-year study, chlorophyll a concentration (and ocean color satellite imagery) indicated that phytoplankton blooms occurred in January/February during mixing conditions and in early autumn under stratified conditions. The chlorophyll a concentrations ranged from 0.25 microgram 1(exp -1) to 15.49 microgram 1(exp -1) during the 2-year period. We were able to discriminate approximately 116 different species under phase contrast microscopy. Dominant phytoplankton included Skeletonema costatum, Rhizosolenia spp., and Pseudo-nitzschia pungens. In an attempt to determine phytoplankton species competition/succession within the assemblage, we calculated a Shannon Weaver diversity index for our diatom microscopy data. Diatom diversity was greatest during the winter and minimal during the spring. Diatom diversity was also greater at nearshore stations than at offshore stations. Individual genera appeared patchy, with surface and subsurface patches appearing abruptly and persisting for only 1-2 months at a time. The distribution of individual species differed significantly from bulk variables of the assemblage (chlorophyll a ) and total phytoplankton assemblage (cells), which indicates that phytoplankton species may be limited in growth in ways that differ from those of the total assemblage. Our study demonstrated a highly diverse phytoplankton assemblage throughout the year, with opportunistic species dominating during spring and fall in response to seasonal changes in temperature and nutrients in the southern MAB.

Mid-Atlantic↗

Observation Platform for Dynamic Biomedical and Biotechnology Experiments Using the International Space Station (ISS) Light Microscopy Module (LMM)

Techshot, Inc., has developed an observation platform for the LMM on the ISS that will enable biomedical and biotechnology experiments. The LMM Dynamic Stage consists of an electronics module and the first two of a planned suite of experiment modules. Specimens and reagent solutions can be injected into a small, hollow microscope slide-the heart of the innovation-via a combination of small reservoirs, pumps, and valves. A life science experiment module allows investigators to load up to two different fluids for on-orbit, real-time image cytometry. Fluids can be changed to initiate a process, fix biological samples, or retrieve suspended cells. A colloid science experiment module conducts microparticle and nanoparticle tests for investigation of colloid self-assembly phenomena. This module includes a hollow glass slide and heating elements for the creation of a thermal gradient from one end of the slide to the other. The electronics module supports both experiment modules and contains a unique illuminator/condenser for bright and dark field and phase contrast illumination, power supplies for two piezoelectric pumps, and controller boards for pumps and valves. This observation platform safely contains internal fluids and will greatly accelerate the research and development (R&D) cycle of numerous experiments, products, and services aboard the ISS.

Kurk, Michael A. (Andy)↗

Observation Platform for Dynamic Biomedical and Biotechnology Experiments Using the International Space Station (ISS) Light Microscopy Module (LMM)

Techshot, Inc., has developed an observation platform for the LMM on the ISS that will enable biomedical and biotechnology experiments. The LMM Dynamic Stage consists of an electronics module and the first two of a planned suite of experiment modules. Specimens and reagent solutions can be injected into a small, hollow microscope slide-the heart of the innovation-via a combination of small reservoirs, pumps, and valves. A life science experiment module allows investigators to load up to two different fluids for on-orbit, real-time image cytometry. Fluids can be changed to initiate a process, fix biological samples, or retrieve suspended cells. A colloid science experiment module conducts microparticle and nanoparticle tests for investigation of colloid self-assembly phenomena. This module includes a hollow glass slide and heating elements for the creation of a thermal gradient from one end of the slide to the other. The electronics module supports both experiment modules and contains a unique illuminator/condenser for bright and dark field and phase contrast illumination, power supplies for two piezoelectric pumps, and controller boards for pumps and valves. This observation platform safely contains internal fluids and will greatly accelerate the research and development (R&D) cycle of numerous experiments, products, and services aboard the ISS.

Kurk, Michael A. (Andy)↗

Biomolecular Analysis Capability for Cellular and Omics Research on the International Space Station

International Space Station (ISS) assembly complete ushered a new era focused on utilization of this state-of-the-art orbiting laboratory to advance science and technology research in a wide array of disciplines, with benefits to Earth and space exploration. ISS enabling capability for research in cellular and molecular biology includes equipment for in situ, on-orbit analysis of biomolecules. Applications of this growing capability range from biomedicine and biotechnology to the emerging field of Omics. For example, Biomolecule Sequencer is a space-based miniature DNA sequencer that provides nucleotide sequence data for entire samples, which may be used for purposes such as microorganism identification and astrobiology. It complements the use of WetLab-2 SmartCycler"TradeMark", which extracts RNA and provides real-time quantitative gene expression data analysis from biospecimens sampled or cultured onboard the ISS, for downlink to ground investigators, with applications ranging from clinical tissue evaluation to multigenerational assessment of organismal alterations. And the Genes in Space-1 investigation, aimed at examining epigenetic changes, employs polymerase chain reaction to detect immune system alterations. In addition, an increasing assortment of tools to visualize the subcellular distribution of tagged macromolecules is becoming available onboard the ISS. For instance, the NASA LMM (Light Microscopy Module) is a flexible light microscopy imaging facility that enables imaging of physical and biological microscopic phenomena in microgravity. Another light microscopy system modified for use in space to image life sciences payloads is initially used by the Heart Cells investigation ("Effects of Microgravity on Stem Cell-Derived Cardiomyocytes for Human Cardiovascular Disease Modeling and Drug Discovery"). Also, the JAXA Microscope system can perform remotely controllable light, phase-contrast, and fluorescent observations. And upcoming confocal microscopy capability will allow for optical sectioning of biological tissues to determine microanatomical localization of biomarkers. Furthermore, NASA's geneLAB effort addresses integration of genomic, epigenomic, transcriptomic, proteomic and metabolomic datasets, by applying an innovative open source science platform for multi-investigator high throughput utilization of the ISS. In sum, the expanding ISS capability for analysis of biomolecules is enabling innovative research in a broad spectrum of areas such as cellular and molecular biology, biotechnology, tissue engineering, biomedicine, and Omics, providing manifold benefits for humanity.

Guinart-Ramirez, Y.↗

Science camera calibration for extreme adaptive optics

The nascent field of planet detection has yielded a host of extra-solar planet detections. To date, these detections have been the result of indirect techniques: the planet is inferred by precisely measuring its effect on the host star. Direct observation of extra-solar planets remains a challenging yet compelling goal. In this vein, the Center for Adaptive Optics has proposed a ground-based, high-actuator density extreme A0 system (XAOPI), for a large (~10 m) telescope whose ultimate goal is to directly evidence a specific class of these objects: young and massive planets. Detailed system wave-front error budgets suggest that this system is a feasible, if not an ambitious, proposition. One key element in this error budget is the calibration and maintenance of the science camera wave front with respect to the wave-front sensor which currently as an allowable contribution of ~ 5 nanometers rms. This talk first summarizes the current status of calibration on existing ground-based A0 systems, the magnitude of this effect in the system error budget and current techniques for mitigation. Subsequently, we will explore the nature of this calibration error term, it's source in the non-commonality between the science camera and wave front sensor, and the effect of the temporal evolution of non-commonality. Finally, we will describe preliminary plans for sensing and controlling this error term. The sensing techniques include phase retrieval, phase contrast and external metrology. To conclude, a calibration scenario that meets the stringent requirement for XAOPI will be discussed.

MacIntosh, Bruce↗

Intracranial Effects of Intermittent Lower Body Negative Pressure with Head Down Tilt Bed Rest: Comparison to Upright Posture

INTRODUCTION Spaceflight-associated neuro-ocular syndrome (SANS) affects a majority of astronauts during long-duration spaceflight. SANS is hypothesized to result from an unrelenting headward fluid shift that occurs in the microgravity environment. Altered intracranial structure and physiology documented in spaceflight and head-down tilt (HDT) experiments(1, 2) are also theorized to be related to chronic headward fluid shift and thereby can provide an independent quantitative assessment related to this mechanism. As a potential countermeasure, lower body negative pressure (LBNP) applied in the supine posture has shown efficacy in reducing headward fluid shift(3). However, it remains unknown if intermittent LBNP simulating daily upright posture fluid redistribution can mitigate SANS and intracranial changes associated with long-duration spaceflight. The goal of this study was to quantify the effects of daily application of LBNP or daily exposure to the upright posture on intracranial structure and physiology during long-term HDT in order to evaluate the potential efficacy of LBNP as a countermeasure to SANS. METHODS 22 healthy volunteers (11 men; 11 women; mean age = 35 years (SD=9.2)(age range = 24 to 52 years); mean BMI = 24.0 kg/m2 (SD=2.8)) completed an MRI study performed at the German Aerospace Facility in Cologne, Germany. Strict six-degree head-down tilt (HDT) bedrest was used as a spaceflight analog to induce a continuous headward fluid shift for 30 days. The subjects were divided equally into two groups of interventions: 1) LBNP for 3-hour sessions twice daily and 2) seated position for 3-hour sessions twice daily. Interventions were divided into morning and afternoon sessions for both groups. The LBNP intervention was maintained at 25 mmHg  2 mmHg. Pulse-gated MRI phase-contrast flow imaging was used to quantify cerebral artery stroke volume (CASV) and peak-to-peak cerebral spinal fluid (CSF) velocity (CSFVp-p) within the cerebral aqueduct. A 3D T1-MPRAGE sequence was used to quantify volumetric changes of the brain and intracranial CSF spaces using MRI Cloud software. MRI acquisitions were obtained at baseline (BDC, supine posture), 15 days into HDT (HDT15), 29 days into HDT (HDT29), and 12 days after recovery (R12, supine posture). The data were analyzed by a mixed model, which included intervention, time (four nominal levels BDC, HDT15, HDT29, R12), and intervention-time interaction as the fixed effects and included subject as a random effect. RESULTS Compared to BDC there was no statistically significant difference in CASV and CSFVp-p during HDT except for CASV at HDT29 (seated group) where there was a 1.7 mL (12%) decrease (P<0.01). Compared to BDC there was a statistically significant increase in intracranial volume (ICV; ICV = white matter + gray matter + CSF) for both interventions at HDT15 (Δ13 mL, 0.9 % (LBNP group); Δ15 mL, 1.0%, (seated group)) and HDT29 (Δ19 mL, 1.2%, (LBNP group); Δ23 mL, 1.5%) (seated group)) (All Ps<.001). Compared to baseline, lateral ventricular volume increased at HDT15 (Δ0.9 mL, 5.5%) and HDT29 (Δ1.8 mL, 10%)) for LBNP only (P=.001 for each). During HDT, white matter volume remained stable compared to baseline for both interventions. There were no significant intervention effects in the overall response to HDT (All Ps >.2). CONCLUSION LBNP had a similar response to the seated posture during 29 days of HDT. Although there was an increase in ICV and lateral ventricular volume with HDT there was no change in intracranial physiological parameters with LBNP suggesting an overall diminished response to the long-term effects of HDT. The lack of any significant increase in white matter volume during HDT with LBNP suggests maintenance of cerebral interstitial fluid transport. Final conclusions are pending the data collection for the control group (no intervention) which will be completed in 2023.

Larry A Kramer↗

Advancing Metasurfaces Towards New Frontiers: Nonvolatile Reconfigurable Optics

The applications of adaptive optics extend across multiple sectors, encompassing areas such as LiDAR, biological and chemical sensing, and free-space communications. In this study, we report on the design, fabrication, testing, and modeling of electrically reconfigurable metasurfaces using a low-loss high contrast phase change material, Ge2Sb2Se4Te integrated with an IR-transparent silicon microheater. Through this work, we introduce a reliable architecture for switching PCM-based metasurfaces within an integrated circuit configuration which is compatible with standard foundry fabrication processes. We demonstrate the capability of controlling the transmission of electromagnetic waves through the precise stimulation of PCM-based pixels, each spanning a few hundred microns, over numerous cycles. By leveraging PCM-based pixels, we unlock the potential to create metasurfaces encompassing a diverse range of functionalities such as dielectric filters, metalens, or beam steering devices, which is governed by the design of the meta-atoms. Further, we perform an in-depth investigation into the failure mechanism utilizing techniques such as Fourier transform IR spectroscopy (FTIR), transmission electron microscopy (TEM), energy dispersive spectroscopy (EDS), and thermal modeling. According to our results, due to a sharp temperature rise at the PCM/heater interface, we observe severe delamination of the PCM from the heater. More uniform PCM deposition, better adhesion at the PCM/heater interface, and a more uniform temperature distribution in the device could potentially mitigate the failure and lead to a longer life-time. By addressing these challenges, we aim to unlock the full potential of PCM-based devices and advance the field of adaptive optics.

Phase change material↗

Development of scalable design optimization parameters for bi-component protective systems

Bi-component protection-systems need to withstand a variety of extreme loading conditions such as high-velocity projectile impact to shock and blast mitigation. The large number of parameters at each stage of bi-component protection system design process results in a near-infinite number of possible variables for optimization. The aim of this project is to identify the scaling laws linking material and geometric scales of the problem to the final impact performance, further including the effects of wave propagation/interaction and inter-component bonding. Specifically, the impact dynamics for different optimal projectile/target density ratios and relative component mass fractions are quantified for bonded ceramic/titanium alloy systems. The impact behavior such as wave mechanics and damage propagation within the target system is characterized and quantified via digital image correlation or via x-ray phase-contrast imaging.

36 MATERIALS SCIENCE↗

Fast and bright scintillators for ultrafast materials dynamics using 4th generation synchrotron

We present recent advances in fast and bright scintillators for ultrafast X-ray phase contrast imaging of dynamic materials experiments at the upgraded Advanced Photon Source (APS-U), a fourth generation synchrotron. APS-U enables hard X-ray imaging at frame rates of at least 13 MHz (corresponding to 77 ns or shorter interframe intervals), creating a new need for scintillators with faster response and higher light output than lutetium yttrium oxyorthosilicate (LYSO). For indirect imaging and diffraction with ultrafast cameras, commercial lanthanum bromide (LaBr3) and cerium bromide (CeBr3) are promising candidates. These materials exhibit decay times approximately a factor of two shorter than LYSO (around 40 ns) and lutetium oxyorthosilicate (LSO), while maintaining comparable light yield per incident X-ray photon. However, their implementation at APS-U requires addressing several challenges, including material limitations due to hygroscopicity, efficient optical coupling to imaging systems, and high quantum efficiency for conversion of scintillation light, predominantly at wavelengths below 400 nm, into detectable electronic signals. We report results from material characterization, detector integration and packaging, and beamline experiments of materials with impact. In addition, emerging scintillator classes, including perovskites and high-entropy materials, are discussed as potential alternatives for next-generation ultrafast X-ray diagnostics.

Wang, Zhehui [Los Alamos] (ORCID:0000000178264063)↗

Comparison of Simulated Contrast Performance of Different Phase Induced Amplitude Apodization (PIAA) Coronagraph Configurations

We compare the broadband contrast performances of several Phase Induced Amplitude Apodization (PIAA) coronagraph configurations through modeling and simulations. The basic optical design of the PIAA coronagraph is the same as NASA's High Contrast Imaging Testbed (HCIT) setup at the Jet Propulsion Laboratory (JPL). Using a deformable mirror and a broadband wavefront sensing and control algorithm, we create a "dark hole" in the broadband point-spread function (PSF) with an inner working angle (IWA) of 2(f lambda/D)(sub sky). We evaluate two systems in parallel. One is a perfect system having a design PIAA output amplitude and not having any wavefront error at its exit-pupil. The other is a realistic system having a design PIAA output amplitude and the measured residual wavefront error. We also investigate the effect of Lyot stops of various sizes when a postapodizer is and is not present. Our simulations show that the best 7.5%-broadband contrast value achievable with the current PIAA coronagraph is approximately 1.5x10(exp -8).

adaptive optics↗

Long-Range Ordered Amorphous Atomic Chains as Building Blocks of a Superconducting Quasi-One-Dimensional Crystal

Crystalline and amorphous structures are two of the most common solid-state phases. Crystals having orientational and periodic translation symmetries are usually both short-range and long-range ordered, while amorphous materials have no long-range order. Short-range ordered but long-range disordered materials are generally categorized into amorphous phases. In contrast to the extensively studied crystalline and amorphous phases, the combination of short-range disordered and long-range ordered structures at the atomic level is extremely rare and so far has only been reported for solvated fullerenes under compression. Here, a report on the creation and investigation of a superconducting quasi-1D material with long-range ordered amorphous building blocks is presented. Using a diamond anvil cell, monocrystalline (TaSe4)(2)I is compressed and a system is created where the TaSe(4)atomic chains are in amorphous state without breaking the orientational and periodic translation symmetries of the chain lattice. Strikingly, along with the amorphization of the atomic chains, the insulating (TaSe4)(2)I becomes a superconductor. The data provide critical insight into a new phase of solid-state materials. The findings demonstrate a first ever case where superconductivity is hosted by a lattice with periodic but amorphous constituent atomic chains.

combination of crystalline and amorphous structure↗

Beyond Contrast Transfer: Spectral SNR as a Finite-Dose Metric for STEM Phase Retrieval

The contrast transfer function (CTF) is widely used to evaluate phase retrieval methods in scanning transmission electron microscopy (STEM), including center-of-mass imaging, parallax imaging, direct ptychography, and iterative ptychography. However, the CTF reflects only the maximum usable signal, neglecting the effects of finite electron fluence and the Poisson-limited nature of detection. As a result, it can significantly overestimate practical performance, especially in low-dose regimes. Here, we employ the spectral signal-to-noise ratio (SSNR), as a finite-dose statistical framework to evaluate the recoverable signal as a function of spatial frequency. Using numerical reconstructions of white-noise objects, we show that center-of-mass, parallax, and direct ptychography exhibit dose-independent SSNRs, with close-form analytic expressions. In contrast, iterative ptychography exhibits a surprising dose dependence: at low fluence, its SSNR converges to that of direct ptychography; at high fluence, it saturates at a value consistent with the maximum detective quantum efficiency predicted by recent quantum Fisher information bounds. The results highlight the limitations of CTF-based evaluation and motivate SSNR as a more accurate, finite-dose metric for assessing STEM phase retrieval methods.

STEM phase retrieval↗

Pressure-induced suppression of charge density phases across the entire rare-earth tritellurides by optical spectroscopy

The rare-earth tritellurides (RTe 3 ) are a distinct class of 2D layered materials that recently gained significant attention due to hosting such quantum collective phenomena as superconductivity or charge density waves (CDWs). Many members of this van der Waals (vdW) family crystals exhibit CDW behavior at room temperature, i.e., RTe 3 compound where R = La, Ce, Pr, Nd, Sm, Gd, and Tb. Here, our systematic studies establish the CDW properties of RTe 3 when the vdW spacing/interaction strength between adjacent RTe 3 layers is engineered under extreme hydrostatic pressures. Using a non-destructive spectroscopy technique, pressure-dependent Raman studies first establish the pressure coefficients of phonon and CDW amplitude modes for a variety of RTe 3 materials, including LaTe 3 , CeTe 3 , PrTe 3 , NdTe 3 , SmTe 3 , GdTe 3 , and TbTe 3 . Results further show that the CDW phase is eventually suppressed at high pressures when the interlayer spacing is reduced and interaction strength is increased. Comparison between different RTe 3 materials shows that LaTe 3 with the largest thermodynamic equilibrium interlayer spacing (smallest chemical pressure) exhibits the most stable CDW phases at high pressures. In contrast, CDW phases in late RTe 3 systems with the largest internal chemical pressures are suppressed easily with applied pressure. Overall results provide comprehensive insights into the CDW response of the entire RTe 3 series under extreme pressures, offering an understanding of CDW formation/engineering in a unique class of vdW RTe 3 material systems.

36 MATERIALS SCIENCE↗

Berry Curvature and Spin-One Color Superconductivity

Here, we explore the interplay between Berry curvature and topological properties in single-flavor color superconductors, where quarks form spin-one Cooper pairs. By deriving a new relation, we connect the topological nodal structure of the gap function in momentum space to the (non-Abelian) Berry flux associated with paired quarks. This generalizes the early work by Li and Haldane [Phys. Rev. Lett. 120, 067003 (2018)] to systems with additional internal quantum numbers, such as color. In the ultrarelativistic limit, we uncover rich topological structures driven by the interplay of spin, chirality, and color. Specifically, we identify chirality-induced topological nodes in the transverse (opposite chirality pairing) polar and 𝐴 phases. In contrast, the color-spin-locking phase lacks these nodes due to a nontrivial color Berry flux, which in turn induces gapless excitations with total Berry monopole charges of ±3/2—differing from conventional Weyl fermions. Our findings can be potentially extended to other fermionic systems carrying additional internal degrees of freedom.

Berry curvature↗

Topological approach to electron correlations at fractional quantum Hall effect

Highlights: • Braids in 2D electron systems in magnetic field acquire a cyclotron metrics. • Commensurability of 2D braids with Wigner crystal of electrons leads to FQHE. • Homotopy invariants define the hierarchy of FQHE universal in all 2D Hall systems. • Composite fermions illustrate multiloop braids in the simplest homotopy case. • Correlations in FQHE reveal long-range quantum entanglement of all electrons. The classification of homotopy invariants in interacting multi-electron 2D systems at quantizing magnetic fields is presented, explaining the topologically protected correlations occurring at integer and fractional quantum Hall effects. The long-range quantum entanglement is essential for homotopy correlated phases in contrast to the binary entanglement for conventional phases with local order parameters. The classification of homotopy long-range correlated phases induced by the Coulomb interaction of electrons has been derived in terms of homotopy invariants, which are universal and robust against local disorder and single-particle crystal field, as illustrated by experimental observations in various materials with different microscopic structure, like GaAs 2DES, graphene monolayer and bilayer and in Chern topological insulators. The homotopy phases are demonstrated to be topologically protected and immune to single-particle perturbations, temperature chaos and variation of the electron interaction strength. The nonzero repulsive interaction between electrons is shown, however, to be essential for the definition of the homotopy invariants, which disappear in gaseous systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗