172 Statistics under extreme conditions
existence. Itis worthmentioningthat the2intheh/ 2 eflux quantum arisesdirectly
from the pairing mechanism, and is an experimental confirmation of the unlikely
ideas ofBCS!
Inrecentyears, thetopicofsuperconductivityhasarousedconsiderablenewinterest
with the discovery of ‘high-temperature superconductivity’ in certain oxide materi-
als. Transition temperatures around100 K are availablein some ofthese remarkable
materials, andalot ofstudy hasbeen madeofYBCO (yttriumbarium copper oxide)
and similar layered materials, in which it seems that superconductivity is associated
withcopper oxideplanesinthe structure. These oxides are miserable conductorsin
the normal state aboveTTTCcompared to conventional metals. It has been shown that
Cooper pairs are again involved in the superconductivity. However, the precise mech-
anismfor the attractiveinteractionis a matter ofmuchcontroversyanduncertainty
(ajoke aboutNtheoretical physicists producingN(N− 1 )/2 theories isperhapsin
order here?). It is exciting to meet a technologically important field in which the basic
physicsisinsecure, so thereisalot ofcurrent activityinthis area.
1 5.1.2 Superfluid^3 He
The other Fermi–Dirac system of interest is (yet again) liquid^3 He. In Fig. 8. 5 ,we
introducedthe^3 Hephasediagram, which illustrates that at reasonably low pressures
there is no solidphase. Instead liquid exists down to the lowest temperatures, and it is
of relevance to be curious about the nature of the liquid ordered state as the absolute
zerois approached.Infactit wasdiscoveredinthe early1970s that, rightdowninthe
millikelvin range, the liquid does become a superfluid. The low-temperature phase
diagram is shown in Fig. 1 5 .2.
Again, the reader mustbereferredto specialistlow-temperature textsfordetail,
but a brief outline of some salientpoints follows.
Cooper pairs (two odds make an even!) are again involved. The mechanism is as
before a second-order process, but the intermediary is now not the phonon system.
Ratheritisthemagneticpolarization ofthebackground^3 Hefluid.Aswe noted
in section 14.2.2 the magnetic moment of one spin-^123 He atom interacts strongly
with the others. Hence in the second-order process, one half of a Cooper pair leaves
apolarization trail inthe surroundingfluidandthisisthen sensedbythe second
half of the pair. This effect is a subtle one, which is whyTTTCis in the millikelvin
range rather thanbeing oforderkelvin (asitisin^4 He).
However,itis muchmore exoticthan most (ifnot all) superconductivity.The
pairs are betweenparallel spins, not antiparallel ones. ThusS= 1 andL=1in
superfluid^3 He. Thisgives an extra complexity andauniqueinterest to this topic.
The complexityiswitnessedbytheexistence oftwo very different phases (theA-
and the B-phases ...guess which was discovered first!) as shown in Fig. 1 5 .2. The
orderinginthe^3 He superfluidneedstobedescribedby vector quantities, rather
than thesimple scalarofthesuperconductor.