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Institute of Solid State PhysicsTechnische Universität Graz
17. Microwave engineering/ Superconductivity
Nov. 29, 2018
Intraband transitions
( ) ( )c vE k E k
When the bands are parallel, there is a peak in the absorption (")
Ibac
h &
Luet
h
Intraband (d-band) absorption
1 R
y =
13.6
ev
Reflection Electron Energy Loss Spectroscopy
Fast electrons moving through the solid generate and a time dependent electric field. If the polarization moves out of phase with this field, energy will be lost. This is detected in the reflected electrons.
e-
Microwave engineering
Microwave frequencies are a few GHz
The wavelength is smaller than the circuit
Losses in metals increase with increasing frequency
Losses in dielectrics increase with increasing frequency
There is a characteristic length scale called the skin depth which tells us how far into a metal fields penetrate before they are reflected out.
Skin depth << 1
0B J
Ohm's law0J E
Take the curl0
1 dBJ Edt
0 0
1 dBBdt
Ampere's law
Faraday's law
2B B B
Vector identity0
2
0 0
1 dBBdt
02 2
11
ine ne
<< 1
Skin depth
0 0
2
2
0 0
1 dBBdt
2
0 0
k i
Assume harmonic dependence 0
i kx tB e
0 0 0 00 0 2 2
k i i
Exponential decaySkin depth
Light p is reflected out of a metal. The waves penetrate a length .
Skin depth
//0 ˆi x txB B e e z
//0
0 0
(1 )1 ˆi x txB iJ B B e e y
/ / 4/0
0 0 0
2 ˆi x txBJE e e y
/ / 4/0
0
2 ˆi x txBJ e e y
/ 41 2 ii e
The electric field lags behind the magnetic field by 45 degrees.
Surface resistance
0
Rw
wfor
0
1sR
Complex signal processing at high frequencies > 1 GHz is difficult because the losses increase with frequency.
Usually you mix down to a lower frequency as soon as possible.
At low frequencies: 0
Rwt wt
When < t :
Superconducting filter
Complex signal processing at high frequencies > 1 GHz is difficult because the losses increase with frequency.
Simulation
Institute of Solid State PhysicsTechnische Universität Graz
Superconductivity
Primary characteristic: zero resistance at dc
There is a critical temperature Tc above which superconductivity disappears
About 1/3 of all metals are superconductors
Metals are usually superconductors OR magnetic, not both
Good conductors are bad superconductors
Kittel chapter 10
Superconductivity
Heike Kammerling-Onnes
Superconductivity was discovered in 1911
Critical temperature
Superconductivity
No measurable decay in current after 2.5 years. < 10-25 m.
Antiaromatic molecules are unstable and highly reactive
Meissner effect
Superconductors are perfect diamagnets at low fields. B = 0 inside a bulk superconductor.
Superconductors are used for magnetic shielding.
T >Tc T <Tc
SuperconductivityCritical temperature Tc
Critical current density Jc
Critical field Hc
2 2 210 2 22B c c c
mn nk T H nmv Jne