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