Table Of ContentNonlinear optical probe of tunable surface electrons on a topological insulator
D. Hsieh*,1 J. W. McIver*,1,2 D. H. Torchinsky,1 D. R. Gardner,1 Y. S. Lee,1 and N. Gedik1
1Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
2Department of Physics, Harvard University, Cambridge, MA 02138, USA
(Dated: January 11, 2011)
Weuseultrafastlaserpulsestoexperimentallydemonstratethatthesecond-orderopticalresponse
of bulk single crystals of the topological insulator Bi2Se3 is sensitive to its surface electrons. By
performingsurfacedopingdependencemeasurementsasafunctionofphotonpolarization andsam-
pleorientationweshowthatsecondharmonicgenerationcansimultaneouslyprobeboththesurface
1
1 crystalline structure and the surface charge of Bi2Se3. Furthermore, we find that second harmonic
0 generation using circularly polarized photons reveals the time-reversal symmetry properties of the
2 system and is surprisingly robust against surface charging, which makes it a promising tool for
spectroscopic studies of topological surfaces and buried interfaces.
n
a
J
Electrons on the surface of a three-dimensional (3D) rial. In this Letter, we generate SHG from Bi Se (111)
2 3
7
topologicalinsulator[1–3]arepredictedtoexhibitexotic by utilizing the highpeak photon flux of ultrafastlasers.
electrical properties including protection against local- Byperformingsurfacedopingdependencemeasurements
]
i ization from non-magnetic impurities [1, 2] and photo- as a function of photon polarizationand sample orienta-
c
induced spin-polarized currents [4, 5]. When interfaced tion[Fig.1(a)]weshowthatSHGissurfacesensitiveand
s
- with ordinary materials, these surface states are pre- is a simultaneous probe of both the surface crystalline
l
r dicted to evolve into new broken symmetry electronic structureandthe surfaceFermilevelofBi Se . Further-
2 3
t
m phaseswithunconventionalresponsessuchasananoma- more, we find that circular dichroism SHG probes the
lous half-integerquantumHall effect[2, 6] ortopological time-reversal symmetry properties of the system and is
.
t superconductivity [2]. The recent discovery of 3D topo- robustagainstsurfacecharging,whichmakesitapromis-
a
m logical insulators in Bi1−xSbx [7, 8], Bi2Se3 and related ing tool for spectroscopic studies of topological surfaces
materials [9–11] has generated great interest to measure and buried interfaces.
-
d the symmetry and electrical properties of a single sur- Reflection SHG from the (111) surface of metallic
n face or buried interface. However transport techniques Bi Se bulksinglecrystals,whicharebulkinversionsym-
2 3
o havedifficultyseparatingtheresponsefromdifferentsur- metric (space group D5 [11]), was measured using 80 fs
3d
c
faces and the bulk [12, 13], and require deposition of laser pulses derived from a Ti:sapphire oscillator. The
[
contactsandgatesthatmayperturbtheelectronicstruc- laser pulses have a center wavelength of 795 nm (1.56
1 ture. Opticaltechniqueshavebeenproposedasacontact eV) anda repetition rate of1.6 MHz, andare focusedto
v free alternative that canbe focused onto a single surface a 20 µm spot on the sample at an incident angle of 45◦
1 [4, 6, 14, 15] or interface. However, experiments so far with an incident power density of 0.63 kW/cm2, which
4
have been limited to the linear optical regime, which is isbelowthe damagethreshold. Specularlyreflectedpho-
5
again dominated by the bulk carrier response [16–18]. tons at the second harmonic energy (3.12 eV) were se-
1
1. A contact free probe that is potentially surface or in- lectively isolated through spectral filtering and collected
by calibrated photomultiplier tubes sensitive to 3.12 eV
0 terface sensitive is second-order nonlinear optical spec-
light.
1 troscopy. In general, the electrical polarization of a ma-
1 terialP (ω)hasadominantcomponentlinearinthedriv- We first demonstrate that our measurements are con-
i
v: ingopticalfieldEj(ω)aswellasweakercomponentspro- ssiysmtemntetwriythisSrHedGufcreodmfrtohme(D1151)tsourCface, wwhhiecrhetchoenscirsytsstoafl
i portional to higher powers of Ej(ω), where ω is the op- 3d 3v
X anaxis(zˆ)of3-foldrotationalsymmetryandthreeplanes
tical frequency and the indices run through three spa-
r tial coordinates. Components that contain two powers of mirror symmetry [Fig.1(b)]. In general, the reflected
a surface SHG intensity I(2ω) is given by [20]
of E (ω) are responsible for second harmonic genera-
j
tion(SHG).Forelectricdipoleprocesses,thepolarization
Pi =χ(ij2k)EjEk is obtainedfroma thirdranksusceptibil- I(2ω)=A×|eˆi(2ω)χ(ij2k)eˆj(ω)eˆk(ω)|2I(ω)2 (1)
ity tensor χ(2) that vanishes under inversion symmetry.
ijk whereAisaconstantdeterminedbytheexperimentalge-
Therefore dipole induced SHG is forbidden in bulk crys-
ometry, eˆis the polarizationof the incoming oroutgoing
tals with inversionsymmetry and is only allowed at sur-
photons, I(ω) is the intensity of the incident beam and
faces or interfaceswhere inversionsymmetry is necessar-
χ(2) is a 27 component tensor. Application of C sym-
ilybroken[19]. However,highermultipolebulkcontribu- ijk 3v
tionstoSHGarestillallowedevenininversionsymmetric metry reduces χ(2) to four non-zero independent com-
ijk
systems, which can obscure the surface dipole contribu- ponents χ = −χ = −χ , χ = χ , χ =
xxx xyy yxy zxx zyy xxz
tion. Therefore it is unclear that SHG can be used as a χ andχ . Bycontrollingtherelativeorientationbe-
yyz zzz
surfaceorinterfacesensitiveprobeforaparticularmate- tween the beam polarizations and crystal axes as shown
2
c( 2 ) = 0
(a) (c) P - P (d) S - P (e) P - S (f) S - S
in out in out in out in out
w) 0.4 121200 60 f 0.10.515 121200 60 0.106.16 121200 60 0.008.08 112200 60
w(1y11) xfP S 2w t = 0 minmaxI (2) / I (2wpp 0000....2240000000......024024180 242040 300 00000000.....11001.00000000.......0555000100110500505180 242400 300 000000...100. 00000068.....80000108086180 242400 300 000000...000.000000844.....0000004804180 242400 300 00
(b) Bi Se (111) (g) (h) (i) (j)
2 3
120 120 120 120
Se n 2w) 1.01.0 120 60 0.40.4 120 60 0.40.4 120 60 0.20.2 120 60
yBi t = 200 mi maxI (2) / I (wpp 0100 ....005500100.....05005180 242400 300 00 0000 ....402200000.....02024180 242400 300 00 0000....024200000.....02402180 242400 300 00 0000 ....012100000.....01012180 242400 300 00
x
z
FIG. 1: (a) Schematic of the SHG experimental geometry. Surface and bulk regions are colored white and gray respectively.
(b) Crystal structure of the Bi2Se3 (111) surface showing the topmost Se layer and underlying Bi layer. (c) Normalized SHG
intensity I(2ω) from the (111) surface of Bi2Se3 measured as a function of azimuthal angle φ between the bisectrix (11¯2) and
the scattering plane. Measurements taken immediately after cleavage in Pin-Pout, (d) Sin-Pout, (e) Pin-Sout and (f) Sin-Sout
incident and outgoing photon polarization geometries. Panels (g) to (j) shows analogous scans measured 200 minutes after
sample cleavage. All datasets are normalized to themaximum intensitymeasured at t=200 mins in Pin-Pout geometry. The
fewer data points in the early time scans is due to the need for faster data collection. Solid red lines are theoretical fits to
Eqn.(2) [21].
in Fig.1(a),components describing the in-plane and out- nating from the Se-Bi bonds, which have a 3-fold sym-
of-plane electrical responses can be isolated via: metric arrangement. A fit of equations (2) to the SHG
patterns measured at a given time after cleavage using
a single set of susceptibility tensor elements [21] yields
IPP(2ω) = A×|a(3)−0.025a(1)cos(3φ)|2 excellent agreement[Figs.1(c)-(f) & Figs.1(g)-(j)], which
I (2ω) = A×|a(2)+0.016a(1)cos(3φ)|2 showsthat the data is consistentwith surface SHG from
SP
Bi Se .
I (2ω) = A×|0.020a(1)sin(3φ)|2 2 3
PS
I (2ω) = A×|0.013a(1)sin(3φ)|2 (2) ToprovethatthesurfacecontributiontoSHGisdomi-
SS
nant,westudyitsresponsetochangesinthesurfacecar-
where the first and second sub-indices of I(2ω) denote rier concentration. It is known from angle-resolved pho-
the input and output polarizations respectively, φ is the toemission spectroscopy (ARPES) [22] that after cleav-
angle between the scattering plane and the mirror (xz) agethesurfaceelectronconcentrationofBi Se increases
2 3
plane of the crystal surface, a(1) ≡ χ is an in-plane monotonicallyoveranhourslongtimescalebeforestabi-
xxx
responseanda(2) ≡0.061χ anda(3) ≡−0.007χ + lizing. To study the effect ofthis surfaceelectrondoping
zxx xxz
0.096χ +0.002χ are out-of-plane responses [21]. onSHGwemeasureitstimedependenceimmediatelyaf-
zxx zzz
Figure 1 shows the φ dependence of SHG intensity ter cleavage. Figure 1(c)-(j) shows a clear change in the
from the (111) surface of Bi Se measured under dif- magnitudeofallSHGpatternsbetweent=0andt=200
2 3
ferent polarization geometries. The experiments were mins but no change in their rotational symmetry, which
performed in air at room temperature and data were precludes a trigonal symmetry breaking atomic recon-
taken both immediately after and 200 minutes after the struction. Toinvestigatethepossibilityofsurfaceatomic
sample was cleaved. The time (t) dependence of the displacements that preserve overall trigonal symmetry
SHG patterns is related to surface charging as discussed such as a change of inter-layerdistance, which would af-
later in the text. The SHG patterns exhibit a 6-fold fect the in- and out-of-plane susceptibilities differently,
or 3-fold rotational symmetry depending on whether S- we compare the complete time dependence of SHG in-
or P-polarized output photons are selected respectively. tensities under different linear polarization geometries.
Because S-polarized light only has in-plane electric-field Figure 2 shows that different combinations of suscepti-
components, it is only sensitive to the in-plane response bility components all undergo the same monotonic in-
a(1) likely originating from anharmonic polarizability of crease by as much as 400% between t = 0 and t = 50
Se-Se bonds [Fig.1(b)], which have a 6-fold symmetric mins following cleavage, after which they saturate to a
arrangement. On the other hand, because P-polarized value that remains constant out to at least 600 mins,
light contains an electric-field component along zˆ, it is a trend highly consistent with the evolution of the sur-
sensitive to out-of-plane responses a(2) and a(3) origi- face Fermilevelobservedusing ARPES[22]. To rule out
3
(a) P - P (b) S - P (a) Surface molecular doping (b) SHG active regions
in out in out
maxI (2) / I (2ww)pp 011000Y Axis Title......000011202864......246802 0060 50 0110000 150 220000 250 0000.Y Axis Title...30000421....1234 0060 50 0110000 150 220000 250 maxI (2) / I (2ww)pp 00000.....Y Axis Title1122200000.....260481122226048 9300 P Bi2 O S2e3 S (c EEE)CFV 2O 2AirO
(c) PX A-xis STitle (d) SX A x-is TSitle
in out in out 00 50 110000 150 220000 250 c(3)E¹ 0
maxI (2) / I (2ww)pp 000Y Axis Title...000342...234 9300 01Y Axis Title0000011......02468000PP0PS 6230X A0x0is Title PPPS4069001nnoorrmm50 000000......Y Axis Title111100000000......642086001111680246 9300 00..06Y Axis Title0000....0246100SS0SP 302X0 Ax0is Title SS4PS0103n0onromr5m0 tbFmOiuIo2eGln.aks.gAuce3oro:ensmdidm(ueaintic)lrtaiPiSerosienn.dle-eb(ScTcbatorime)nXeud AadteSxis scp( temThmiiotlmeewilinnamea)irmsaizdtuaaiectmlpsiooeonfn(EodtgbheCense)oetermavnpcneee(e 2dtd r)a=rgkyb iy0nuaielnfokvtttoeevhrlnauesclrteilitenopyacncove( 2cl io)a¹unbfrr gai0tvznhaiendes-
00 50 Ti1Xm1 0A00x0eis T i(tlem150in)220000 250 00 50 TiX1m1 A000xei0s T i(tlem150in) 220000 250 maximum (EV) relative to the Fermi level (EF) as a func-
tion of distance to the O2 or (c) air covered surface. Typical
Bi2Se3 samples show bulk conducting character (EF > EC)
FIG. 2: Normalized SHG intensity along high symmetry di-
owing to Se vacancies [9, 22]. The gray, white and yellow re-
rectionsofthe(111)surfaceBrillouinzoneofBi2Se3measured
gions correspond tothebulk,accumulation layerand surface
as a function of time after cleavage in air with (a) Pin-Pout,
(b) Sin-Pout, (c) Pin-Sout and (d) Sin-Sout photon polariza- of Bi2Se3. Schematic of the bulk (black) and surface (red)
band structureis drawn near thesurface region.
tion geometries. Insets in panels (c) and (d) show the time
evolution of peak intensities measured starting 100 minutes
after cleavage in air, prior to which the sample was not ex-
in an O environment. We find that the SHG inten-
posed to laser light. 2
sity exhibits an initial fast upturn reaching about 50%
of the saturation intensity value in air, followed by a
gradual decrease back to its initial value. These results
photo-inducedeffects,weperformedtimedependenceex-
show that electron transfer from the Bi Se surface to
periments without exposing the sample to light for the O molecules takesplace only after some2fini3te E~ hasde-
first100minsaftercleavage. Inthiscasewefindthatthe 2
veloped, and that O can restore the surface back to an
SHG intensities remain constant at the previous satura- 2
un-charged(E~=0)statebutcannotholedopebeyondthis
tion values [insets Fig.2(c) & (d)], which indicates that
the initial rise in SHG intensity is purely a surface dop- state. ThesebehaviorsareconsistentwithE~arisingfrom
ing effect and not a photo-induced effect [23–25]. Such the migration of negatively charged Se vacancies to the
large percentage changes in SHG intensity with surface surface,whichactstolowerthesurfaceenergyofthetop-
electron doping suggest that SHG comes predominantly most Se layer. Assuming that charge transfer only takes
from electrons at the surface. place when an O2 molecule is adsorbed at a surface Se
vacancysite,noadditionalholedopingwilloccuronceall
Microscopically the increased surface carrier concen-
vacancies are occupied. Such a mechanism naturally ex-
tration affects SHG intensity through the perpendicular
surface electric field E~ that it creates. SHG is highly plainstheslowtimescaleonwhichE~ develops,aswellas
why the same behavioris observedregardlessofwhether
sensitive to a static electric field because it breaks in-
the sample is cleavedin air or in ultra-highvacuum [22].
version symmetry over the region that it penetrates,
which is typically around 20 ˚A for metallic Bi Se [26]. Havingestablishedanopticalmethodtoprobethespa-
2 3
tial symmetry and Fermi level of the surface electrons
Electric-field induced SHG is commonly observed in
of Bi Se , we consider how SHG can be used to mon-
the context of metal/electrolyte interfaces, and is the- 2 3
itor time-reversal symmetry at a topological insulator
oretically described by a third order process P (2ω) =
i
surface. It has been proposed that new time-reversal
χ(3) E (0)eˆ (ω)eˆ(ω)[19,23]thatactsinadditiontoχ(2).
ijkl j k l symmetry broken phases can be measured through the
Because χ(3) has the same symmetry constraints as χ(2) differential index of refraction of right- (R) versus left-
[21], the overallsymmetry of the SHG patterns must re- (L) circularly polarized light [6, 14, 15]. However, it is
main unchanged in the presence of E~, with each tensor known that the linear response of Bi Se to circularly-
2 3
element in equation (2) simply being enhanced by the polarized light is only sensitive to bulk electrons [16]. In
addition of a χ(3)E tensor element. To demonstrate that ordertounderstandwhethersecondharmonicversionsof
SHG is sensitive to tuning the surface Fermi levelwe de- such experiments are feasible, it is necessary to measure
posit O on the surface, which has been shown to be an the intrinsic second-order surface response of Bi Se to
2 2 3
effective electron acceptor on Bi Se (111) [27]. Figure circularly-polarizedlight.
2 3
3 shows the time dependence of I (2ω) after cleaving Second harmonic circular dichroism (CD), the differ-
PS
4
(a) L - S R - S (b) L - P R - P such bulk terms are known to be greatly suppressed rel-
in out in out in out in out
w) 00..032.3 121020 60 f RLRLSSSSFoFofifi0tftfss.e0e4.t4tccuutt 121020 60 RLRLPPPPFoFofifitftfsseettccuutt apthiovteontoensuerrfgayceexdciepeodlsarthteerbmuslkinbatnhde rgeagpim[2e8]w.hOeruertehxe-
max) / I (2pp 00..000010....0120 180 00 00..00020...002 180 00 ps(Fheorigiwmsne1nt-h3t)ai.tsWtihnehtishleuisrCfarDecgeiimscoegnetanrniebdruatlwliyoennhoiasnv-ienzederxeoep,defirdigmoumreenint4aa(lncly)t
2w 0.01.1 0.02.2 shows that it vanishes when φ is an integer multiple of
I ( 0.02.2 0.04.4 60◦, angles where the scattering plane coincides with a
0.03.3 240240 300 242040 300 mirror plane of the (111) surface. Such zeroes are pro-
(c) RS-LS RP-LP (d) tected by mirror symmetry because R- and L-polarized
RPLPcut
RSLScut light transform into one another under mirror reflection
2w) 0.02.2 0.02.2 RR RRPSPSLL--PSLLddiiffPSff ((ffiinnaall -- iinniittiiaall)) aboutthescatteringplane. Becauseamagnetizationcan
max) / I (wpp 00Y Axis Title..0010..01 00Y Axis Title..0010..01 bipnrreoCabDkemoafliortrinmogret-shryeemvseemrssepatelrcysi,yfimmcemvaaesltuurreyisnbgorfedaφekpcianargntuobrneestahfresoesmnusrizftaeivrcoee
I (2 --00..-021.1 --00.-.021.1 of Bi2Se3. Remarkably, we find that CD at a general
-0.2 t = 200 min -0.2 φ is insensitive to surface charging, as evidenced by the
00 60 112200 180 224400 300 336600 00 60 112200 180 224400 300 336600 lack of measurable change as a function of time after
f X( Adxise Titgle) f X( Adxise Titgle)
cleavage [Fig.4(d)]. This suggests that sensitive searches
fortime-reversalsymmetrybreakinginducedCDmaybe
FIG.4: Normalizedφ-dependentSHGintensitypatternsmea-
carried out without the need for careful control of sur-
sured 200 minutesafter cleavage in air under(a) left-circular
face charging, which is an important and robust way of
in (Lin) Sout and right-circular in (Rin) Sout, and (b) Lin-
studying the physics of surface doped topological insu-
PoutandRin-Poutphotonpolarizationgeometries. Solidlines
aretheoreticalfits(seetext). (c)Circulardichroism(IR−IL) latorsorburied interfacesbetween topologicalinsulators
correspondingtodatainpanels(a)and(b). (d)Differencebe- and ordinary materials [1, 2].
tweencirculardichroismmeasuredat200minutesaftercleav-
age and immediately after cleavage.
The realization of surface second harmonic genera-
tionfromBi Se andthe demonstrationofits sensitivity
2 3
ence in SHG yield using incident R- versus L-polarized to the surface Fermi level, crystal symmetry and time-
fundamental light, was measured from Bi Se 200 min- reversalsymmetry providesa novelcontact-freeprobe of
2 3
utes after cleavage in air. Figures 4(a) and (b) show the properties of a single surface of a topological insula-
thattheSHGpatternsobtainedusingR-andL-polarized tor. This will make it possible to probe the structural
incident light are clearly different for both P- and S- and electronic properties of a buried topological insula-
polarized output geometries, which are well described tor interface, and to search for exotic broken symmetry
using equation (1) with the same set of susceptibility interface phases. The use of ultrashort laser pulses will
values fitted to Figs.1(g) to (j). Although higher mul- also make it possible to selectively study time-resolved
tipole bulk contributions to SHG, which are allowed in non-equilibrium dynamics of a surface or interface fol-
inversion symmetric crystals, may contribute to CD due lowing an excitation, which for example can be applied
to an interference with the surface dipole radiation [19], to probe photo-induced spin-polarized currents.
[1] J. E. Moore, Nature464, 194 (2010). Herrero, NanoLett. (2010).
[2] M. Z. Hasan and C, L. Kane, Rev.Mod. Phys.82, 3045 [13] J. G. Checkelsky, Y. S. Hor, R. J. Cava and N. P. Ong,
(2010). <http://arxiv.org/abs/cond-mat/1003.3883> (2010).
[3] X.-L.Qi and S.-C. Zhang, Phys. Today 63, 33 (2010). [14] W.-K.TseandA.H.MacDonald, Phys.Rev.Lett.105,
[4] S.Raghu,S.B.Chung,X.-L.QiandS.-C.Zhang,Phys. 057401 (2010).
Rev.Lett. 104, 116401 (2010). [15] J. Maciejko, X.-L.Qi, H.DennisDrew andS.-C. Zhang,
[5] P. Hosur, <http://arxiv.org/abs/cond-mat/1006.5046> Phys. Rev.Lett. 105, 166803 (2010).
(2010). [16] A. B. Sushkovet al., Phys. Rev.B 82, 125110 (2010) .
[6] X.-L. Qi, T. L. Hughes and S.-C. Zhang, Phys. Rev. B [17] A. D. LaForge et al., Phys. Rev.B 81, 125120 (2010) .
78, 195424 (2008). [18] N. P. Butch et al., Phys. Rev.B 81, 241301(R) (2010).
[7] D.Hsieh et al., Nature452, 970 (2008). [19] Y.R.Shen,inTheprinciplesofnonlinearoptics,(Wiley-
[8] D.Hsieh et al., Science 323, 919 (2009). Interscience, NewYork,1984).
[9] Y.Xia et al., Nature Phys.5, 398 (2009). [20] V. Mizrahi and J. E. Sipe, J. Opt. Soc. Am. B 5 660
[10] D.Hsieh et al., Phys. Rev.Lett. 103, 146401 (2009). (1988).
[11] H.Zhang et al., NaturePhys. 5, 438 (2009). [21] Details of calculation presented in Online Auxiliary In-
[12] H. Steinberg, D. R. Gardner, Y. S. Lee and P. Jarillo- formation.
5
[22] D.Hsieh et al., Nature460, 1101 (2009). Acknowledgements. This work was supported
[23] J. Bloch, J. G. Mihaychuk and H. M. van Driel, Phys. by Department of Energy award number DE-FG02-
Rev.Lett. 77, 920 (1996). 08ER46521. D.H. is supported through a Pappalardo
[24] J. Qi, M. S. Yeganeh, I. Koltover, A. G. Yodh and W. PostdoctoralFellowship. J.W.MissupportedbyanNSF
M. Theis, Phys.Rev. Lett.71, 633 (1993).
Graduate Research Fellowship.
[25] S. A. Mitchell, T. R. Ward, D. D. M. Waynerand G. P.
Lopinski, J. Phys. Chem. B 106, 9873 (2002).
[26] J. G. Analytis et al., Phys. Rev.B 81, 205407 (2010). Authorcontributions. *D.H.andJ.W.M.contributed
[27] Y.L. Chen et al., Science 329, 659 (2010). equally to this work.
[28] F.-X.Wang et al., Phys.Rev. B 80, 233402 (2009).
