condensed-matter

## What I do - Analyze crystal structures and symmetry - Model electronic band theory - Study superconductivity and superfluidity - Calculate phonon dispersion relations - Analyze magnetic properties and phase transitions - Apply density functional theory concepts ## When to use me When studying solid-state physics, materials science, or semiconductor devices. ## Key Concepts - **Crystal Lattices**: Bravais lattices, Miller indices for planes - **Bloch's Theorem**: ψ_{k}(r) = e^{ik·r} u_k(r) for periodic potentials - **Band Theory**: Energy bands arise from periodic potentials, band gaps - **Fermi Surface**: Boundary between occupied and empty states at T=0 - **Phonons**: Quantized lattice vibrations, acoustic and optical modes - ** BCS Theory**: Superconductivity from electron pairing below T_c