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Superconductivity—a brief introduction


Reductionism vs. “more is different” 2 different paradigms for physics

• search for smaller and smaller entities • huge machines, 1000’s of scientists

• search for fundamentally new states of matter consisting of many particles • tabletop experiments, small groups


Heike Kammerling Onnes (1911)

Discovery of superconductivity in Hg


Many elements are superconductors


•Search for an understanding of superconductivity: series of failures and a success

- During 46 years, from 1911 to 1957, superconductivity remains a mystery

- Around 1950 it’s recognized as one of the most important problems in

theoretical physics - Richard Feynman:

Conventional superconductors

“No one is brilliant enough to figure it out”


• BCS theory (1957)

John Bardeen*

Leon Cooper

Robert Schrieffer

Nobel prize : 1972

Quantum mechanical behavior at the macroscopic scale

*John Bardeen : the only person to receive two Nobel prizes in physics!

Conventional superconductors


- -

Understanding the BCS idea: Ingredient #1

Attraction & formation of Cooper pairs


+

+ +

+

+

+ + + + + + + + + + + + + +

+ + + + + + + + + + + + + - - - - - - -

+ + + + + + + + + + + + + + + +

+ + + + + + + + + + + + + + + +

How Cooper pairs form Prelude to superconductivity


χ = -1 Perfect screening (Meissner effect)


No animals were harmed during this

experiment!


More practical application:

sumo wrestler levitation


Levitation, the movie

http://www.youtube.com/watch?v=Ws6AAhTw7RA


High temperature superconductivity

Alex Müller and Georg Bednorz

Z. Physik, June 1986


BCS Theory

Low temperature BCS

Cuprates non-BCS

Bednorz and Müller

Fe-based ?

Superconductivity timeline


Hg1Ba2Ca2Cu3O8

Tc = 135 K under pressure: 153 K

A. Schilling, M. Cantoni, J. Guo, H.R. Ott, Nature 363, 56 (1993)

M.S. Kim

Hg

Ba

interstitial O

Ca

Cu/O

Cuprate high-Tc superconductors


Iron-based superconductors



• Rotter et al. arXiv: PRL (2008)

• Ni et al Phys. Rev. B 2008 (single xtals)

• Kamihara et al JACS (2008) •Ren et al

Chin. Phys. Lett. (2008)

Wang et al

Sol. St. Comm. 2008

Tc=18K Tc=38K Tc=28K

(55K for Sm)

Tc=8K

Hsu et al

PNAS 2008

No arsenic !



• Rotter et al. PRL (2008)

• Ni et al Phys. Rev. B 2008 (single xtals)

• Kamihara et al JACS (2008) •Ren et al

Chin. Phys. Lett. (2008)

Wang et al Sol. St. Comm. 2008

Tc=18K Tc=38K Tc=28K

(55K for Sm)

Tc=8K

Hsu et al PNAS 2008

No arsenic !

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Superconductivity: Theory

BCS: Phonon mediated pairing Phonon

Cooper pair

Electron

Ground state of a superconductor


Superconductivity: High Tc

Cooper pair

Electron What is the ”glue”?


Cooper pairs

Superconductivity: Ground state


Cooper pairs

quasiparticle

Superconductivity: excited state


Normal State

Normal State (Metal)

KK

K

FX

Y

Degenerate ~free electron gas

Fermi Surface


Normal State (Metal) Low Temp. Cooper Pairing

L=0 S=0

KK

K

FX

Y

|k> |-k>

Degenerate ~free electron gas

SC Ground State



L=0 S=0

KK

K

FX

Y

KK

K

FX

Y

|k> |-k>

Superconducting Ground State

~ Gas of Cooper Pairs Degenerate ~free electron gas

SC Ground State



s-wave Ψ symmetry

Macro. Quantum State

Ψ ~ ∆0eiφ

L=0 S=0

KK

K

FX

Y

KK

K

FX

Y

|k> |-k>

( ) >+=Ψ ∏ ∗↓−

∗↑ 0|

kkkkkBCS ccvu

Superconducting Ground State

~ Gas of Cooper Pairs Degenerate ~free electron gas

SC Ground State


SC Ground State: Cooper Pairs

k

x

k y


SC Excited States: Bogoliubov Quasiparticles

k

x

k y


SC Excited States: Quasiparticles

k

x

k y

No QP

States

∆ E F

E

density of states

−∆

Energy Gap

Study with quantum tunneling!


- -

+ -

Type s (L=0)

Type p (L=1)

Type d (L=2)

Types of 2-electron Cooper pair wavefunctions

These wave functions for 2 electrons have shapes similar to atomic 1-electron wavefunctions (see Hydrogen atom)

- +

+ +

-

-


Cuprates

Unconventional Superconductors


Gap magnitude vs. k

density of states for a dx2-y

2 Superconductor

d-wave

s-wave

node


US:

Energy transported in powerlines per year: ~ 3*1012 kWh

Use of high-Tc cables and transformers:

• reduction of transmission and distribution losses: ~ 6*1010 kWh / year

• emissions avoided: 100 000 t NOx 200 000 t SOx 30 000 000 t CO2

R. D. Blaughter, Research and Innovation, Siemens, Vol. 1/ 98, March 1998

Potential applications of HTS: power transmission


transmission lines

BiSrCaCuO

Ag


MAGLEV


Magnetic resonance imaging (MRI)

Research: 1) higher fields 2) detection of weak fields (SQUID)


Conclusions

Challenges for superconductivity physics: • find materials with Tc>200K, then room T! • make devices, wires for power transmission

and magnets • Hirschfeld group: understand how the #$!@%$! things work!


Superconductivity in the popular imagination c. 1987

Television show, “MacGyver”

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