费米面研究中的试验方法

ExperimentalmethodsinfermisurfacestudiesExperimentalmethods:magnetoresistanceanomalousskineffectcyclotronresonancemagneto-acousticgeometriceffectsShubnikow-deHaaseffectdeHaas-vanAlpheneffectdeHaas-vanAlpheneffectexhibitsverywellthecharacteristicperiodicityin1/Bofthepropertiesofametalinauniformmagneticfield.费米面研究中的试验方法Quantizationoforbitsinamagneticfieldthekineticmomentum:

thepotentialmomentum:

(22)

(23)

费米面研究中的试验方法Quantizationoforbitsinamagneticfield

(24)Theequationofmotionofaparticleofchargeqinamagneticfieldis

(25a)

Thusoneofthepathintegralsin(24)is

(25b)

费米面研究中的试验方法Theotherpathintegralin(24)isQuantizationoforbitsinamagneticfield

(25c)

Thus

(26)Thetotalmagneticflux

(27)

费米面研究中的试验方法Quantizationoforbitsinamagneticfield

(28)Itfollowsthat

(29)

(30)费米面研究中的试验方法QuantizationoforbitsinamagneticfieldTheareasareequalwhen

(31)Equalincrementsof1/Breproducesimilarorbits.ThepopulationoforbitsonorneartheFermisurfaceoscillatesasBisvaried,causingawidevarietyofeffects.

费米面研究中的试验方法DeHaas-vanAlphenEffectThedeHaas-vanAlpheneffectistheoscillationofthemagneticmomentofametalasafunctionofthestaticmagneticfieldintensity.Theeffectcanbeobservedinpurespecimensatlowtemperaturesinstrongmagneticfields.foratwo-dimensional(2D)system(absolutezero):Theareabetweensuccessiveorbits:

(32)

费米面研究中的试验方法DeHaas-vanAlphenEffectThenumberoffreeelectronorbitalsthatcoalesceinasinglemagneticlevelis

(33)

SuchamagneticleveliscalledaLandaulevel.费米面研究中的试验方法DeHaas-vanAlphenEffectLandaulevelthetotalenergyoftheelectronsraised费米面研究中的试验方法DeHaas-vanAlphenEffectAllowedelectronorbitalsintwodimensionsTheangularpositionofthepointshasnosignificanceAmagneticfieldnomagneticfieldTheareabetweensuccessivecircles：

Theareaoftheadjacentcircle:

费米面研究中的试验方法DeHaas-vanAlphenEffectasystemofNelectronsatabsolutezero

partlyfilledentirelyfillednofilledFermilevelmovesdowntothelevelsLandaulevelWhens+1isvacated,theFermilevelmovesdownabruptlytothenextlowerlevels.费米面研究中的试验方法DeHaas-vanAlphenEffectTheelectrontransfertolowerLandaulevelscanoccurbecausetheirdegeneracyDincreasesasBisincreased.

AsBisincreasedthereoccurvaluesofBatwhichthequantumnumberoftheuppermostfilledleveldecreasesabruptlybyunity.AtthecriticalmagneticfieldslabeledBsnolevelispartlyoccupiedatabsolutezero,sothat

(34)费米面研究中的试验方法DeHaas-vanAlphenEffecttheenergyoftheLandaulevel:

cyclotronfrequency:

Thetotalenergyoftheelectronsinlevelsthatarefullyoccupiedis

(35)Thetotalenergyoftheelectronsinthepartlyoccupiedlevels+1is

(36)费米面研究中的试验方法DeHaas-vanAlphenEffect

ThethermalandtransportpropertiesofthemetalalsooscillateassuccessiveorbitallevelscutthroughtheFermilevelwhenthefieldisincreased.费米面研究中的试验方法DeHaas-vanAlphenEffect

ThisoscillatorymagneticmomentoftheFermigasatlowtemperaturesisthedeHaas-vanAlpheneffect.Theoscillationsoccuratequalintervalsof1/Bsuchthat

(37)SistheextremalareaoftheFermisurfacenormaltothedirectionofB.费米面研究中的试验方法Extremalorbits

费米面研究中的试验方法ExtremalorbitsThedominantresponseofthesystemcomesfromextremalorbits.Essentiallyitisaquestionofphasecancellation.Thecontributionsofdifferentnonextremalorbitscancel,butneartheextremathephasevariesonlyslowlyandthereisanetsignalfromtheseorbits.SharpresonancesareobtainedevenfromcomplicatedFermisurfacesbecausetheexperimentselectstheextermalorbits.费米面研究中的试验方法Fermisurfaceofcopper

TheFermisurfaceofcopperisdistinctlynonspherical:eightnecksmakecontactwiththehexagonalfacesofthefirstBrillouinzoneofthefcclattice.

(38)费米面研究中的试验方法FermisurfaceofcopperTheshortestdistanceacrosstheBrillouinzone(thedistancebetweenhexagonalfaces)：

Thefreeelectronspheredoesnottouchthezoneboundary,butweknowthatthepresenceofazoneboundarytendstolowerthebandenergyneartheboundary.ThusitisplausiblethattheFermisurfaceshouldneckouttomeettheclosest(hexagonal)facesofthezone.Thesquarefacesofthezonearemoredistant,withseparation12.57/a,andtheFermisurfacedoesnotneckouttomeetthesefaces.费米面研究中的试验方法Example:fermisurfaceofgold

费米面研究中的试验方法Example:fermisurfaceofgold

Anotherextremalorbit:“dog’sbone”It’sareainAuisabout0.4ofthebellyarea.费米面研究中的试验方法

Multiply-connectedholesurfaceofmagnesiuminbands1and2费米面研究中的试验方法MagneticbreakdownElectronsinsufficientlyhighmagneticfieldswillmoveinfreeparticleorbits.Herethemagneticforcesaredominant,andthelatticepotentialisaslightperturbation.Theeventualbreakdownofthisdescriptionasthemagneticfieldisincreasediscalledmagneticbreakdown.

费米面研究中的试验方法Theonsetofmagneticbreakdownwillberevealedbyphysicalpropertiessuchasmagnetoresistancethatdependsensitivelyonth