# Technical Data Extraction: Streamline and Heatmap Analysis This document provides a detailed technical extraction of the provided image, which consists of two side-by-side scientific plots (labeled 'f' and 'h') representing physical simulations, likely related to electron flow or current density in a nanostructure. ## 1. Global Metadata * **Language:** English * **Primary Components:** Two subplots with heatmaps, streamline overlays, and color bars. * **X-Axis (Common):** `length (nm)` ranging from approximately -50 to 50. * **Y-Axis (Common):** `width (nm)` ranging from -15 to 15. * **Directional Indicator:** A black arrow at the bottom of both plots points from right to left (from +40 to -45 on the x-axis). --- ## 2. Subplot (f) Analysis ### Header Information * **Label:** (f) * **Title:** $K_2: E_F = +0.035t$ ### Axis and Scale * **X-axis Markers:** -40, -20, 0, 20, 40 * **Y-axis Markers:** -10, 0, 10 * **Color Bar Range:** 0.0 to 0.3 (linear scale). * **Color Bar Gradient:** Light beige/white (0.0) to dark orange/brown (0.3). ### Data Visualization (Heatmap & Streamlines) * **Heatmap Trend:** The highest intensity (dark orange, ~0.3) is concentrated in horizontal bands along the top and bottom edges (approx. $y = \pm 10$ nm) and in "bottleneck" regions between circular voids. * **Streamline Behavior:** * Blue lines with arrows indicate flow direction. * The flow enters from the right and moves toward the left. * The streamlines form four distinct "cells" or vortices centered along the $y=0$ axis at roughly $x = -30, -10, 10, 30$. * The flow is most compressed and intense (darker blue) at the narrow passages between these cells. * **Spatial Features:** There are four low-intensity (white) circular regions centered at $y=0$, suggesting areas of zero or near-zero magnitude. --- ## 3. Subplot (h) Analysis ### Header Information * **Label:** (h) * **Title:** $K_2: E_F = -0.035t$ ### Axis and Scale * **X-axis Markers:** -40, -20, 0, 20, 40 * **Y-axis Markers:** -10, 0, 10 * **Color Bar Range:** 0.0 to 0.4 (linear scale). Note: This scale is higher than subplot (f). * **Color Bar Gradient:** Light beige/white (0.0) to dark orange/brown (0.4). ### Data Visualization (Heatmap & Streamlines) * **Heatmap Trend:** Compared to (f), the intensity is much more concentrated along the central horizontal axis ($y=0$). The edges of the channel (top and bottom) show very low intensity (white). * **Streamline Behavior:** * Blue lines with arrows indicate flow from right to left. * The flow is highly collimated along the center of the channel. * While there are subtle "pinching" effects at the same x-coordinates as subplot (f) ($x \approx \pm 10, \pm 30$), the streamlines do not form the wide, expansive loops seen in the previous plot. * The flow appears "squeezed" into a narrow central filament. * **Spatial Features:** The high-intensity regions (dark orange) are located at the "nodes" or pinch points along the $y=0$ line. --- ## 4. Comparative Summary | Feature | Subplot (f) | Subplot (h) | | :--- | :--- | :--- | | **Fermi Energy ($E_F$)** | $+0.035t$ (Positive) | $-0.035t$ (Negative) | | **Max Intensity Value** | ~0.3 | ~0.4 | | **Flow Distribution** | Broad, filling the width of the channel. | Narrow, concentrated along the center. | | **Vortex/Cell Formation** | Strong, expansive cells around $y=0$. | Weak, highly compressed flow along $y=0$. | | **Edge Intensity** | High at $y = \pm 10$ nm. | Low at $y = \pm 10$ nm. | **Conclusion:** The change in the sign of the Fermi energy ($E_F$) from positive to negative causes a dramatic shift in the spatial distribution of the flow, moving it from the edges and wide cells (f) to a highly concentrated central stream (h).

# Technical Document Extraction: Heatmap Analysis of K₂ with Varying E_F ## Image Overview The image contains two side-by-side heatmaps labeled **(f)** and **(h)**, depicting streamline flow patterns in a 2D spatial domain. Both panels share identical axis labels and color scales but differ in the sign of the Fermi energy parameter **E_F**. --- ### **Panel (f): K₂ with E_F = +0.035t** #### Labels and Axis Titles - **X-axis**: `length (nm)` ranging from -40 nm to 40 nm. - **Y-axis**: `width (nm)` ranging from -10 nm to 10 nm. - **Title**: `(f) K₂: E_F=+0.035t` - **Color Bar**: - **Range**: 0.0 (white) to 0.4 (red). - **Position**: Right of the panel. - **Spatial Grounding**: Legend located at `[x=45 nm, y=-10 nm]` (relative to the heatmap's coordinate system). #### Components and Flow - **Streamlines**: Blue arrows indicate vector direction and magnitude. - **Color Gradient**: - **High Intensity (Red)**: Central region (x ≈ 0 nm, y ≈ 0 nm). - **Low Intensity (White)**: Edges (x ≈ ±40 nm, y ≈ ±10 nm). - **Trend Verification**: - Arrows in the central region point outward radially, with density decreasing toward the edges. - Color intensity peaks at the center (red) and diminishes toward the edges (white). --- ### **Panel (h): K₂ with E_F = -0.035t** #### Labels and Axis Titles - **X-axis**: `length (nm)` ranging from -40 nm to 40 nm. - **Y-axis**: `width (nm)` ranging from -10 nm to 10 nm. - **Title**: `(h) K₂: E_F=-0.035t` - **Color Bar**: - **Range**: 0.0 (white) to 0.4 (red). - **Position**: Right of the panel. - **Spatial Grounding**: Legend located at `[x=45 nm, y=-10 nm]`. #### Components and Flow - **Streamlines**: Blue arrows indicate vector direction and magnitude. - **Color Gradient**: - **Low Intensity (White)**: Central region (x ≈ 0 nm, y ≈ 0 nm). - **High Intensity (Red)**: Edges (x ≈ ±40 nm, y ≈ ±10 nm). - **Trend Verification**: - Arrows in the central region point inward radially, with density increasing toward the edges. - Color intensity peaks at the edges (red) and diminishes toward the center (white). --- ### Key Observations 1. **Symmetry**: Both panels exhibit bilateral symmetry about the x=0 nm axis. 2. **E_F Dependency**: - Positive **E_F** (+0.035t) in (f) correlates with outward flow and central intensity. - Negative **E_F** (-0.035t) in (h) correlates with inward flow and edge intensity. 3. **Legend Consistency**: - Red (0.4) and white (0.0) values match the intensity peaks in both panels. - Arrows align with the gradient direction (e.g., outward flow in red regions of (f)). --- ### Notes - **Language**: All text is in English. - **Data Extraction**: No numerical tables or embedded text beyond axis labels and titles. - **Missing Information**: No explicit units for **t** (likely a material constant, e.g., thickness or temperature).