The discovery of
fluxoid quantization:
eo
or not
ot 2e
e
2e
Dietrich Einzel
W lth M iß
Walther-Meißner-Institut
I tit t für
fü Tieftemperaturforschung
Ti ft
t f
h
Bayerische Akademie der Wissenschaften
D-85748 Garching
g
R.Doll
M.Näbauer
•
•
•
•
•
Outline
B.S.Deaver
Theoretical insights: then and now
The Doll-Näbauer experiment
The Deaver-Fairbank
Deaver Fairbank experiment
The IBM conference 1961
Post 1961
W Fairbank
W.Fairbank
75th Annual Meeting 2011, DPG Spring Meeting, Condensed Matter Section, Dresden, March 13 – 18, 2011
Theoretical insights: then and now
Consider particles of mass km0 and charge ke:
condensate:
qm (bosonic)
wave function
charged bosons
fermion pairs
Madelung
representation
magnitude:
condensate
d
t
density
phase:
uniqueness
requirement
2
Theoretical insights: then and now
The condensate density ns(T)
off diagonal
off-diagonal
long-range
order
BCS 1957:
pairing
hypothesis
implies k=2
more
theories
for ns(T)/k
Gor‘kov, 1958
((near Tc)
Landau, Ginzburg
1950 ((near Tc)
London‘s
1935,, 1950
ns(T)
k
k
3
Theoretical insights: then and now
condensate
current density
d
i
canonical
momentum
gauge
invariance
Bohro
Sommerfeld
quantization
fluxoid
quantization
4
=hc/ke: what was known in 1961?
Nambu-Goldstone mode
1
BCS, 1957:
BCS
no prediction of
fluxoid quantization
2
Fritz London
1950: k=1
3
Lars Onsager
1959: kk=2
2
4
rumours
1960: k=N
N: number of particles
5
N Byers
B
&CNY
Yang
1961: k=2
p
pairing
g correlations
imply hc/2e periodicity
of the free energy
private communication with W. M. Fairbank
experimental
check
required!
5
The Doll-Näbauer experiment
1934 Walther Meißner accepts the chair of Technical Physics at the TU Munich
1943 WWII: Meißner‘s Institute moves to Herrsching/Ammersee into two barracks
1946 Walther Meißner founds the Commission of Low Temperature Research
(CLTR) iin th
the B
Bavarian
i A
Academy
d
off S
Sciences
i
d
during
i hi
his presidentship
id t hi 46
46-50
50
1949 Robert Doll joins the CLTR (diploma 1953, PhD 1959)
1951 Martin Näbauer joins the CLTR (diploma 1949, PhD 1955, VL 1958)
W. Meißner
1882-1974
The Herrsching barracks
(1943 - 1967)
M. Näbauer
1919-1962
R. Doll
(88 years)
6
The Doll-Näbauer experiment
1960 Doll and Näbauer start experiment to measure the fluxoid in a
(Pb) superconducting hollow cylinder in Herrsching (Meißner not involved!)
1961 April
Clear evidence for quantized flux, however, with 0=½ (hc/e)
June 15 Näbauer attends the IBM conference in Yorktown Heights
June 19 Submission to PRL by Robert Doll after considerable time delay
7
The Deaver-Fairbank experiment
1952 William Fairbank joins the Faculty of Physics at Duke University, Durham.
Collaboration with Fritz London on 3He Fermi
Fermi-Dirac
Dirac degeneracy temperature
temperature.
Idea of measuring the fluxoid quantum in superconductors.
1959 William Fairbank jjoins the Faculty
y of Physics
y
at Stanford University
y
(invited by Felix Bloch)
Bascom S. Deaver accepts Fairbank‘s offer to do his PhD work on the
measurement of quantized flux in a superconducting hollow cylinder
Fritz London
1900-1954
W.M. Fairbank
1917-1989
B.S. Deaver Jr.
(80 years)
8
The Deaver-Fairbank experiment
1960 Deaver starts his experiment to measure the fluxoid in a superconducting
hollow cylinder at Stanford
Stanford.
1961 May
Clear evidence for quantized flux, however, with 0=½ (hc/e).
June 15 Bill Little attends the IBM conference in Yorktown Heights.
June 16 Submission to PRL by Deaver and Fairbank.
9
The IBM conference, June 15 – 17, 1961
IBM Conference of Fundamental Research in
S
Superconductivity,
d ti it Yorktown
Y kt
Heights,
H i ht N.
N Y.
Y
June 14: Bill Little meets Martin Näbauer in his hotel room.
L.: „Is the flux quantized?“ („Ist der Fluss quantisiert?“)
N.: „Sure!“
(„Ja freilich ist er quantisiert!“)
June 15: Martin Näbauer presents a talk on the flux quantization
effect observed in Herrsching/Bavaria
Bill Little presents his own talk and afterwards shows
the data on the flux quantization effect observed by
Deaver and Fairbank in Stanford/California.
W.A. Little
(80 years)
After a heated discussion everybody in the audience is convinced that
k=2 is needed to understand both experimental data sets.
Little: „It
It came as a big surprise and some relief that both parties had
recognized the factor of two“
10
Post 1961
1962 Doll and Näbauer receive Awards from both the Academy of Sciences in
Munich and Göttingen
Göttingen. BA
BA-Medal
Medal „Bene
Bene Merenti“
Merenti for Robert Doll in 1986
1986.
1962 Martin Näbauer dies unexpectedly the day before signing the contract for a
professorship
p
p at the TU Munich.
1965 Bascom Deaver starts his career as a Professor at the University of Virginia.
1967 The CLTR moves from Herrsching to Garching (20 km north of Munich) and
is renamed 1982 into „Walther-Meißner Institute“ (WMI).
1988 Robert Doll retires, but continues to frequent the WMI almost daily, dealing
with various problems in physics, even theory (Ginzburg-Landau).
2000 Bascom Deaver receives various Awards for good teaching, such as the
George B.
B Pegram Award for „Excellence
Excellence in Teaching of Physics“
Physics .
2010 (May) Bascom Deaver retires, but continues to have his research lab at UVA.
(16 8 ) Bascom Deaver can celebrate his 80th birthday in the best of health
(16.8.)
health.
2011 (16.1.) Robert Doll can celebrate his 88th birthday in the best of health.
11
Summary: 50 years of fluxoid quantization
BCS theory (1957) has side aspects (fluxoid quantization), which have remained
unrecognized until as late as 1961.
Remarkable coincidences on the Bavarian and Californian side:
basic idea, starting time (around 1960), duration (until 1961), IBM conference, PRL
Complete agreement of both parties w
w.r.t.
r t fluxoid quantum showing the pair charge
charge.
Therefore Doll/Näbauer and Deaver/Fairbank should always be cited together.
The existence
Th
i t
off quantized
ti d flflux iin superconductors
d t
ranks
k as one off th
the mostt
exciting experimental discoveries of the last century.
R. Doll
M. Näbauer
B.S. Deaver Jr.
W.M. Fairbank
12
Appendix: Fritz London‘s footnote
The famous footnote in the book „Superfluids“ by Fritz London, 1950
A1
Appendix: The difference between flux and fluxoid
superconducting
p
g hollow
cylinder: trapped flux
differs from fluxoid
R
d
Hext
i
L
C
London-BCS magnetic
penetration depth
A2
Appendix: the energy gap (T)
Ginzburg-Landau regime
1
EX
k=5
k=1
k=2
low temperature limit
2(T)
2(0)
( )
interpolation procedure for (T)
0
0.1
T/T
/ c
1.0
A3
Appendix: the superfluid density ns(T)
Ginzburg-Landau regime
1
EX
k=1
k 5
k=5
k=2
low temperature limit
ns(T)
n
interpolation procedure for ns(T)
0
01
0.1
T/Tc
10
1.0
A4
Appendix: how to connect | with the BCS gap 
superfluid density
scaling behavior:  vs. near Tc
1
2(T)
2(0)
superrfluid den
nsity, gap
p
energy
gy g
gap
p
ns(T)
n
relative
deviation
0
0.1
T/T
/ c
1.0
A5
Appendix: BCS spin susceptibility, analytic results
BCS spin susceptibility
0.65
1
quasiparticle Yosida function
Ginzburg-Landau expansion
a/k
/ BT))2
low-T expansion:
b(kBT/, cexp(‐ /kBT)
a, bc known to all orders!
Yosida functtion
Y(T)/Yint(T)
Y(T)
Yint(T)
YLT(T)
Y‐Yint
Y
YGL(T)
0
0.1
T/Tc
T/T0
1.0
A6
Appendix: BCS energy gap and the -function
pair binding energy  
order parameter
‐
e
energy spectrum
develops gap 
superfluid
p
density
y
order parameter
‐
e
Ginzburg-Landau
A7
Appendix: On nonequilibrium superconductivity
Nambu
matrices
dynamics
y
in
phase space
gradients
collisions
von-Neuman equation
q
(integro-differential eq.)
external potentials
interactions, collective modes
integral
equations
order parameter dynamics:
gauge mode/collective modes
conservation vs. relaxation laws
elastic vs. inelastic scattering
observables
;
vertex
A8
Appendix: 2e or not 2e in the Doll-Näbauer experiment
A9
Appendix: Doll/Näbauer publication in Z. Physik
A10