Chapter1BoltzTraP
ThispackagecontainstheprogramBoltzmannTransportProperties(BoltzTraP)forcalculat-ingthesemi-classictransportcoe?cients.Itcanbeobtainedfromwww.icams.de/boltztrap.TheprogramhasdocumentedinComp.Phys.Commun.[1]Ifyoupublishresultsobtainedusingtheprogramthispapershouldbesited.
TheprogramwasoriginallyinterfacedtotheWIEN2kcode,butcaneasilybeinterfacedtootherbandstructurecodes.MarcosAlvesandMatthieuVerstraetehaveprovidedSiestaandab-initinterfaces.This?leformatisdocumentedattheendofthis?le.Pleasecontributeifyoumakesuchaninterface.
1.1
1.1.1
Gettingstarted
Unpacking
Runthecommandbunzip2BoltzTraP.tar.bz2;tarxvfBoltzTrap.tarThiswillunpackseveraldirectoriessrctestdocutil
Thesourcecode
Example?les,Al,Bi2Te3,LiZnSbandCoSb3This?le
AperlscripttogatherWIENenergy?les
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1.1.2Compiling
Thedistributionincludesamake?lefortheintelfortrancompilerandthemkllibraries.OnceyouhavesuccesfullycompiledtheprogramyoushouldhaveanexecutablenamedBoltzTrap.Furthermorethescriptxtranscanbefoundinthedirectory.
1.1.3Runningtestexamples
Thedistributionincludestwoexamples:CoSb3andBi2Te3.BothexamplesarealsodescribedintheBoltzTraPpaper[1]ToruntheexamplesyoumustchangetooneofthesetwodirectoriesCoSb3
OnceyouareintheCoSb3directoryyoucanrunBoltzTrapbythefollowingcommand(Re-memberthecapitalletters)
\toBoltzTrap\transBoltzTraP
Thextransscriptwillmakea?lecalledBoltzTrap.defandexecutesBoltzTrap.TheBoltzTrap.def?lenamestheinputandoutput?les(describedbelow)Bi2Te3
TheBi2Te3exampleincludesspin-orbitcouplingintheHamiltonian.Thereforetheexampleshouldbythefollowingcommand:
\toBoltzTrap\transBoltzTraP-so
Noticethe-sooption.Thiswilltelltheprogramtoreadtheeigenvaluesfromthe?lecase.energyso(seeBoltztrap.def)andtheprogramwillthenautomaticallyknowtheeachstatecontainsonlyoneelectron.LiZnSb
Thisexamplecanbefoundinref.[2]anddocumentstheuseofthemomentummatrixelementsdirectly.[3]TheoptionwasaddedLasseBjerg
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1.2
1.2.1
Usingtheprogram
Input?les
Toruntheprogramyoumusthavea?ledescribingtheparametersforBoltzTraPnamedcase.intrans(wherecaseisthenameofthedirectory).Furthermoreyouneeda?lewiththeband-structureandthecrystalstructure,case.energy(so)andcase.struct,wherecaseisthenameofthedirectory.Presentlycase.energy(so)andcase.structhavetobeintheformatoftheWIEN2kcode.
WIENFormatofDOS.EitherWIENfortouseWIENlikecase.structandcase.energyorGENEforthe?lestyleoutputbySIESTAandABINIT0000.0isetfermiidebugsetgapgapchange
isetfermi>0setfermileveltomiddleofgapidebugsetsthelevelofoutput
setgap=1willforcethegaptobegapchange(inRy)
0.554750.00050.4240.Fermilevel(Ry),deltae,ecut,numberofvalenceelectrons
deltaedeterminesthestepsizeoftheDOSgrid
ecutgivestherangearoundefermiinwhichthebandsareincluded
CALCCALC(calculateexpansioncoe?,Eq.(p1),NOCALC(readfrom?le)5lpfac,numberoflatt-pointsperk-point
lpfac=5:?vetimesasmanyRpointsareusedaskpointswereinput
BOLTZrunmode(onlyBOLTZissupported).15efcut.energyrangeofchemicalpotentialaroundefermithatisused
forintegrals(Eqs.(p12-p15))
800.50.Tmax,temperaturegrid-1EnergyrangeofbandsgivenindividualDOSoutputsigxxxanddosxxx(xxxisbandnumber).Negative:noindividualDOS.
HISTOschemetoobtainDOS.HISTO/TETRA:histogram/thetrahedron[4]
sampling
00000τ-model.Notdocumented2numberof?xeddopings1E20-1E20?xeddopinglevelsincm?3
Table1.1:Input?leforCoSb3.TheEquationsrefertothepaper[1].
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1.2.2Output?les.BOLTZoption
ThetracesoftheconductivitytensorsarewrittenasafunctionofμandTinthe?lecalledcase.trace.Youmustwriteyourownprogram/scripttoextracttheinformationyouneed.Thecolumnquantityunit
12μTRyK
345Nn(μ)Se/uce/ucV/K
6789σ/τRHκ0c3
1/(?ms)m/CW/(mKs)J/(molK)
10χ3
m/mol
Table1.2:Outputincase.trace
lastcolumnswereaddedafterthepaperwasacceptedandaretheelectronicspeci?cheatc
?????f(T;ε)??
μ
c(T;μ)=n(ε)(ε?μ)dε(1.1)
?TandthePaulimagneticsusceptibility
χ(T;μ)=
μ0μ2B
??
???f(T;ε)??
μ
n(ε)?dε
?ε
(1.2)
Theprogramoutputstheindividualcomponentsoftheconductivitytensors(?lescase.condtensandcase.halltens).The?rstthreecolumsarelikeinthecase.trace?le.
Incase.condtensnextninecolumsaretheσ/τcomponents(3x3tensor).ThesearefollowedbythenineSeebeckcomponentsand?nallythenineκ0components.Incase.halltens27columnsfollow(TheHalltensoris3x3x3tensor)
Thecoordinate-systemusedisde?nedsothatthexaxisisparalleltothecrystallographica-axis(oftheconventionalcell).They-axisliesinthecrystallographicabplaneandisorthogonaltothex-axisandthez-axisisorthogonaltothexandyaxes.Ifyouwantadi?erentcoordinatesystemyoumustworkouttheappropriatetransformationyourself(agoodreferenceis”J.F.Nye,PhysicalPropertiesofCrystals”).Theaxessetupisdoneinthesubroutinelatgen2.f.
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1.3FrequentlyAskedQuestion
Howmanyk-pointsshouldIuseforatransportcalculation.
Thisof-coursedependsonyoursystem,butgenerally“alot”.Aruleofthumbisthatyourconvergencetestsshouldstartat16×106/Vpuc,whereVpucisthevolumeoftheprimitiveunitcell.Pleasenotethatyoudonotneedtoredothefullscfcyclewiththedensek-meshIhavecalculatedmyenergy?lesinparallelhowdoIincludetheminBoltzTraPTheutility
gatherenergy.pl
willstickyourcase.energy(so)*intoonecase.energy(so)?lethatcanbefedintoBoltzTrapHowcanIcalculatetheconductivity.
Onecanonlycalculatetheconductivityifoneknowsτ.ThedistributionincludesacalculationforAlforwhichAshcroftandMermin[5]listρ=2.45μ?cm=2.45×10?8?m(page8).IfyoulookinTable1.2you’llseethatBoltzTraPoutputsσ/τ.At270Koneobtainsσ/τ≈3.17×1021(?m)?1.Usingτ=0.8×10?14s(page9)onegetfortheresistivityρ=1/(3.17×1021·0.8×10?14)=3.9×10?8?mwhichisaniceagreementconsideringthelargeuncertaintyinτ(AshcroftandMerminusefreeelectronbands)
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