Nanoscale imaging of equilibrium quantum Hall edge currents and of the magnetic monopole response in graphene

The recently predicted topological magnetoelectric effect and the response to an electric charge that mimics an induced mirror magnetic monopole are fundamental attributes of topological states of matter with broken time reversal symmetry. Using a SQUID-on-tip, acting simultaneously as a tunable scanning electric charge and as ultrasensitive nanoscale magnetometer, we induce and directly image the microscopic currents generating the magnetic monopole response in a graphene quantum Hall electron system. We find a rich and complex nonlinear behavior governed by coexistence of topological and nontopological equilibrium currents that is not captured by the monopole models. Furthermore, by utilizing a tuning fork that induces nanoscale vibrations of the SQUID-on-tip, we directly image the equilibrium currents of individual quantum Hall edge states for the first time. We reveal that the edge states that are commonly assumed to carry only a chiral downstream current, in fact carry a pair of counterpropagating currents, in which the topological downstream current in the incompressible region is always counterbalanced by heretofore unobserved nontopological upstream current flowing in the adjacent compressible region. The intricate patterns of the counterpropagating equilibrium-state orbital currents provide new insights into the microscopic origins of the topological and nontopological charge and energy flow in quantum Hall systems

Imaging resonant dissipation from individual atomic defects in graphene

Conversion of electric current into heat involves microscopic processes that operate on nanometer length-scales and release minute amounts of power. While central to our understanding of the electrical properties of materials, individual mediators of energy dissipation have so far eluded direct observation. Using scanning nano-thermometry with sub-micro K sensitivity we visualize and control phonon emission from individual atomic defects in graphene. The inferred electron-phonon 'cooling power spectrum' exhibits sharp peaks when the Fermi level comes into resonance with electronic quasi-bound states at such defects, a hitherto uncharted process. Rare in the bulk but abundant at graphene's edges, switchable atomic-scale phonon emitters define the dominant dissipation mechanism. Our work offers new insights for addressing key materials challenges in modern electronics and engineering dissipation at the nanoscale

Visualizing thickness-dependent magnetic textures in few-layer Cr2Ge2Te6\text{Cr}_2\text{Ge}_2\text{Te}_6

Magnetic ordering in two-dimensional (2D) materials has recently emerged as a promising platform for data storage, computing, and sensing. To advance these developments, it is vital to gain a detailed understanding of how the magnetic order evolves on the nanometer-scale as a function of the number of atomic layers and applied magnetic field. Here, we image few-layer $\text{Cr}_2\text{Ge}_2\text{Te}_6$ using a combined scanning superconducting quantum interference device and atomic force microscopy probe. Maps of the material's stray magnetic field as a function of applied magnetic field reveal its magnetization per layer as well as the thickness-dependent magnetic texture. Using a micromagnetic model, we correlate measured stray-field patterns with the underlying magnetization configurations, including labyrinth domains and skyrmionic bubbles. Comparison between real-space images and simulations demonstrates that the layer dependence of the material's magnetic texture is a result of the thickness-dependent balance between crystalline and shape anisotropy. These findings represent an important step towards 2D spintronic devices with engineered spin configurations and controlled dependence on external magnetic fields.Comment: 15 pages, 4 figures, and supplementary informatio

A verification approach for crosscutting features based on extension join points

Recently, one arguing question in the context of product line development is how to improve the modularization and composition of crosscutting features. However, little attention has been paid to the closely related issue of testing the crosscutting features. This paper proposes a verification approach for the crosscutting features of a product line based on the use of a previously proposed concept called Extension Join Points

Oxidative Tearing of Graphene Sheets: Insights into the Probable Situations by Computational and Experimental Studies

Nanometer size graphene sheet has become a subject of interest both for technological as well as medical applications. In this work, we have focused on the oxidative tearing of nanoscale graphene sheets using ab initio density functional theory. We have geometry optimized several model systems depicting all possible graphene oxide sheets containing either a single or multiple oxygen atoms. We have found that a single oxygen atom prefers to bind to two carbon atoms of the cis-edge by forming an epoxy linkage. Such epoxidation also induces a large curvature into the graphene sheet by breaking the involved C–C bond. This initial epoxidation also favors formation of similar epoxy-linkages at nearby sites in a cooperative manner during the oxidation of a nascent graphene sheet. Such bond breaking, however, is not observed when we try similar epoxidation at the trans-edge. A series of epoxidation starting from the cis-edge thus can cause tearing of the graphene oxide sheet leading to formation of smaller size graphene sheets containing exposed functionalized trans-edges. Because of symmetry in a graphene sheet, we can expect to obtain a smaller functionalized graphene sheet of triangular shape having predominantly trans-edges (cis edges may appear at the corners) during the oxidation process. Our subsequent experiment of magnetic hysteresis compliments the theoretical finding of the tearing pattern

Visualizing thickness-dependent magnetic textures in few-layer Cr₂Ge₂Te₆

Magnetic ordering in two-dimensional (2D) materials has recently emerged as a promising platform for data storage, computing, and sensing. To advance these developments, it is vital to gain a detailed understanding of how the magnetic order evolves on the nanometer-scale as a function of the number of atomic layers and applied magnetic field. Here, we image few-layer Cr2Ge2Te6 using a combined scanning superconducting quantum interference device and atomic force microscopy probe. Maps of the material’s stray magnetic field as a function of applied magnetic field reveal its magnetization per layer as well as the thickness-dependent magnetic texture. Using a micromagnetic model, we correlate measured stray-field patterns with the underlying magnetization configurations, including labyrinth domains and skyrmionic bubbles. Comparison between real-space images and simulations demonstrates that the layer dependence of the material’s magnetic texture is a result of the thickness-dependent balance between crystalline and shape anisotropy. These findings represent an important step towards 2D spintronic devices with engineered spin configurations and controlled dependence on external magnetic fields.</p

Imaging resonant dissipation from individual atomic defects in graphene

Conversion of electric current into heat involves microscopic processes that operate on nanometer length scales and release minute amounts of power. Although central to our understanding of the electrical properties of materials, individual mediators of energy dissipation have so far eluded direct observation. Using scanning nanothermometry with submicrokelvin sensitivity, we visualized and controlled phonon emission from individual atomic-scale defects in graphene. The inferred electron-phonon “cooling power spectrum” exhibits sharp peaks when the Fermi level comes into resonance with electronic quasi-bound states at such defects. Rare in the bulk but abundant at graphene’s edges, switchable atomic-scale phonon emitters provide the dominant dissipation mechanism. Our work offers insights for addressing key materials challenges in modern electronics and enables control of dissipation at the nanoscale