石墨烯光学介绍

1、optics on graphenegate-variable optical transitions in graphenefeng wang, yuanbo zhang, chuanshan tian, caglar girit, alex zettl, michael crommie, and y. ron shen, science 320, 206 (2008).direct observation of a widely tunable bandgap in bilayer grapheneyuanbo zhang, tsung-ta tang, caglar girit1, zh

2、ao hao, michael c. martin, alex zettl1, michael f. crommie, y. ron shen and feng wang (2009)graphene(a monolayer of graphite)2d hexagonal lattice electrically: high mobility at room temperature, large current carrying capability mechanically: large youngs modulus. thermally: high thermal conductance

3、.properties of graphenequantum hall effect, barry phaseballistic transport,klein paradoxothersexotic behaviorsquantum hall effecty. zhang et al, nature 438, 201(2005)optical studies of graphene optical microscopy contrast; raman spectroscopy; landau level spectroscopy.other possibilites spectroscopi

4、c probe of electronic structure. interlayer coupling effect. electrical gating effect on optical transitions. otherscrystalline structure of graphitegraphene2d hexagonal latticeband structure of graphene monolayer12int1122( )tight-binding calculation on bands:, ( ) *( ), ( )1 ( )|( )| 3atppik aik ap

5、phhhkef kuuhuufkef keeekef ke122122cos2cos2cos () 14cos ( 3/2)4cos( 3/2)cos(3/2) near k pointspxxypfk ak ak aaek ak ak aev kp.r.wallace, phys.rev.71,622-634(1947)band structure of monolayer graphereelectron bands of graphene monolayerband structure in extended bzrelativistic dirac fermion.band struc

6、ture near k points10 evvertical optical transitionvan hove singularityk kk kmonolayerbilayerband structures of graphene monolayer and bilayer near kef is adjustablexxexfoliated graphene monolayers and bilayersmonolayerbilayerreflecting microscope images.k. s. novoselov et al., science 306, 666 (2004

7、). 20 mraman spectroscopy of graphenea.s.ferrari, et al, prl 97, 187401 (2006)(allowing id of monolayer and bilayer)reflection spectroscopy on grapheneexperimental arrangementdoped sigraphenegold290-nm silicaopadetinfrared reflection spectroscopyto deduce absorption spectrumdifferential reflection s

8、pectroscopy:difference between bare substrate and graphene on substrate ab-d dr/r (ra-rb)/ra versus w wra: bare substrate reflectivityrb: substrate + graphene reflectivity20 mdr/r = -reh(w)s(w)h(w)s(w)h(w) h(w) from substrates(w)s(w) from graphene: interband transitons free carrier absorptionre s(w)

9、s(w)/w: absorption spectrumspectroscopy on monolayer graphenemonolayer spectrumxd dr/rew2 2ef22000#electrons/holes = ( )/( v )v|() p-doped: 0 can be adjusted by carrier injection through .feffffgfgne deeennc vvvev 2( )2/feevc: capacitanceexperimental arrangementdoped sigraphenegold290-nm silicaopade

10、tvggate effect on monolayer graphene 2( )2/vfeex xx xx xsmall density of states close to dirac point e = 0 carrier injection by applying gate voltage can lead to large fermi energy shift .ef can be shifted by 0.5 ev with vg 50 v; shifting threshold of transitions by 1 evd dr/rw2 2efif vg = vg0 + vmo

11、d, then should be a maximum at mod(/)r rvd2fewvary optical transitions by gatinglaser beamvary gate voltage vg.measure modulated reflectivity due to vmod at v( analogous to di/dv measurement in transport)0(/)vr rvdresults in graphene monolayerw= 350 mev00( ) ( -) / ( -) /0bt b bbbt t t tvd d v vd d

12、v dd 0 ( f r o m 0 w i t h 0 )d d dd the maximum determines vg for the given ef.mapping band structure near kfor different w w, the gate voltage vg determined from maximum is different, following the relation , mod(/)r rvd220( v )| ffgec vvd dr/rw2 2efslope of the line allows deduction of slope of t

13、he band structure (dirac cone) 60.83 10/fvm snoimage2d plot of monolayer spectrumexperimenttheorywd(dd(dr/r) (dr/r)(dr/r) 60v (dr/r) (dr/r) 50vvg 0 0strength of gate modulationbilayer graphene(gate-tunable bandgap)band structure of graphene bilayerfor symmetric layers, d d = 0for asymmetric layer, d

14、 d 0 0e. mccann, v.i.falko, prl 96, 086805 (2006);doubly gated bilayerasymmetry:d d (db + dt)/2 0carrier injection to shift ef: df dd = (db - dt)sample preparation0 ( -)/bbbbbdvvd 0t ( -)/ttttdvvd 0,b tveffective initial bias due to impurity dopingtransport measurementmaximum resistance appears at e

15、f = 000, btvv0220v|() =( v )|ffgffgennc vvec vv lowest peak resistance corresponds to db = dt = 0 .070 vv optical transitions in bilayeri: direct gap transition (tunable, 250 mev)ii, iv: transition between conduction/valence bands(400 mev, dominated by van hove singularity)iii, v: transition between

16、 conduction and valence bands (400 mev, relatively weak)if def=0, then ii and iv do not contributebandstructure change induced bynoimagetransitions ii & iv inactivetransition i activexxiviidifferential bilayer spectra (dd = 0)(difference between spectra of d0 and d=0)iilarger bandgap stronger tr

17、ansition i because ot higher density of statesiv2fewcharge injection without change of bandstructure (d fixed)xdd = 0dd 0transition iv becomes activepeak shifts to lower energy as d increases.transition iii becomes weaker and shifts to higher energy as d increases.iviiidifference spectra for differe

18、nt d between dd=0.15 v/nm and d dd=00ddlarger dbandgap versus dd d(dr/r) (dr/r) 60v -(dr/r) -50vis comparable to d dr/r in valuestrength of gate modulationsummarygrahpene exhibits interesting optical behaviors:. gate bias can significantly modify optical transitions over a broad spectral range. single gate bias shifts the fermi level of monolayer graphene.spectra provides information on bandstructure, allowing deduction of vf (slope of the dirac cone in the bandstru