NNSE618-L3-SSP-Bloch_theorem

NNSE618-L3-SSP-Bloch_theorem - 1 Lecture contents Solid...

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NNSE 618 Lecture #3 1 Lecture contents Solid state physics review Approximations Bloch theorem k-vector Brillouin zone Tight-binding model
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NNSE 618 Lecture #3 2 Few concepts from Solid State Physics 1. Adiabatic approximation ) ( ) ( R E R H L L ) , ( ) , ( r R E r R H Mass of ions >1000 (for most semiconductors >10 2 times greater than mass of electrons Ion velocities >100 times slower Electrons adjust „instantaneously” to the positions of atoms When valence and core ectrons are separated, general Schrödinger equation for a condensed medium without spin ) ( ) , ( ) , ( R R r r R Separate ion and electron motion (accuracy ~m/M) = H L + H e ) , ( ) , ( R r E R r H e e
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NNSE 618 Lecture #3 3 Few concepts from Solid State Physics 2. Phonons     anhar m l m l m l m l m l l l l L U u u C R R U M p H , 2 , , 0 0 0 2 2 1 2 1 exp 1 ) ( kT n t i ikr k e u u 0 , Hamiltonian for lattice motion (harmonic oscillations) : Displacements show up as plane waves with weak interaction via anharmonicity: Phonon dispersion relation in GaAs     2 1 , , k n k E Energy in a mode: Equilibrium distribution (Bose Einstein):
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NNSE 618 Lecture #3 4 Few concepts from Solid State Physics 3. One-electron (mean-field) approximation i i i R r R r ) , ( ) , ( Schrödinger equation for the electrons (no spin): e e i i e V r V ) ( Introduce one-electron states, i :   e e ph e l l i i ei V V R r V m p H 0 2 2 Small perturbation   ) ( ) ( 2 2 r E r r V m p One-electron
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This note was uploaded on 11/07/2011 for the course NNSE 618 taught by Professor Sergeoktyabrsky during the Spring '11 term at SUNY Albany.

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NNSE618-L3-SSP-Bloch_theorem - 1 Lecture contents Solid...

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