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1、SupplementaryFiguresSupplementaryFigure1
2、ElectronicbandstructuresofbulkBPcalculatedwithdifferent1,23,4functionals.a,HSE06(redsolidlines)andLDA-mBJ(bluedashedlines)5,6bandstructuresbasedontheatomicstructureoptimizedbyoptB86b-vdW,denotedmBJ(optB86b-vdW)andHSE06(optB86b-vdW).b,Ban
3、dstructurescalculatedwithHSE067,87(PBE-G06)(red),PBE(blue)andPBE-G06(black).SupplementaryFigure2
4、Electronicbandstructuresofmonolayer,a,andbilayer,b,BP.ResultswereobtainedusingtheHSE06functionalbasedontheatomicstructurefromPBE-G06(red)andPBEfunctional(blue).SupplementaryFigure3
5、
6、Electronicbandstructuresofbulk,a,andmonolayer,b,BP,calculatedbyPBEwith(greendashedlines)andwithout(blacksolidlines)SOC.InsetsprovideamagnificationtoshowSOCeffectsaroundtheN(M)point.z0.51-layer3.200.02-layer4.02.910.06.03-layer2.690.04-layer8.02.530.08.05-layerAbsorbance(%)2.440
7、.0Bulk3.02.440.01.01.52.02.53.03.54.0Energyofincidentlight(eV)SupplementaryFigure4
8、Theoreticallypredictedopticalabsorptionspectraoffew-layerBPsystemsforlightincidentalonganin-planedirectionandpolarizedinc(z)direction.Blackdashedlinesindicatethelinearfitusedtoestimatetheabsorpti
9、onedge.Noappreciableabsorptionisfoundforenergiesbelow2.0eV.Asforthecaseofy-polarizedlightshowninFig.3b,thebandgapprocessissymmetry-forbiddenandabsorptionprocessesbeginonlybeyond2eV.Thustheabsorptionexhibitsanexplicitanisotropyforlightpolarizedinallthreepolarizationdirections.Th
10、isbehaviourshouldbereadilydetectableinspectroscopicmeasurementsandmaybeexploitedforoptoelectronicapplications.SupplementaryFigure5
11、Relativeerrorinthedeformationpotential.BandenergyoftheCBMofmonolayerBPaandoftheVBMsof5-layer,b,andmonolayer,c,BPwithrespecttothevacuumenergyasafunc
12、tionoflatticedilation.BandenergieswerecalculatedwiththeHSE06functional.Redsolidlinesarethefittingcurves.Insetsshowthestandarderrorsofthefittedslope,whichcorrespondstothedeformationpotential.Allrelativeerrorsforthedeformationpotentialoffew-layerBPforthexandydirectionsaresummariz
13、edinpaneld.SupplementaryTablesSupplementaryTable1
14、Latt
