# Technical Document Extraction: Graph Analysis
## Graph (a)
- **Parameters**:
- λ_I = 0.015t
- Δ = 0
- E_F = 0.035t
- **Axes**:
- **y-axis**: G (e²/h)
- **x-axis**: λ_R/t
- **Key Features**:
- **K₁ Region**: Peaks in G (e²/h) between λ_R/t ≈ 0.05–0.15.
- **K₂ Region**: Lower G values (shaded area) between λ_R/t ≈ 0.15–0.25.
- **Inset**:
- **G_K1** (red line): Oscillatory behavior with peaks at λ_R/t ≈ 0.15 and 0.20.
- **G_K2** (blue line): Oscillatory behavior with peaks at λ_R/t ≈ 0.10 and 0.25.
## Graph (b)
- **Parameters**:
- λ_I = 0.015t
- Δ = 0.02t
- E_F = 0.035t
- **Axes**:
- **y-axis**: G (e²/h)
- **x-axis**: λ_R/t
- **Key Features**:
- **K₁ Region**: Reduced peak amplitude compared to graph (a), with a prominent peak at λ_R/t ≈ 0.10.
- **K₂ Region**: Shaded area with minimal G values.
- **Inset**:
- **G_K1** (red line): Single peak at λ_R/t ≈ 0.15.
- **G_K2** (blue line): Double-peaked structure at λ_R/t ≈ 0.10 and 0.20.
## Cross-Reference: Legend Colors vs. Line Placement
- **Red (G_K1)**:
- Peaks in both graphs align with K₁ regions.
- **Blue (G_K2)**:
- Peaks in both graphs align with K₂ regions.
## Observations
1. **Effect of Δ**:
- Increasing Δ from 0 to 0.02t (graph a → b) reduces G_K1 amplitude and shifts K₁ peak positions.
2. **Shaded Area**:
- Represents K₂ region with suppressed conductance (G < 1 e²/h).
3. **Inset Trends**:
- G_K1 and G_K2 exhibit distinct oscillatory patterns, suggesting coupling between K₁ and K₂ states.
