100 lat fizyki niskich temperatur i nadprzewodnictwa

100 lat fizyki niskich
temperatur i
nadprzewodnictwa
Tadeusz Wasiutyński
IFJ PAN
9 maja 2013
Wstep
˛
teoria BCS
teoria Ginzburga Landaua
nowe nadprzewodniki wysokotemperaturowe
co z tego mamy
Heike Kamerlingh Onnes(1853–1926)
1913 nagroda Nobla "for his
investigations on the properties of
matter at low temperatures which led,
inter alia, to the production of liquid
helium"
Heike Kamerlingh Onnes(1853–1926)
1913 nagroda Nobla
1908 skroplenie helu
Heike Kamerlingh Onnes(1853–1926)
1913 nagroda Nobla
1908 skroplenie helu
1911 odkrycie nadprzewodnictwa
Heike Kamerlingh Onnes(1853–1926)
1913 nagroda Nobla
1908 skroplenie helu
1911 odkrycie nadprzewodnictwa
pierwsze cztery dekady
1931 nadprzewodnictwo w stopie (de Haas i Keesom)
1933 efekt Meissnera (Meissner i Ochsenfield)
1935 Fritz i Heinz London zapostulowali:
~j = − 1 A
~
λ2L
~ =
∇2 B
1~
B
λ2L
λL =
m 1/2
e
µ0 ns e2
teorie Bloch, Einstein, Bohr, Brillouin, Born, Feynmann
...
John Bardeen
John Bardeen
oddziaływanie elektron-fonon
• efekt izotopowy
• H. Fröhlich Phys. Rev
(1950):
• Leon Cooper Phys. Rev
(1956): Bound electron
Pairs in a Degenerate
Fermi Gas
oddziaływanie elektron-fonon
• efekt izotopowy
• H. Fröhlich Phys. Rev
(1950):
• Leon Cooper Phys. Rev
(1956): Bound electron
Pairs in a Degenerate
Fermi Gas
φ(k~1 , k~2 ; r~1 , r~2 ) =
1 i(k~1 ·r~1 +k~2 ·r~2 )
e
V
~ = k~1 +k~2 , ~k = (k~2 −k~1 )/2
~r = r~2 −r~1 , K
oddziaływanie elektron-fonon
• efekt izotopowy
• H. Fröhlich Phys. Rev
(1950):
φ(k~1 , k~2 ; r~1 , r~2 ) =
~ = k~1 +k~2 , ~k = (k~2 −k~1 )/2
~r = r~2 −r~1 , K
Z
χ(r , K ) =
• Leon Cooper Phys. Rev
(1956): Bound electron
Pairs in a Degenerate
Fermi Gas
1 i(k~1 ·r~1 +k~2 ·r~2 )
e
V
~
ei k ·~r N(K , (k )) d ~
dk
EK + (k ) − E dk
oddziaływanie elektron-fonon
• efekt izotopowy
• H. Fröhlich Phys. Rev
(1950):
φ(k~1 , k~2 ; r~1 , r~2 ) =
1 i(k~1 ·r~1 +k~2 ·r~2 )
e
V
~ = k~1 +k~2 , ~k = (k~2 −k~1 )/2
~r = r~2 −r~1 , K
Z
χ(r , K ) =
E F − ωD
~
ei k ·~r N(K , (k )) d ~
dk
EK + (k ) − E dk
k↑
E F + ωD
• Leon Cooper Phys. Rev
(1956): Bound electron
Pairs in a Degenerate
Fermi Gas
-k ↓
EF
Bardeen, Cooper, Schriefer
Phys. Rev. (1957)
2
)
V ρ(EF )
T 1/2
∆(T )
= 1.74 1 −
∆(0)
Tc
∆ = 2}ωD exp(−
Tc ≈ 0.57∆(0)
teoria Ginzburga Landaua
Zh. Eksper. Theor. Fiz. 1950
• przejście fazowe jest ciagłe
˛
• parametr porzadku
˛
zależy od pola magnetycznego
• parametr porzadku
˛
jest liczba˛ zespolona:
˛
ψ(~r ) = |ψ(~r )|eiθ(~r ) =
q
ñs (~r )eiθ(~r )
teoria Ginzburga Landaua
Zh. Eksper. Theor. Fiz. 1950
• przejście fazowe jest ciagłe
˛
• parametr porzadku
˛
zależy od pola magnetycznego
• parametr porzadku
˛
jest liczba˛ zespolona:
˛
ψ(~r ) = |ψ(~r )|eiθ(~r ) =
f = f0 +
q
ñs (~r )eiθ(~r )
1
2
~
|(−i~∇ − q A)ψ|
+ a(T − Tc )|ψ|2 + 2b|ψ|4
2m∗
teoria Ginzburga Landaua
Zh. Eksper. Theor. Fiz. 1950
• przejście fazowe jest ciagłe
˛
• parametr porzadku
˛
zależy od pola magnetycznego
• parametr porzadku
˛
jest liczba˛ zespolona:
˛
ψ(~r ) = |ψ(~r )|eiθ(~r ) =
f = f0 +
q
ñs (~r )eiθ(~r )
1
2
~
|(−i~∇ − q A)ψ|
+ a(T − Tc )|ψ|2 + 2b|ψ|4
2m∗
i
h 1
~ 2 + a(T − Tc ) + 2b|ψ|2 ψ = 0
(−i~∇
−
q
A)
2m∗
2
~j = − iq~ (ψ ∗ ∇ψ − ψ∇ψ ∗ ) − q |ψ|2 A
~
2m∗
m∗
kwantowanie strumienia magnetycznego
2
2
~j = −( e~ ∇θ + 2e A)|Ψ|
~
m
mc
|Φ| = n
hc
= nΦ0
2e
SQUID:
złacze
˛
Josephsona:
j = j0 sin(θ1 − θ2 )
j0 = e~ns Ke
−Kd
j = j0 sin δ1 +j0 sin δ2 = j̃ cos(δ1 −δ2 )
δ1 − δ2 = 2π
Φ
Φ0
In the 100 years since the discovery of superconductivity, progress has come in fits and starts. The graphic below shows various types of superconductor
sprouting into existence, from the conventional superconductors to the rise of the copper oxides, as well as the organics and the most recently
discovered iron oxides. Experimental progress has relied on fortuitous guesses, while it was not until 1957 that theorists were finally able to explain
how current can flow indefinitely and a magnetic field can be expelled. The idea that the theory was solved was overturned in 1986 with the discovery
of materials that superconduct above the perceived theoretical limit, leaving theorists scratching their heads to this day. In this timeline, Physics World
charts the key events, the rise in record transition temperatures and the Nobel Prizes for Physics awarded for progress in superconductivity.
1987
Paul Chu and his team break the 77 K liquidnitrogen barrier and discover superconductivity at
93 K in a compound containing yttrium, barium,
copper and oxygen, now known as “YBCO”
140
120
superconducting transition temperature, Tc (K)
100
1908 and 1911
Heike Kamerlingh Onnes wins
the race against James Dewar
to liquefy helium (1908), then
discovers zero resistance in
mercury with Gilles Holst (1911)
1987
Georg Bednorz
Alexander Müller
1957
JohnBardeen,
Bardeen,Leon
LeonCooper
Cooperand
andRobert
Robert
John
Schriefferpublish
publishtheir
their(BCS)
(BCS)theory,
theory,which
which
Schrieffer
builds
buildson
onthe
theidea
ideaofofCooper
Cooperpairs
pairsproposed
proposed
the
theprevious
previousyear,
year,and
anddescribes
describesall
allthe
the
electronstogether
togetheras
asone
onewavefunction.
wavefunction.
electrons
Thetheory
theorypredicts
predictsthat
thatsuperconductivity
superconductivity
The
cannot
cannotoccur
occurmuch
muchabove
above20
20KK
1931
Wander Johannes de Haas and
Willem Keesom discover
superconductivity in an alloy
1973
Brian Josephson
1972
John Bardeen
Leon Cooper
Robert Schrieffer
80
60
T > Tc
40
20
1910
T < Tc
1920
1930
1940
boiling point of
liquid nitrogen
1962
Lev Landau
1933
Walther Meissner and Robert
Ochsenfeld discover that
magnetic fields are expelled
from superconductors. This
“Meissner effect” means
that superconductors can be
levitated above magnets
1962
Brian Josephson predicts
that a current will pass
between two superconductors
separated by an insulating
barrier. Two of these
“Josephson junctions”
wired in parallel form a
superconducting quantum
interference device (SQUID)
that can measure very weak
magnetic fields
1935
Brothers Fritz and Heinz
London make a long-awaited
theory breakthrough,
formulating two equations
that try to describe how
superconductors interact with
electromagnetic fields
1913
Heike Kamerlingh Onnes
0
1900
2003
Alexei Abrikosov
Vitaly Ginzburg
2006
Hideo Hosono and colleagues
discover superconductivity
in an iron compound. The
highest Tc found in these
materials to date is 55 K
2001
Jun Akimitsu announces that
the cheap and simple chemical
magnesium diboride (MgB2)
superconducts up to 39 K
1986
Georg Bednorz (right) and Alexander
Müller (left) find superconductivity at
30 K, over the 20 K limit of BCS theory,
and not in a metal, but a ceramic
1981
Superconductivity is found by Klaus
Bechgaard and colleagues in a
salt – the first organic material to
superconduct at ambient pressure. To
date the organic superconductor with
the highest Tc is Cs 3C60 at 38 K
1950
1960
1970
1980
1990
2000
2010
Image credit s (lef t to right): Physics Today Collection/American Institute of Physics/Science Photo Librar y; Wikimedia Commons; Eye of Science/Science Photo Librar y; Univer sity of Birmingham Consor tium on High T c Superconductor s/
Science Photo Librar y; Y Kohsaka/Cornell Univer sity/RIKEN; Emilio Segrè Visual Archives/American Institute of Physics/Science Photo Librar y; Supercond. Sci. Technol. 21 125028
Superconductivity at 100