Table Of ContentGernot Goll
Unconventional
Superconductors
Experimental Investigation
of the Order-Parameter Symmetry
With67Figures
ABC
GernotGoll
UniversitätKarlsruhe
PhysikalischesInstitut
Wolfgang-Gaede-Str.1
76128Karlsruhe
Germany
E-mail:[email protected]
LibraryofCongressControlNumber:2005933767
PhysicsandAstronomyClassificationScheme(PACS):
74.70.Tx,74.70.Pq,74.20.Rp,74.50.+r,74.25.Bt,74.25.Nf
ISSNprintedition:0081-3869
ISSNelectronicedition:1615-0430
ISBN-10 3-540-28985-2SpringerBerlinHeidelbergNewYork
ISBN-13 978-3-540-28985-2SpringerBerlinHeidelbergNewYork
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OLord,howmanifoldareyourworks!
Inwisdomhaveyoumadethemall;
theearthisfullofyourcreatures.
(Psalm104,24)
ToClaudia,AnneandJulia
S -asinglewordthatstillcausesexcitement,morethan90
yearsafteritsdiscovery
S -anamazingphenomenonoflossfreetransport
andlevitationinamagneticfield
S -a challenging field of scientific
activities between fundamental
condensed-matter research and
industrialapplications
S -fascinating both
experimentalists
andtheorists
S -some-
times
uncon-
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tional
S
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Preface
In the past decades a growing number of metals exhibited evidence for exotic
types of superconductivity. The superconductivity is often called unconventional
inordertoclassifysuperconductorswithrespecttotheorder-parametersymmetry.
Manyintriguingexperimentshavebeencarriedouttoelucidatetheorder-parameter
symmetry.
Thecharacterizationoftheorderparameterofsuperconductingmaterialsneeds
informationon(i)thepairingmechanism,(ii)theparityandspinstate,(iii)thesize
and the nodal structure of the energy gap, and (iv) the macroscopic superconduc-
tive phase. Each property can be accessed by different experiments. For example,
the nodal structure can be investigated by measurements of the temperature de-
pendenceofthermodynamicandtransportproperties,byangular-resolvedthermal-
conductivity measurements, and by the directional dependence of current–voltage
characteristics in point-contact and tunnelling measurements, though the latter ex-
perimentshavebeenmainlyappliedforthedeterminationofgapsizeandthedensity
ofstatesaround E .Ontheotherhand,theobservationofapowerlawinthelow-
F
temperaturebehaviourofoneproperty,forexampleofthepenetrationdepth,isnot
sufficientforthecharacterizationofanunconventionalsuperconductorandmustbe
treatedwithsomecautionsincetheremightbeother,quitedifferentandrathercon-
ventionalexplanationsofthedata.Therefore,itisimportanttohavecorroborating
evidencefromanumberofdifferentexperimentsbeforeaconclusivepictureofthe
order-parametersymmetryisobtained.Asnoneoftheexperimentalmethodsalone
can definitely reveal the order-parameter symmetry, manifold experiments will be
discussed,eachofwhichaccessesacertainaspect.Inparticular,someemphasiswill
beputontheinvestigationoftheenergygapofunconventionalsuperconductorsby
point-contactspectroscopy.Thepoint-contactandtunnelspectrayieldinformation
on the size and the anisotropy of the superconductive energy gap, its temperature,
anditsfielddependence.
This book is subdivided into three parts. In part I, a brief overview on possi-
bleunconventionalsuperconductorsisfollowedbyashorttheoreticalintroduction
ofthemainconceptsofunconventionalsuperconductivitycombinedwithageneral
definition of often-used terms and notations. Part II presents several experimental
methods that allow a characterization of the order-parameter symmetry. This in-
clude measurements of specific heat, thermal conductivity, penetration depth, and
ultrasound attenuation for information on the nodal structure (Chap. 3), nuclear
X Preface
magnetic resonance and muon spin rotation experiments for information on the
parity and spin state (Chap. 4), point-contact and tunnelling spectroscopy for in-
formation about the energy gap (Chap. 5), and phase-sensitive probes, namely the
Josephsoneffect(Chap.6).Thispartisconcludedwithanoverviewofexperimental
methodsthatprobetheeffectsofanunconventionalorderparameteronsinglevor-
ticesandthesymmetryoftheflux-linelattice(Chap.7).PartIIIreviewsthreeclasses
ofunconventionalsuperconductors,namelytheCe-basedheavy-fermionsupercon-
ductors (Chap. 8), the U-based heavy-fermion superconductors (Chap. 9), and the
metal-oxide superconductors (Chap. 10), especially Sr RuO . This book is not in-
2 4
tendedtoreviewthehigh-temperaturesuperconductors.Thereexistavastnumber
ofexcellentreviewarticlesandmonographsthatgiveaquitecompleteoverviewof
thestate-of-the-artresearchonthesematerials.Nevertheless,thehigh-temperature
superconductorswillbementioned,asthehugeamountofresearchonthesecom-
poundshaspushedthewholefield,boththetheoreticalandexperimentalactivities,
andhasshedlightontheunderstandingofmanyothertopicsrelatedtounconven-
tionalsuperconductivity.
Finally,Ithankallpeoplewhocontributedtothisworkinmanyrespectsduring
the past years. First of all, I am grateful to Prof. H. v. Lo¨hneysen for continuous
support,encouragement,andmanystimulatingdiscussions.Itisapleasuretothank
Prof.I.K.Yansonforinitiatingtheinterestintheexperimentaltechniqueofpoint-
contact spectroscopy, and Dr. Y. Naidyuk for helpful discussions and correspon-
dence.IthankProf.L.Taillefer,Prof.Y.Maeno,Dr.Z.Q.Mao,Dr.F.Lichtenberg,
Dr.V.Zapf,andDr.E.Bauerforprovidingthesamplesnecessaryforthesestudies
andforusefuldiscussions.IwouldalsoliketoacknowledgeProf.M.B.Maple,Prof.
E.Dormann,Prof.C.Bruder,Prof.P.Wo¨lfle,Prof.J.Wosnitza,Dr.M.Eschrig,Dr.
M.Fogelstro¨m,Dr.R.Werner,andDr.O.Stockertformanyfruitfulandilluminat-
ingdiscussions.IthankDr.C.Obermair,Dr.F.Laube,T.Brugger,S.Kontermann,
andM.Marzfortheircontributionstothepoint-contactdatareviewedhereandall
my colleagues for good collaboration. I thank L. Behrens for drawing, scanning,
andeditingmanyofthefigures.Last,butnotleast,IthankmywifeClaudiaandmy
daughtersAnneandJuliafortheirpatienceandsympathyduringmyweekendwrit-
ingofthismanuscript.ThisworkwaspartlysupportedbytheDeutscheForschungs-
gemeinschaftthroughSonderforschungsbereich195“LokalisierungvonElektronen
in makroskopischen und mikroskopischen Systemen” and Graduiertenkolleg “An-
wendungenderSupraleitung.”
Karlsruhe,October2005 GernotGoll
Contents
PartI IntroductiontoUnconventionalSuperconductivity
1 ABriefOverview .............................................. 3
References..................................................... 7
2 BasicTheoreticalConcepts...................................... 11
References..................................................... 18
PartII ExperimentalMethods
3 ProbingtheNodalStructure..................................... 21
3.1 SpecificHeatandThermalConductivity ....................... 21
3.2 MagneticPenetrationDepth.................................. 23
3.3 UltrasoundAttenuation...................................... 24
References..................................................... 26
4 ProbingtheParityandSpinState................................ 27
4.1 H Measurements.......................................... 27
c2
4.2 NuclearMagneticResonanceandKnightShift .................. 28
4.3 MuonSpinRotation ........................................ 30
References..................................................... 32
5 ProbingtheEnergyGap ........................................ 35
5.1 PlanarTunnellingSpectroscopy .............................. 35
5.2 ScanningTunnellingSpectroscopy(STS) ...................... 37
5.3 Point-ContactSpectroscopy.................................. 39
References..................................................... 53
6 ProbingthePhase.............................................. 55
6.1 JosephsonEffect ........................................... 55
6.2 Zero-BiasAnomalies ....................................... 59
References..................................................... 59
XII Contents
7 ProbingtheVortices:LatticeSymmetry
andInternalStructure.......................................... 61
7.1 ScanningTunnellingSpectroscopy ............................ 62
7.2 Small-AngleNeutronScattering(SANS)....................... 62
7.3 MuonSpinRotation ........................................ 63
References..................................................... 63
PartIII PossibleUnconventionalSuperconductors
8 Ce-BasedHeavy-FermionSuperconductors ....................... 67
8.1 CeCu Si ................................................. 67
2 2
8.2 CeCoIn andCeIrIn ........................................ 72
5 5
8.3 CePt Si................................................... 81
3
References..................................................... 84
9 U-BasedHeavy-FermionSuperconductors ........................ 89
9.1 UPt ..................................................... 89
3
9.2 UBe ....................................................103
13
9.3 URu Si ..................................................107
2 2
9.4 UNi Al andUPd Al ......................................111
2 3 2 3
References.....................................................115
10 Metal-OxideSuperconductors ...................................121
10.1 Sr RuO ..................................................122
2 4
10.2 High-TemperatureSuperconductors ...........................140
References.....................................................147
A Appendix .....................................................153
References.....................................................161
Index .............................................................169
