Explore the physical and computational transition of electronic structure concepts, mapping Fermi surface geometries to key observables like quantum oscillations, Lifshitz phase transitions, superconducting gap symmetries, and density of states integration.

https://youtu.be/2DP0mrNpIE4

<aside> 👏

1. https://www.instagram.com/reel/Dd8-fpJMv7N/?utm_source=ig_web_copy_link
2. 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
3. https://pin.it/eWEfXevSh
4. https://bsky.app/profile/researcherdean.bsky.social/post/3mwszkrc3yc27
5. https://x.com/d54223/status/2105660783506178256?s=20
6. 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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    Trans["⚡ Apply Theoretical Extrapolations & Enhanced Numerical Models"]:::transition

    %% --- Potential Orientations Section ---
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        direction TB
        P1["🌀 Quantum Phenomena & Topology"]:::domain
        P2["📊 Computational & Numerical Physics"]:::domain

        %% P1 Sub-topics
        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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