The Nobel Prize in Physics 2003
The Nobel Prize in Physics 2003
Gianni Blatter
Vadim Geshkenbein
Theoretische Physik
ETH Zurich
Switzerland
The GinzburgLandau Theory
he phenomenology of condensed quantum liquids has been T the winning theme in last year's Nobel competitionAlexei A. Abrikosov (Argonne National Laboratory), Vitaly 1. Ginzburg (Lebedev Institute in Moscow), and Anthony J. Leggett (University of Illinois at Urbana) share the 2003 Nobel prize in physics for their "pioneering contributions to the theory of superconductors and superfluidity:' Their names are added to the illustrious list of Nobellaureates in the field oflow temperature physics. Superconductivity/fluidity has always been the most glamorous topic in condensed matter physics. The milestones characterizing the field start with the discovery of superconductivity in mercury by Kamerlingh Onnes in 1911. In 1938, the superfluid phase of 4He was found by Kapitsa in Moscow and independently by Alien and Misener in Cambridge. Since metallic mercury transports electric current free of dissipation the original name 'super conductor' stuck; liquid He is uncharged and hence the dissipationfree mass flow is termed superfluidity. While the superfluid properties ofbosonic 4He were quickly understood in terms of a condensation into a macroscopic quantum state (Landau, 1941), the microscopic origin of superconductivity remained a puzzle over haif a century, uIltil Bardeel1, Cooper, and Schrieffer (1957) proposed a pairing mechanism allowing bound fermions to condense. This paved the way for the theoretical prediction that fermionic 3He should become superfluid as well, but it took another decade until Lee, Osheroff, and Richardson observed the superfluid phases of 3He in 1972. The unexpected discovery of hightemperature superconductors by Bednorz and Miiller in 1986 defined the most prominent research direction in condensed matter physics for the decade to follow. Last year the spectacular insights that follow from phenomenological theories have been properly recognized.

Upon cooling to sufficiently low temperatures, electrons or atoms
must lose entropy and organize themselves into a more ordered
state. In doing so, the system undergoes a reduction of symmetry,
the central idea of Landau's phenomenological theory of phase
transitions dating back to 1937. The symmetry breaking is cap
tured by an order parameter, whose nature is most obvious in a
ferromagnet where it quantifies the material's magnetization. Also,
the idea of BoseEinstein condensation into a macroscopically
occupied quantum state suggests a superfluid order parameter in
the form of a complex wave function 'P. Because of the Pauli prin
ciple, it remained completely unclear, however, what could be a
proper order parameter for the fermionic electron system in a
superconducting metal and it required the remarkable intuition of
Ginzburg and Landau to propose an order parameter in the form
of a complex electronic wavefunction 'P = vP exp(itp). The
GinzburgLandau free energy functional, which they constructed
based on this order parameter set the foundation for the complete
phenomenological understanding of superconducting materials.
Quite astonishingly, the rich phenomenology of the supercon
ducting state could be quantitatively described without knowledge
ofthe underlying microscopic mechanism responsible for the con
densation in the first place. Early work of Gorter, Casimir, and the
London brothers, explained numerous thermodynamic and elec
tromagnetic aspects ofthe superconducting state. In particular, the
London equation relating the superconducting current js to the
vector potential A via the superconducting density ps, js = PsA,
properly explained the MeissnerOchsenfeld effect, the complete
expulsion of a magnetic field from the interior ofa superconductor.
However, discrepancies with experiment remained, particularly in
films subject to a parallel magnetic field where the expression for
the critical field Hell destroying superconductivity failed. Further
more, the London theory was unable to provide a positive surface
energy for the superconductingnormal interface, hence a basic
ingredient to Landau's intermediate state (1937) remained unex
plained. These practical shortcomings were overcome in the 1950
paper of Ginzburg and Landau. In setting up their famous energy
functional they allowed for the presence of a magnetic field. The
minimal gauge invariant coupling I(ihV(e/c)A)'¥12 led them to
the subtle remark that'e is a charge, which there is no reason to
consider as different from the electronic charge', thus accepting
the possibility that it may take a different value. The ability to incor
porate variations in the ,¥field due to boundary conditions,
external magnetic fields, and currents, allowed them to remedy
the deficiencies of the London theory. With the GinzburgLandau
energy functional, the vector potential A(r) properly described
within the London theory got its partner field, the macroscopic
wave function 'P(r), thus providing the complete phenomenologi
cal description of a charged quantum fluid. However, it still
required Gorkov's derivation from the microscopic BCS theory
(1959) until the GinzburgLandau equations acquired their defin
itive status with an effective charge 2e.
Viith the appearance of a secoIlli (~) lldJ a Hew dimensionless
parameter comparing the relative 'stiffness' of the two fields enters
the theory: the GinzburgLandau parameter IC= ').J~ measures the
ratio in lengths associated with changes in the electromagnetic
response (the London penetration depth A) and in the supercon
ducting density (the coherence length ~). The limiting value
IC= 1IV2separating superconductors with positive surface energy
(IC < ltV2) from those with negative surface energy at large
IC> 11'0, was properlyidentified and the instability associated with
the negative surface energy was noted, but the consequences were
not pursued. At the time, superconductivity had been observed in
elementary superconductors characterized by a smalllC, hence
Ginzburg and Landau decided that 'since from experimental data it
follows that IC ~ 1 ... another limiting case when IC + 00 does not
offer any intrinsic interest (and) we shall not discuss it'.
Type 11 Superconductors
It remained for Alexei Abrikosov to uncover the scientific gold mine
that opened up with the 'superconductors of the second group'
involving large IC, nowadays called type II superconductors.
Abrikosov's first contact with these 'unconventional' superconduc
tors dates back to the early fifties, when Nikolay Zavaritskii changed
the fabrication mode of his thin Sn and Tl films, keeping the sub
strate at low temperatures in order to improve their homogeneity.
While the behavior of his previous room temperature evaporated
films was in good agreement with theory, the new ones deviated
strongly. This led Abrikosov and Zavaritskii to propose that these
new films belong to the 'second group' of superconductors with
IC> ll'v'2 and indeed their critical field matched well the theoretical
result found byAbrikosov in 1952. The breakthrough came in 1957,
when Abrikosov obtained the basic phenomenological description
oftype II superconductors in a single stroke. The instability noticed
... Photog@phs: From left to rightAbrikosov, Ginzburg, and
Leggett receiving the Nobel Prize in Physics 2003.
by Ginzburg and Landau allowed the magnetic field to enter the
superconductor without destroying it This leads to the appearance
of an interesting new thermodynamic phase, the mixed or Shub
nikov phase, where superconducting and normal regions peacefully
coexist. The normal regions appear in the cores (of size ~) of vortices
binding individual magnetic flux quanta <1>0 = he !2e on the scale A.,
with the charge '2e' appearing in <1>0 a consequence of the pairing
mechanism; since A> ~, the vortices repel and arrange in a stable lat
tice, nowadays named after its inventor Alexei Abrikosov. In his 1957 .
paper, Abrikosov derived the periodic vortex structure near the
upper critical field Ha, where the superconductivity is totally sup
pressed, determined the magnetization M(H), calculated the field
Hc1 of first penetration, analyzed the structure of individual vortex
lines, found the structure of the vortex lattice at low fields, and com
pared his findings with experiments on what appeared to be the
first observation of this novel mixed state, the B(H) curves measured
on Pb alloys by Shubnikov, Khotkevich, Shepelev, and Riabinin in
1937. Although this already makes an impressive list, the phenome
nology of type II superconductors continued to develop for many
years. It turns out that all technologically useful superconductors
are 'of the second group'; these materials smoothly incorporate the
large magnetic fields appearing in most technological applications,
hence they 'bend' rather than 'break' under the action of fields and
currents. In particular, the cuprate high temperature superconduc
tors (discovered by Bednorz and Miiller in 1986) are strong type IT
materials exhibiting an amazing variety ofvortex phases with novel
properties. Meantime, the Abrikosov lattice has undergone a'meta
morphosis' to the field ofVortex Matter, the filigrane arrangements
formed by vortexlines residing within conventional matter made of
atoms and electrons.
As so often in the field of superconductivity it took many years
to understand the rich and complex phenomenology of these
materials. Political events also hampered the developments: in
1937 Shubnikovwas accused of'antiSoviet activity' and sentenced
to death; the same accusation led to the imprisonment of Landau
in Moscow. Thus, Shubnikov's 1937 results on the mixed state failed
to catch the attention of the community for 20 years. Similarly, the
cold war hampered the diffusion of the amazing achievements of
Russian theoreticians in the west.
Superfluid 3He
3He is an uncharged quantum fluid with a repulsive interatomic
interaction at short distances favoring pairing in a finite angular
momentum state. The order parameter field then assumes a com
plex structure incorporating additional internal degrees of
freedom: the unconventional pairing involves atoms with parallel
spins (triplet channel with S = 1) and orbital momentum L = 1. As
a result, the superfluid phase is anisotropic, with d and 1two
direceurophysics news MARCH!APRIL 2004
tions associated with the additional spin and orbital degrees of
freedom. Hence cooling 3He down to low temperatures, leads not
only to the breaking of gauge symmetry but also of the rotational
symmetry in spin and orbital space, thus requiring a macroscop
ic wavefunction with a tensorial structure involving 3 x 3 complex
components (at least in principle). In practice, the lowest energy
state is isotropic, with the spin and orbital angular momenta
adding to zero (the BW state first found by Balian and Werthamer
in 1963). Its excitation spectrum exhibits a constant energy gap just
like a conventional BCS superconductor. Even earlier, Anderson
and Morel hac! proposed an anisotropic state, with zero energy
gap along the Iaxis (the AM state). But another decade passed
until Lee, Osheroff, and Richardson finally observed the superflu
id phases of3He in 1972, anAphase at elevated temperatures and
pressures and a Bphase in the remainder of the low temperature
phase diagram. It was Anthony Leggett who unravelled the puzzle
of interpreting the experimental data with the correct theoretical
picture. The NMR (nuclear magnetic resonance) data identifying
the new phases exhibited sharp resonance frequencies, unexpect
edly shifted in the A but not in the B phase, which Leggett
explained in terms of a new 'spontaneously broken spinorbitsym
metry'. While this symmetry is trivially broken in the AM state
through selection of specific directions d and 1, the situation is
more subtle for the isotropic BW state, where neither d nor 1but
only their relative orientation is fixed. This subtly broken rotation
al symmetry manifests itself only in the dynamical response. Soon
after the discovery of the new superfluids, Leggett presented his
explanation for the observed shift in terms of a dipole field
enhanced by the macroscopic alignment of nuclear spins and pre
dicted the existence of additional longitudinal modes in the AM
and BW phases. He identified the AM state as a possible candidate
for the observed A phase but noted the competition with the lower
energy BW state. This led Anderson and Brinkman (1973) to
reconsider the AM state and they demonstrated its stabilization
due to the feedback effects of the condensation on the interparti
cle interactions (nowadays the ABM state carries the initials of all
three authors). Finally, Ambegaokar and Mermin (1973) identified
the third phase (termed AI) appearing at finite magnetic fields as
the first magnetic superfluid.
In retrospect, the complexity of 3He teaches us an interesting
story. At first sight 4He and 3He are two fluids characterized by the
same isotropic LennardJones type interaction. The source of
their difference lies in the absence of one neutron in the nucleus of
a 3He atom which is enclosed in a rigid electronic shell governing
the interaction between atoms. Still, the low temperature properties
of the two fluids are as different as one could imagine, owing to the
quantummechanical properties of their light constituents. One
may wonder what ingenuity it would take for an observer living at
low temperatures and confronted with this complexity to guess
the correct simple highenergy Hamiltonian responsible for this
diversity of phases. This inverse task, guessing the correct "high
energy Hamiltonian" from observations at low energies, is
analogous to the central problem facing the particle physics com
munity. In condensed matter theory the program of deriving the
correct microscopic Hamiltonian from experimental observations
has been carried out many times, with the BCS Hamiltonian serv
ing as a prominent example. One should appreciate, however, the
amazing insights that phenomenologicallowenergy theories, such
as those introduced and used by Ginzburg, Abrikosov, and Leggett,
have contributed to our understanding of the world we live in.
Acknowledgements
We thank M. Rice, D. Vollhardt, and P. Wolfle for discussions.