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

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

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

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

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

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

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

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

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

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

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

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

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

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

16

consequences from (1) and (2):

persistent currents

screening and magneticpenetration depth

∂js

∂t=ns

m(eE−∇µ) + js × eB

mc

λ2L =mc2

4πnse2

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

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

Superconductivity and superfluidity in a nutshell

Example for theoretical results: gap symmetries proposed for UPt3

singlet

triplet

triplet

singlet

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 processing20

Pre-1908: Cooling attack on the „permanent gases“Walther Meißner (WM)Walther Meißner (WM)Improved Cooling MethodsSuperconductivity: then and nowBose superfluid 4He