The sharp, sudden cliff at the surface of this sphere creates a mathematical singularity. The electrons can't form a smooth screening cloud; instead, this sharp boundary causes them to ripple outward.

https://youtu.be/SYamJKw5QC4

<aside> 👏

1. https://www.instagram.com/reel/Dd7_uaMt_P6/?utm_source=ig_web_copy_link&stkn=MzRlODBiNWFlZA==
2. https://bsky.app/profile/researcherdean.bsky.social/post/3mws4berfj22z
3. https://x.com/d54223/status/2105528475117568307?s=20
4. https://via-dean.gitbook.io/all/multifaceted-viewpoint/mathematical-structures-underlying-physical-laws/animated-results/fermi-surface-from-3d-spheres-to-quasi-2d-corrugated-cylinders-and-2d-honeycomb-pockets
5. https://hackmd.io/@bafMjVSBQ6e7vlO7NdkhXA/BJJ0t9bYGe </aside>

<aside> <img src="/icons/download_yellow.svg" alt="/icons/download_yellow.svg" width="40px" />

🍄Deliverables 17

Fermi Surface From 3D Spheres to Quasi-2D Corrugated Cylinders and 2D Honeycomb Pockets

https://payhip.com/b/BacMg

Documents

• Computational Models
• Snippets
• A conceptual guide distilling the fundamental behavior of electrons in momentum space into key physical takeaways.

Exploration Frontiers

• 3D Free Electron Sea $\rightarrow$ Quantum Oscillations (dHvA / SdH)
• 2D Honeycomb Lattices $\rightarrow$ Lifshitz Phase Transitions
• Quasi-2D Systems $\rightarrow$ Superconducting Gap Mapping
• Brillouin Zone Geometry $\rightarrow$ Nesting Vector Calculation
• Surface Extraction $\rightarrow$ Density of States (DOS) Integration

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    %% --- Main Title ---
    Title["🔬 <b>Transition: Fermi Surface Exploration to Potential Orientations</b>"]:::domain

    %% --- Current Exploration Section ---
    subgraph Current ["Current Exploration"]
        direction TB
        C1["⚛️ Solid-State & Fermi Physics"]:::domain
        C2["💻 Computational Physics & Visualization"]:::domain

        %% C1 Sub-topics
        C1 --> CP1["3D Fermi Sphere Models"]:::core
        C1 --> CP2["Friedel Oscillations & Kohn Anomaly"]:::core
        C1 --> CP3["2D Hexagonal Lattices & Graphene"]:::core
        CP3 --> CPS3a["Dirac Point Fermi Pockets"]:::sub
        CP3 --> CPS3b["Voltage Tuning"]:::sub
        CP3 --> CPS3c["Trigonal Warping"]:::sub
        C1 --> CP4["Quasi-2D Layered Systems"]:::core
        CP4 --> CPS4a["Tight-Binding Dispersion"]:::sub
        CP4 --> CPS4b["Corrugated Cylindrical Surfaces"]:::sub

        %% C2 Sub-topics
        C2 --> CV1["Python Scripting (Matplotlib/VPython)"]:::core
        C2 --> CV2["3D Mesh Marching Cubes"]:::core
        C2 --> CV3["Dynamic Animations (FuncAnimation)"]:::core
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        direction TB
        P1["🌀 Quantum Phenomena & Topology"]:::domain
        P2["📊 Computational & Numerical Physics"]:::domain

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        P1 --> PP1["Lifshitz Phase Transitions"]:::potential
        P1 --> PP2["Quantum Oscillations (dHvA/SdH)"]:::potential
        P1 --> PP3["Anisotropic Superconducting Gap Mapping"]:::potential

        %% P2 Sub-topics
        P2 --> PV1["Nesting Vector Calculation for CDW/SDW"]:::potential
        P2 --> PV2["Interactive 3D Visualization (WebGL/PyVista)"]:::potential
        P2 --> PV3["Density of States (DOS) Mesh Integration"]:::potential
    end

    %% --- Connecting Edges ---
    Title -.- Current
    Current ==> Trans
    Trans ==> Potential

<aside> 👏

1. http://youtube.com/post/UgkxLLBpD4ZvCQRxj5hyw4Wau-PKub33TWz8?si=lUqpuu_jnbfRxK1w
2. https://pin.it/6mLUx2ayg </aside>

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