Physics / advanced
Electrons in periodic potentials
Derive electronic bands and transport observables through Bloch states, reciprocal geometry, effective masses, and controlled electronic-structure approximations.
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Module 01 advanced
Electrons in periodic potentials
Derive electronic bands and transport observables through Bloch states, reciprocal geometry, effective masses, and controlled electronic-structure approximations.
- 01
Use translation symmetry to label electronic states
Declare reciprocal conventions and distinguish crystal momentum from mechanical momentum.
27 min - 02
Open a gap by mixing degenerate plane waves
Use a two-state block at a Bragg plane and state the approximation’s limits.
27 min - 03
Build a band from localized orbitals
Keep hopping signs, Hermitian conjugation, and basis overlap explicit.
27 min - 04
Count energy states across the whole Brillouin zone
Derive dimensional density-of-states laws and identify velocity-related singularities.
27 min - 05
Count electrons from occupied reciprocal volume
Separate Fermi-surface shape, spin channels, filled bands, and interacting assumptions.
27 min - 06
Move a wavepacket through an isolated band
Combine band velocity, force-driven crystal momentum, and Berry curvature.
27 min - 07
Read acceleration from the curvature tensor
Distinguish local band mass, holes, and an orbit-dependent cyclotron mass.
27 min - 08
Turn a band subspace into localized orbitals
Use unitary Fourier transforms while keeping gauge freedom and orthogonality explicit.
27 min - 09
Build a ground-state density through auxiliary orbitals
Separate the exact density-functional framework from functional approximations and eigenvalue interpretation.
27 min - 10
Validate the quantity a band calculation is meant to predict
Separate model error, numerical convergence, filling, and comparison with experiment.
27 min