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4/6/2015PHY 752 Spring Lecture 283 Treatment of electromagnetic fields in solids periodic potential
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PHY 752 Spring 2015 -- Lecture 28 14/6/2015
PHY 752 Solid State Physics11-11:50 AM MWF Olin 107
Plan for Lecture 28:
Chap. 21 in Marder & pdf file from Bassani’s text Optical properties of solids
Interband transitions Excitons
PHY 752 Spring 2015 -- Lecture 28 24/6/2015
PHY 752 Spring 2015 -- Lecture 28 34/6/2015
Treatment of electromagnetic fields in solids
2
0
2
1
Zero order Hamiltonian for electron
( )2
Hamiltonian in the presence of an elect
First order perturbation
romagnetic field
1 ( )2
( )2
pH Um
eH U em c
e em
Hc
r
p A r
A p p A
periodic potential
PHY 752 Spring 2015 -- Lecture 28 44/6/2015
1
First order perturbati
( )
on
2e emc
H A p p A
Treatment of electromagnetic fields in solids
0
Possibility #1:
and 0 i tc ei
EA
0
Possibility #2:
0 and i te A r E
PHY 752 Spring 2015 -- Lecture 28 54/6/2015
Treatment of electromagnetic fields in solids using possibility #1 and following Bassani’s text
Fermi Golden Rule:
In this case: 00
cAi
Ee
PHY 752 Spring 2015 -- Lecture 28 64/6/2015
Treatment of electromagnetic fields in solids using possibility #1 and following Bassani’s text
PHY 752 Spring 2015 -- Lecture 28 74/6/2015
Treatment of electromagnetic fields in solids using possibility #1 and following Bassani’s text
spin
Normalizing the result in terms of imaginary part of dielectric constant:
PHY 752 Spring 2015 -- Lecture 28 84/6/2015
Treatment of electromagnetic fields in solids using possibility #1 and following Bassani’s text
From Kramers-Kronig transform:
Special results:
PHY 752 Spring 2015 -- Lecture 28 94/6/2015
Treatment of electromagnetic fields in solids using possibility #1 and following Bassani’s text
Sometimes can use group theory to determine “forbidden” transitions
When matrix elements are constant; structure depends sensitively on joint density of states
PHY 752 Spring 2015 -- Lecture 28 104/6/2015
PHY 752 Spring 2015 -- Lecture 28 114/6/2015
Band structure of Si (as calculated by Brust)
PHY 752 Spring 2015 -- Lecture 28 124/6/2015
Integration region of Brillouin zone
PHY 752 Spring 2015 -- Lecture 28 134/6/2015
Experiment
Calculation with matrix elements
PHY 752 Spring 2015 -- Lecture 28 144/6/2015
First principles calculation
PHY 752 Spring 2015 -- Lecture 28 154/6/2015
Experiment
Theory without exciton
Theory with exciton
PHY 752 Spring 2015 -- Lecture 28 164/6/2015
PHY 752 Spring 2015 -- Lecture 28 174/6/2015
Exciton effects
-
+
rn-rp
PHY 752 Spring 2015 -- Lecture 28 184/6/2015
Exciton effects (using Marder’s materials)
p
Wannier approximation
PHY 752 Spring 2015 -- Lecture 28 194/6/2015
Self-trapped excitons (RT Williams) NaCl