Physics 250-06 “Advanced Electronic Structure”

Lecture 7.1. Response to Time-Dependent Fields

Contents:

1. Time-Dependent DFT and Linear Response.

2. Response to Magnetic Fields and Dynamical Susceptibilities

3. Applications to Fe, Ni, Cr

4. Response to electromagnetic fields: optical properties

5. Optical Properties of Metals and HTSCs

TD-DFT.

TD-DFT.

TD-DFT.

Linear Response Theory within TD-DFT.

Linear Response Theory within TD-DFT.

Adiabatic LDA.

Response to Time Dependent Magnetic Field.

Variational Linear Rsponse.

Variational Linear Response.

Sternheimer Equations.

Dynamical Spin Susceptibility of Fe.

Dynamical Spin Susceptibility of Ni.

Dynamical Spin Susceptibility of Cr.

Response to Electric Fields.

Similar Discussion can be consdered:

General Difficulty: non-periodic potential, when q->0 itproduces infinite field.

Static limit in insulators determines static dielectric constant 0.

Response to Electromagnetic Fields.

Transverse response to

0

0

( , ) exp( )

( , ) exp( )

E r t E ikr t

B r t B ikr t

Transverse dielectric function is determined as follows

Dispersion relations for the photon in the media

( ) ( ) ( )effE k k E k

2 22( )

( )

c kk

k

Response to Electromagnetic Fields.

Optical Response Functions 1 2( ) ( ) ( )k k i k

Optical Conductivity( ) ( ) ( )

4 ( )( ) 1

J k k E k

i kk

Reflectivity

1

1

2 2

2 2

22 1

1

22 1

1

( 1)

( 1)

1 4

2

1 4

2

n KR

n K

n

K

Optical Properties (Maximov et.al, 1988)

Local Field Effects.

Intraband and Interband Transitions.

Sum Rules.

Optical Properties of Metals.

Optical Properties of Metals: Al and Pd

Optical Properties of Metals: Rh and Mo

Optical Properties of Metals: Nb and Zr

Optical Properties of Metals: Y and Rt

Optical Properties of Metals: Tc and Cr

Optical Properties of Metals: V and Ag

Optical Properties of Metals: Cu and Cd

Optical Properties of Metals.

Optical Properties of Metals.

Optical Properties of YBCO.

Optical Properties of YBCO.

Optical Properties of Metals.