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Dietrich EinzelWalther-Meißner-Institut für
Tieftemperaturforschung
der Bayerischen Akademie der Wissenschaften
The Centennial of Helium Liquefaction –
a Century of Low Temperature Physics*
Outline
- Helium liquefaction & cooling methods- Superconductivity-
Superfluidity of Bose- and Fermi liquids- Theory
J. Bardeen
L. D. Landau10
0 YEA
RS
* Presented as an Invited Talk at the 72nd Annual Meeting 2008
and the DPG Spring Meeting of the Condensed Matter Section, Berlin,
February 25 – 29, 2008 1
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1852 Discovery of the Joule-Thomson effectJames Prescott Joule
[1818-1889]Sir William Thomson [Lord Kelvin, 1824-1907]Cooling of
compressed gases by expansion (T
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1883 First liquefaction of N2- and O2- gas in substantial
quantities: Zygmunt Florenty Wroblenski [1845-1888]Stanislav
Olszewski [1846-1915]
1895 First liquefaction of air: Carl von Linde [1842-1934]
1898 First liquefaction of gaseous hydrogenusing the first
thermos bottle („Dewar flask“) and a cascade method: James Dewar
[1842-1923]
Pre-1908: Cooling attack on the „permanent gases“
Z. Wroblenski S. Olszewski C. v. Linde J. Dewar3
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Heike Kamerlingh Onnes (HKO)
1853 HKO is born in Groningen (21. 9.)
1871 - 73 HKO student of Bunsen and Kirchhoffin Heidelberg.
„Seminarpreis“ entitleshim for assistantship under Kirchhoff.
1879 HKO receives PhD from the University of Groningen
1882 HKO becomes Professor and Director of the Laboratory in
Leiden. IntroductoryLecture „Door meten tot weten“. Strongexchange
of ideas with Diderik van der Waals.
1884 HKO becomes member of the Royal Academy of Sciences in
Amsterdam
Onnes
van der Waals
4
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Heike Kamerlingh Onnes (HKO)
1905 Breakthrough in Leiden: HKO receives considerablequantities
of monazite (rare earth phosphate) -sand from US gravel pits
1908 July 10: HKO liquefies helium successfully for the first
time after careful theoretical estimates. Temperatures down to 1 K
are reached!
1911 HKO discovers vanishing resistance in mercury at 4.2 K,
later referred to as superconductivity!
1913 HKO receives the Physics Nobel Prize („For theinvestigation
of the properties of matter at low temperatures“)
1926 HKO dies at the age of 72 in Leiden (21. 2.)
Beginning of Low Temperature Physics!
5
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Low Temperature Laboratories around the World
1908 Leiden Heike Kamerlingh Onnes1923 Toronto Sir John
Cunningham McLennan, Jack Allen 1925 Berlin Walther Meißner 1928
Kharkov Lev Shubnikov1930 Cambridge Peter L. Kapitza1933 Oxford
Kurt Mendelssohn, Franz Simon, Nicholas Kürti1934 Moscow Peter L.
Kapitza1950 Tiflis Elevter L. Andronikashvili1957 Manchester U.
Eric Mendoza, Henry Hall, Joe Vinen et al. 1959 Cornell U. John
Reppy, Robert Richardson et al.1962 Grenoble Louis Neel, Louis
Weil1965 Otaniemi Olli Lounasmaa1967 Garching F. X. Eder, W.
Wiedemann, G. Eska et al.
Low Temperature Labs founded more recently: Bayreuth , Berkeley,
Berlin, Brown Univ., Eindhoven, U. Florida, Harvard, Illinois,
Karlsruhe, Konstanz, Lancaster , Madrid, MIT, Northwestern U., Ohio
State, Pohang, Prag, Royal Holloway, Stanford, Tata, Tokyo, Twente,
Yale, …
6
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Walther Meißner (WM)
1882 WM is born in Berlin
1907 WM receives his PhD at the Univ. of Berlin with Max
Planck.
1908 WM enters the Physikalisch-TechnischeReichsanstalt (PTR) in
Berlin-Carlottenburg
1925 WM builds up the third helium liquefierworldwide at the PTR
Berlin
1928 - 34 Discovery of superconductivity in theelements Ta, V,
Ti and Nb
1933 Discovery of the magnetic field expulsioneffect in
superconductors with R. Ochsenfeldat the PTR in Berlin.
1934 WM accepts chair at the TH Munich.
W. Meißner
7R. Ochsenfeld
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Walther Meißner (WM)
1946 – 50 WM Director of the Bavarian Academy of Sciences
(BAS)
1946 Foundation of the Commission of Low Temperature Physicsof
the BAS by WM and K. Clusius.
1952 Retirement of WM.
1954 WM receives the Federal Cross of Merits
1961 Discovery of fluxoid quantization byR. Doll and M. Näbauer.
Settles thequestion „2e or not 2e?“Independent discovery of the
effectby B. S. Deaver and W. M. Fairbank
1974 WM dies at the age of 91 in Munich R. Doll (85 years)8
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Improved Cooling Methods
1926 Adiabatic demagnetization of paramagnetic salts(minimum
temperature: 0.002 K)proposed by Peter Debye [1926] and William
Francis Giauque [1927, Chemistry Nobel Prize, 1949]
1956 Nuclear cooling (minimum temperature: 12 µK … 1 nK)proposed
1934 by C. J. Gorterrealized 1956 by N. Kürti and 1970 by O.
Lounasmaa
1962 Dilution of liquid 3He with 4He (dilution
refrigerator)(minimum temperature: 2.3 mK)proposed by Heinz London
[1907-1970]realized by Hall/Noganov [1966]
1995 Laser cooling (minimum temperatures < 1 nK) proposed
1975: T. Hänsch, A. Schawlov, C. Cohen-Tannouji.realized 1995: S.
Chu, W. Phillips
1995 Observation of BEC in Na, Rb Gas: E. Cornell, W. Ketterle,
C. Wiemann, Physics Nobel Prize, 2001
9
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Superconductivity: then and now
1911 (1913) Discovery of superconductivity in Hg in Leiden
[HKO]
1933 Field expulsion effect [Meißner, Ochsenfeld] (75
years!)
1934 Prediction of type-II superconductivity (vortices)
[Shubnikov]
1935 First phenomenological theory [F. and H. London]
1946 Evidence for an energy gap [Daunt & Mendelssohn]
1950 (2003) Second phenomenological theory [Ginzburg &
Landau]
1954 Superconductivity in A15 compounds [Hulm & Matthias;
Geballe, Gavaler, ...]
1957 (1972) BCS theory [Bardeen, Cooper & Schrieffer]
1957 (2003) Prediction of flux line lattice [Abrikosov]10
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Superconductivity: then and now (ctd.)
1960 (1973) Quasiparticle tunneling [Giaever]
1961 Fluxoid Quantization [Doll, Näbauer/Deaver, Fairbank]
1962 (1973) Josephson (CP) tunneling [Josephson]
1968 Discovery of flux-line lattice (type-II sc) [Essmann,
Träuble]
1979 Superconductivity in heavy electron compounds
[Steglich,...]
1980 Organic superconductors [Bechgaard, …]
1986 (1987) High-Tc superconductivity in cuprates [Bednorz,
Müller]
1994 Spin-triplet superconductivity in Sr2RuO4 [Maeno et
al.]
2001 High-Tc superconductivity in MgB2 [J. Akimitsu et al.]
11
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Bose superfluid 4He
1910 HKO discovers density maximum in liquid 4He at 2.2 K.
1923 λ- shaped specific heat anomaly of liquid 4He at Tλ=2.2 K
by HKO and Dana in Leiden
1924 Prediction of BEC by Bose & Einstein
1927 The terms He-I (T>Tλ) and He-II (T
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Fermi superfluid 3He
1971 Discovery of new (A- and B-) superfluid phases 3He at 2 mK
[D. Lee, D. Osheroff and R. Richardson, Nobel Prize 1996]
1971 Identification of superfluid as condensate of Cooper pairs
in a relative spin-triplet p-wave state [A. J. Leggett, Nobel Prize
2003]
1990 „The Superfluid Phases of Helium Three“ (theory)D.
Vollhardt and P. Wölfle
„Helium Three“ (experiment)E. R. Dobbs
exotic NMR propertiestextures and topological defectstransport
properties of a clean dilute excitation (bogolon) gas order
parameter (massive) collective modes
after 1973: superfluid 3He in rotation (Helsinki, Manchester,
…)after 1994: dirty superfluid 3He: silica aerogel as impurity
system
13
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Superconductivity and superfluidity in a nutshell
(Gauge-invariant) supercurrent [London, 1935; von Laue, 1938;
Ginzburg & Landau, 1950; BCS, 1957; Gross & Pitaevskii,
1961; Eilenberger, 1968; Betbeder-Matibet & Nozieres, 1969;
Wölfle, 1976; …]
k = 1 ; He-II2 ; superconductors2 ; 3He-A,-B
;
superfluid density = k|ψ|2=k|a|2(macroscopic wave function
ψ=a.eiϕ)
vs =1
m
µ~k∇ϕ − e
cA
¶js = nsvs
14
superfluid density ns: (1) continity equation
supercurrent density
∂ns
∂t+∇ · js = 0
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Superconductivity and superfluidity in a nutshell
15
(2) Hamilton-Jacobi equation (quasiclassical limit)
condensate acceleration: Euler equation
−~k
∂ϕ
∂t= eΦ+ µ+
m
2vs2 + . . .
Nota bene: Schrödinger equation for the macroscopic wave
function ψequivalent to continuity eq. (1) and Hamilton-Jacobi eq.
(2)
mdvs
dt= e
µE+
vs
c×B
¶−∇µ
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Superconductivity and superfluidity in a nutshell
Fluxoid quantization [London, 1950; Byers & Yang,
1961;…]
Φ0 =
ZS
dS ·³B +
mc
nse2∇ × js
´= n
hc
ke|{z}≡Φ0
= nΦ0
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consequences from (1) and (2):
persistent currents
screening and magneticpenetration depth
∂js
∂t=ns
m(eE−∇µ) + js × eB
mc
λ2L =mc2
4πnse2
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Superconductivity and superfluidity in a nutshell
Microscopic two-fluid description: thermal excitations
(quasiparticles) [Tisza, 1938; Landau, 1947; Feynman, 1955; BCS,
1957; Bogoliubov, 1957]
quasiparticleenergydispersion
quasiparticlestatistics
He-II
quasiparticledrift velocity
⎧⎪⎨⎪⎩1 ; Bose
−1 ; Fermivn(r, t)
Ep =
⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩
c|p| ; phonons
∆+ (|p|−p0)2
2mr; rotons
qξ2p +∆p ·∆†p ; bogolons
nθp =1
exp³EpkBT
´− θ
17
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Superconductivity and superfluidity in a nutshell
Microscopic two-fluid description: total current density
condensate thermal excitations
Normal fluid density tensor
Superfluid density tensor
„diamagnetic“ „paramagnetic“
nnij =2s+ 1
V
Xp
pipjm
Ã− ∂n
θp
∂Ep
!
nsij = nδij − nnijT→Tc= 0
18
jtoti = nsijv
sj + n
nijv
nj
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Superconductivity and superfluidity in a nutshell
Example for theoretical results: gap symmetries proposed for
UPt3
singlet
triplet
triplet
singlet
19
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Summary and conclusion
Topics in low temperature physics during the last century
Conventional superconductivity / superconducting magnets
Superfluidity of He-II / Critical phenomena in He-II
Superfluidity of liquid 3He / implications to other systems
Unconventional superconductivity
Dirty Bose and Fermi superfluids
BEC / pairing correlations in Fermi gases (optical lattices)
Tunneling systems
Strongly correlated electrons and magnetism
Fractional Quantum Hall effect
Quantum coherence in mesoscopic and nanoscopic systems
Spin electronics
Quantum information processing20
Pre-1908: Cooling attack on the „permanent gases“Walther Meißner
(WM)Walther Meißner (WM)Improved Cooling MethodsSuperconductivity:
then and nowBose superfluid 4He