# Technical Data Extraction: Current Density and Streamline Plots This document provides a detailed technical extraction of the data and visual components from the provided image, which consists of two side-by-side heatmaps with overlaid streamlines, likely representing electronic transport properties in a nanostructure. ## 1. General Metadata * **Language:** English * **Image Type:** Scientific Heatmaps / Streamline Plots * **Coordinate System:** Cartesian (Length vs. Width) * **Units:** Nanometers (nm) for spatial dimensions; $t$ (hopping parameter) for energy. --- ## 2. Component Isolation: Plot (b) ### Header Information * **Label:** (b) * **Title:** $K_2: E_F = +0.035t$ * **Interpretation:** This plot represents the $K_2$ valley/state at a positive Fermi energy of $0.035t$. ### Axis Configuration * **Y-axis (Left):** "width (nm)" * **Range:** -10 to 10 (with visible ticks at -10, 0, 10). * **X-axis (Bottom):** "length (nm)" * **Range:** -40 to 40 (with visible ticks at -40, -20, 0, 20, 40). * **Directional Indicator:** A black arrow at the bottom of the plot area points from left to right (negative to positive length). ### Colorbar (Legend) * **Location:** Right side of plot (b). * **Scale:** Linear, from 0.0 to 0.6. * **Color Gradient:** White (0.0) $\rightarrow$ Light Orange $\rightarrow$ Dark Brown/Rust (0.6). * **Function:** Represents the magnitude of a physical quantity (likely current density). ### Data Visualization & Trends * **Heatmap Trend:** The highest intensity (dark orange/brown, $\approx 0.4 - 0.5$) is concentrated on the far left side (length $\approx -50$ to $-40$ nm) near the center and edges of the width. The intensity decays rapidly as length increases. By length $= 0$ nm, the intensity is nearly zero (white). * **Streamlines:** Blue lines with arrows indicate flow direction. * **Pattern:** On the left, there are circular/vortex-like patterns. * **Flow:** The flow appears to enter from the left, circulate in the region between -50 and -20 nm, and then dissipate. --- ## 3. Component Isolation: Plot (d) ### Header Information * **Label:** (d) * **Title:** $K_2: E_F = -0.035t$ * **Interpretation:** This plot represents the $K_2$ valley/state at a negative Fermi energy of $-0.035t$. ### Axis Configuration * **Y-axis (Left):** "width (nm)" * **Range:** -10 to 10 (ticks at -10, 0, 10). * **X-axis (Bottom):** "length (nm)" * **Range:** -40 to 40 (ticks at -40, -20, 0, 20, 40). * **Directional Indicator:** A black arrow at the bottom points from left to right. ### Colorbar (Legend) * **Location:** Right side of plot (d). * **Scale:** Linear, from 0.0 to 0.4 (Note: The peak scale is lower than in plot b). * **Color Gradient:** White (0.0) $\rightarrow$ Light Orange $\rightarrow$ Dark Brown/Rust (0.4). ### Data Visualization & Trends * **Heatmap Trend:** Unlike plot (b), the intensity in plot (d) is sustained across the entire length of the channel. * **Left Region (-50 to -30 nm):** High intensity (dark orange, $\approx 0.3 - 0.4$) near the top and bottom edges. * **Central/Right Region (-20 to 50 nm):** The intensity fluctuates but remains significant ($\approx 0.1 - 0.2$), showing a "beating" or oscillatory pattern along the length. * **Streamlines:** Blue lines with arrows. * **Pattern:** Shows a more laminar, forward-moving flow compared to plot (b). * **Flow:** The streamlines originate at the left and propagate through the entire length to the right boundary, following a wavy path that corresponds to the intensity fluctuations in the heatmap. --- ## 4. Comparative Summary | Feature | Plot (b) $E_F = +0.035t$ | Plot (d) $E_F = -0.035t$ | | :--- | :--- | :--- | | **Max Intensity** | $\approx 0.6$ (Higher) | $\approx 0.4$ (Lower) | | **Spatial Decay** | High; signal vanishes by $x=0$. | Low; signal persists to $x=50$. | | **Flow Character** | Localized vortices/backflow. | Extended propagation/forward flow. | | **Symmetry** | Concentrated at the injection point. | Distributed throughout the nanostructure. | **Conclusion:** The data indicates a strong asymmetry in transport for the $K_2$ state depending on the sign of the Fermi energy. Positive $E_F$ results in localized, non-propagating states, while negative $E_F$ allows for extended propagation across the length of the device.

# Technical Document Extraction: Heatmap Analysis of K₂ and E_F Parameters ## Panel (b) - K₂: E_F = +0.035t ### Axis Labels - **X-axis**: `length (nm)` (direction: left to right) - **Y-axis**: `width (nm)` (range: -10 nm to +10 nm) ### Color Scale Legend - **Gradient**: White (0.0) → Red (0.6) - **Key Observation**: - High-intensity regions (red) localized near the edges of the plot (left side). - Gradual decay of intensity toward the center and right side. ### Diagram Components - **Arrows**: Black arrow on the X-axis indicating increasing length. - **Color Distribution**: - Blue-to-red gradient indicates varying intensity values. - Symmetric patterns observed along the Y-axis (width). --- ## Panel (d) - K₂: E_F = -0.035t ### Axis Labels - **X-axis**: `length (nm)` (direction: left to right) - **Y-axis**: `width (nm)` (range: -10 nm to +10 nm) ### Color Scale Legend - **Gradient**: White (0.0) → Red (0.6) - **Key Observation**: - High-intensity regions (red) concentrated near the center (X ≈ 0 nm). - Oscillatory patterns with alternating intensity bands along the X-axis. ### Diagram Components - **Arrows**: Black arrow on the X-axis indicating increasing length. - **Color Distribution**: - Blue-to-red gradient with periodic intensity variations. - Asymmetric patterns compared to Panel (b). --- ## Cross-Reference: Legend Colors vs. Diagram - **Panel (b)**: Red regions align with the highest intensity values (0.6) on the legend. - **Panel (d)**: Red regions correspond to peak intensity values, with blue regions near 0.0. ## Summary of Trends 1. **Panel (b)**: Edge-localized high-intensity features under positive E_F. 2. **Panel (d)**: Centralized high-intensity features with oscillatory decay under negative E_F. 3. **Color Consistency**: Red = maximum intensity (0.6), White = baseline (0.0) across both panels.