凝聚态物理导论-中科院课件-苏刚Chapter3.pdf

Chapter 3 Electronic Structures Electronic structure: the energy levels of the electrons and to their distribution in space and in momentum. Two assumptions: Adiabatic approximation; Single electron approximation. Concerns Ordered periodic system; or disordered system Extended states Some localized states §3.1 Bloch theorem The Hamiltonian commutes with the translation operator, equivalent §3.2 Plane wave expansions To calculate the electronic structures, two issues are faced: (1) To solve a Schrödinger equation, for a given Hamiltonian with a known crystal potential; (2) How to determine the crystal potential? Most methods for the calculation of energy levels and wave functions in solids are expansion methods. The unknown wave function ψ(k,r) is expanded in a set of known functions; the coefficients have to be determined. If different kind of atoms at d , then V needed. j j The structure factor S(K) depends only on the positions of the atoms. Fourier transform of V j Perturbation theory H = (k+K )2 δ + V(K -K ) st s st t s When V(K) is small enough, the 2nd-order perturbation theory can apply. Θ: angle between k and K s s