費米面研究中的試驗方法

ExperimentalmethodsinfermisurfacestudiesExperimentalmethods:magnetoresistanceanomalousskineffectcyclotronresonancemagneto-acousticgeometriceffectsShubnikow-deHaaseffectdeHaas-vanAlpheneffectdeHaas-vanAlpheneffectexhibitsverywellthecharacteristicperiodicityin1/Bofthepropertiesofametalinauniformmagneticfield.

目前一頁\總數(shù)二十四頁\編于十二點Quantizationoforbitsinamagneticfieldthekineticmomentum:

thepotentialmomentum:

(22)

(23)

目前二頁\總數(shù)二十四頁\編于十二點Quantizationoforbitsinamagneticfield

(24)Theequationofmotionofaparticleofchargeqinamagneticfieldis

(25a)

Thusoneofthepathintegralsin(24)is

(25b)

目前三頁\總數(shù)二十四頁\編于十二點Theotherpathintegralin(24)isQuantizationoforbitsinamagneticfield

(25c)

Thus

(26)Thetotalmagneticflux

(27)

目前四頁\總數(shù)二十四頁\編于十二點Quantizationoforbitsinamagneticfield

(28)Itfollowsthat

(29)

(30)目前五頁\總數(shù)二十四頁\編于十二點QuantizationoforbitsinamagneticfieldTheareasareequalwhen

(31)Equalincrementsof1/Breproducesimilarorbits.ThepopulationoforbitsonorneartheFermisurfaceoscillatesasBisvaried,causingawidevarietyofeffects.

目前六頁\總數(shù)二十四頁\編于十二點DeHaas-vanAlphenEffectThedeHaas-vanAlpheneffectistheoscillationofthemagneticmomentofametalasafunctionofthestaticmagneticfieldintensity.Theeffectcanbeobservedinpurespecimensatlowtemperaturesinstrongmagneticfields.foratwo-dimensional(2D)system(absolutezero):Theareabetweensuccessiveorbits:

(32)

目前七頁\總數(shù)二十四頁\編于十二點DeHaas-vanAlphenEffectThenumberoffreeelectronorbitalsthatcoalesceinasinglemagneticlevelis

(33)

SuchamagneticleveliscalledaLandaulevel.目前八頁\總數(shù)二十四頁\編于十二點DeHaas-vanAlphenEffectLandaulevelthetotalenergyoftheelectronsraised目前九頁\總數(shù)二十四頁\編于十二點DeHaas-vanAlphenEffectAllowedelectronorbitalsintwodimensionsTheangularpositionofthepointshasnosignificanceAmagneticfieldnomagneticfieldTheareabetweensuccessivecircles：

Theareaoftheadjacentcircle:

目前十頁\總數(shù)二十四頁\編于十二點DeHaas-vanAlphenEffectasystemofNelectronsatabsolutezero

partlyfilledentirelyfillednofilledFermilevelmovesdowntothelevelsLandaulevelWhens+1isvacated,theFermilevelmovesdownabruptlytothenextlowerlevels.目前十一頁\總數(shù)二十四頁\編于十二點DeHaas-vanAlphenEffectTheelectrontransfertolowerLandaulevelscanoccurbecausetheirdegeneracyDincreasesasBisincreased.

AsBisincreasedthereoccurvaluesofBatwhichthequantumnumberoftheuppermostfilledleveldecreasesabruptlybyunity.AtthecriticalmagneticfieldslabeledBsnolevelispartlyoccupiedatabsolutezero,sothat

(34)目前十二頁\總數(shù)二十四頁\編于十二點DeHaas-vanAlphenEffecttheenergyoftheLandaulevel:

cyclotronfrequency:

Thetotalenergyoftheelectronsinlevelsthatarefullyoccupiedis

(35)Thetotalenergyoftheelectronsinthepartlyoccupiedlevels+1is

(36)目前十三頁\總數(shù)二十四頁\編于十二點DeHaas-vanAlphenEffect

ThethermalandtransportpropertiesofthemetalalsooscillateassuccessiveorbitallevelscutthroughtheFermilevelwhenthefieldisincreased.目前十四頁\總數(shù)二十四頁\編于十二點DeHaas-vanAlphenEffect

ThisoscillatorymagneticmomentoftheFermigasatlowtemperaturesisthedeHaas-vanAlpheneffect.Theoscillationsoccuratequalintervalsof1/Bsuchthat

(37)SistheextremalareaoftheFermisurfacenormaltothedirectionofB.目前十五頁\總數(shù)二十四頁\編于十二點Extremalorbits

目前十六頁\總數(shù)二十四頁\編于十二點ExtremalorbitsThedominantresponseofthesystemcomesfromextremalorbits.Essentiallyitisaquestionofphasecancellation.Thecontributionsofdifferentnonextremalorbitscancel,butneartheextremathephasevariesonlyslowlyandthereisanetsignalfromtheseorbits.SharpresonancesareobtainedevenfromcomplicatedFermisurfacesbecausetheexperimentselectstheextermalorbits.目前十七頁\總數(shù)二十四頁\編于十二點Fermisurfaceofcopper

TheFermisurfaceofcopperisdistinctlynonspherical:eightnecksmakecontactwiththehexagonalfacesofthefirstBrillouinzoneofthefcclattice.

(38)目前十八頁\總數(shù)二十四頁\編于十二點FermisurfaceofcopperTheshortestdistanceacrosstheBrillouinzone(thedistancebetweenhexagonalfaces)：

Thefreeelectronspheredoesnottouchthezoneboundary,butweknowthatthepresenceofazoneboundarytendstolowerthebandenergyneartheboundary.ThusitisplausiblethattheFermisurfaceshouldneckouttomeettheclosest(hexagonal)facesofthezone.Thesquarefacesofthezonearemoredistant,withseparation12.57/a,andtheFermisurfacedoesnotneckouttomeetthesefaces.目前十九頁\總數(shù)二十四頁\編于十二點Example:fermisurfaceofgold

目前二十頁\總數(shù)二十四頁\編于十二點Example:fermisurfaceofgold

Anotherextremalorbit:“dog’sbone”It’sareainAuisabout0.4ofthebellyarea.目前二十一頁\總數(shù)二十四頁\編于十二點

Multiply-connectedholesurfaceofmagnesiuminbands1and2目前二十二頁\總數(shù)二十四頁\編于十二點MagneticbreakdownElectronsinsufficientlyhighmagneticfieldswillmovein

freeparticleorbits.Herethemagneticforcesaredominant,andthelatticepotentialisaslightperturbation.Theeventualbreakdownofthisdescriptionasthemagneticfieldisincreasediscalledmagneticbreakdown.

目前二十三頁\總數(shù)二十四頁\編于十二點Theonsetofmagneticbreakdownwillberevealedbyphysicalpropertiessuchasmagnetoresistancethatdepen