The Centennial of Helium Liquefaction –
a Century of Low Temperature Physics*
Dietrich Einzel
Walther-Meißner-Institut für Tieftemperaturforschung
der Bayerischen Akademie der Wissenschaften
YE
AR
S
Outline
- Superconductivity
- Superfluidity of Bose- and Fermi liquids
J. Bardeen
10
0
- Helium liquefaction & cooling methods
- Theory
* 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
L. D. Landau
1
Pre-1908: Cooling attack on the „permanent gases“
1852
Discovery of the Joule-Thomson effect
James Prescott Joule [1818-1889]
Sir William Thomson [Lord Kelvin, 1824-1907]
Cooling of compressed gases by expansion (T<Ti):
Key concept on the way to absolute zero!
1877
First liquefaction of „permanent gases“ in small quantities
oxygen: Louis Paul Cailletet [1832-1913]
oxygen, nitrogen: Pierre Pictet [1846-1929]
J. P. Joule
Lord Kelvin
L. P. Cailletet
P. Pictet
2
Pre-1908: Cooling attack on the „permanent gases“
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 hydrogen
using the first thermos bottle („Dewar flask“)
and a cascade method: James Dewar [1842-1923]
Z. Wroblenski
S. Olszewski
C. v. Linde
J. Dewar
3
Heike Kamerlingh Onnes (HKO)
1853
HKO is born in Groningen (21. 9.)
1871 - 73 HKO student of Bunsen and Kirchhoff
in Heidelberg. „Seminarpreis“ entitles
him for assistantship under Kirchhoff.
1879
HKO receives PhD from the University of
Groningen
1882
HKO becomes Professor and Director of
the Laboratory in Leiden. Introductory
Lecture „Door meten tot weten“. Strong
exchange of ideas with Diderik van der
Waals.
1884
van der
Waals
Onnes
HKO becomes member of the Royal Academy of Sciences in
Amsterdam
4
Heike Kamerlingh Onnes (HKO)
1905
Breakthrough in Leiden: HKO receives considerable
quantities 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!
Beginning of Low Temperature Physics!
1911
HKO discovers vanishing resistance in mercury at 4.2 K,
later referred to as superconductivity!
1913
HKO receives the Physics Nobel Prize („For the
investigation of the properties of matter at low temperatures“)
1926
HKO dies at the age of 72 in Leiden (21. 2.)
5
Low Temperature Laboratories around the World
1908
1923
1925
1928
1930
1933
1934
1950
1957
1959
1962
1965
1967
Leiden
Toronto
Berlin
Kharkov
Cambridge
Oxford
Moscow
Tiflis
Manchester U.
Cornell U.
Grenoble
Otaniemi
Garching
Heike Kamerlingh Onnes
Sir John Cunningham McLennan, Jack Allen
Walther Meißner
Lev Shubnikov
Peter L. Kapitza
Kurt Mendelssohn, Franz Simon, Nicholas Kürti
Peter L. Kapitza
Elevter L. Andronikashvili
Eric Mendoza, Henry Hall, Joe Vinen et al.
John Reppy, Robert Richardson et al.
Louis Neel, Louis Weil
Olli Lounasmaa
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
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-Technische
Reichsanstalt (PTR) in Berlin-Carlottenburg
1925
WM builds up the third helium liquefier
worldwide at the PTR Berlin
W. Meißner
1928 - 34 Discovery of superconductivity in the
elements Ta, V, Ti and Nb
1933
Discovery of the magnetic field expulsion
effect in superconductors with R. Ochsenfeld
at the PTR in Berlin.
1934
WM accepts chair at the TH Munich.
R. Ochsenfeld
7
Walther Meißner (WM)
1946 – 50 WM Director of the Bavarian Academy of Sciences (BAS)
1946
Foundation of the Commission of Low Temperature Physics
of the BAS by WM and K. Clusius.
1952
Retirement of WM.
1954
WM receives the Federal Cross of Merits
1961
Discovery of fluxoid quantization by
R. Doll and M. Näbauer. Settles the
question „2e or not 2e?“
Independent discovery of the effect
by B. S. Deaver and W. M. Fairbank
1974
WM dies at the age of 91 in Munich
R. Doll (85 years)
8
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. Gorter
realized 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
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
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
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<Tλ) are coined by
Keesom and Wolfke in Leiden.
1930
Keesom and van der Ende discover flow of He-II through
small slits (superleaks) in Leiden
1935
Wilhelm, Misener and Clark measure viscosity drop below
Tλ in the viscosity of He-II in Toronto.
1937
Vanishing shear viscosity in He-II in capillary flow experiment
by Allen and Misener in Cambridge and Kapitza in Moscow.
Publication in Nature 141.
1978
Physics Nobel Prize for Kapitza.
12
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 properties
textures and topological defects
transport 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
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; …]
superfluid density ns: (1) continity equation
∂ns
s
+∇·j =0
∂t
supercurrent density
¶
µ
e
~
s
s s ; vs = 1
∇ϕ − A
j =n v
m k
c
superfluid density = k|ψ|2=k|a|2
(macroscopic wave function ψ=a.eiϕ)
k=
1
2
2
; He-II
; superconductors
; 3He-A,-B
14
Superconductivity and superfluidity in a nutshell
(2) Hamilton-Jacobi equation (quasiclassical limit)
~ ∂ϕ
m s2
−
= eΦ + µ + v + . . .
k ∂t
2
Nota bene: Schrödinger equation for the macroscopic wave function ψ
equivalent to continuity eq. (1) and Hamilton-Jacobi eq. (2)
condensate acceleration: Euler equation
µ
¶
s
v
dv
=e E+
× B − ∇µ
m
dt
c
s
15
Superconductivity and superfluidity in a nutshell
consequences from (1) and (2):
persistent currents
ns
eB
∂js
s
=
(eE − ∇µ) + j ×
∂t
m
mc
screening and magnetic
penetration depth
2
mc
λ2L =
4πns e2
Fluxoid quantization [London, 1950; Byers & Yang, 1961;…]
Z
´
hc
mc
0
s
Φ =
dS · B + s 2 ∇ × j = n
= nΦ0
ne
ke
S
|{z}
³
≡Φ0
16
Superconductivity and superfluidity in a nutshell
Microscopic two-fluid description: thermal excitations (quasiparticles)
[Tisza, 1938; Landau, 1947; Feynman, 1955; BCS, 1957; Bogoliubov, 1957]
quasiparticle
energy
dispersion
quasiparticle
statistics
quasiparticle
drift velocity
⎧
⎪
c|p|
; phonons
⎪
⎪
⎪
⎪
⎪
He-II
⎪
⎨
2
(|p|−p0 )
; rotons
∆
+
Ep =
2m r
⎪
⎪
⎪
⎪
q
⎪
⎪
⎪
⎩ ξ 2 + ∆p · ∆†p ; bogolons
p
nθp
=
exp
vn (r, t)
³
1
Ep
kB T
´
−θ
⎧
⎪
⎨1
⎪
⎩
; Bose
−1 ; Fermi
17
Superconductivity and superfluidity in a nutshell
Microscopic two-fluid description: total current density
tot
ji
=
s s
nij vj
n n
nij vj
+
thermal excitations
condensate
Normal fluid density tensor
X pi pj
2s
+
1
nnij =
V
m
p
Ã
∂nθp
−
∂Ep
!
Superfluid density tensor
nsij
= nδij −
„diamagnetic“
n T →Tc
nij =
0
„paramagnetic“
18
Superconductivity and superfluidity in a nutshell
Example for theoretical results: gap symmetries proposed for UPt3
singlet
triplet
singlet
triplet
19
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 processing
20