Ultrafast Evolution of Bulk, Surface and Surface Resonance States in Photoexcited Bi_{2}Te_{3}
Hamoon Hedayat, Davide Bugini, Hemian Yi, Chaoyu Chen, Xingjiang Zhou, Giulio Cerullo, Claudia Dallera, Ettore Carpene
UUltrafast Evolution of Bulk, Surface and Surface Resonance States inPhotoexcited Bi Te Hamoon Hedayat,
1, 2, ∗ Davide Bugini, Hemian Yi, Chaoyu Chen, Xingjiang Zhou, Giulio Cerullo, Claudia Dallera, and Ettore Carpene † IFN-CNR, Dipartimento di Fisica, Politecnico di Milano, 20133 Milan, Italy Dipartimento di Fisica, Politecnico di Milano, 20133 Milan, Italy National Lab for Superconductivity, Institute of Physics,Chinese Academy of Science, 100190 Beijing, China
We use circular dichroism (CD) in time- and angle-resolved photoemission spectroscopy(trARPES) to measure the femtosecond charge dynamics in the topological insulator (TI) Bi Te .We detect clear CD signatures from topological surface states (TSS) and surface resonance (SR)states. In time-resolved measurements, independently from the pump polarization or intensity, theCD shows a dynamics which provides access to the unexplored electronic evolution in unoccupiedstates of Bi Te . In particular, we are able to disentangle the unpolarized electron dynamics inthe bulk states from the spin-textured TSS and SR states on the femtosecond timescale. Our studydemonstrates that photoexcitation mainly involves the bulk states and is followed by sub-picosecondtransport to the surface. This provides essential details on intra- and interband scatterings in therelaxation process of TSS and SR states. Our results reveal the significant role of SRs in the subtleultrafast interaction between bulk and surface states in TIs.
1. Introduction
The increasing quest of efficient ultrafast manipula-tion of spins for applications to spintronics and quan-tum information technology has pushed the investiga-tion of sub-picosecond dynamics beyond traditional ma-terials exhibiting spin order [1–4]. Three dimensionaltopological insulators (TIs) have been the subject of suchstudies due to their conductive topological surface state(TSS), located within the bulk band gap, that hosts spin-polarized Dirac fermions [5, 6]. In TIs, the combinationof spin-orbit coupling (SOC) and time reversal symme-try results in the helical spin-order of the TSS locked tothe electron momentum, which leads to immunity againstbackscattering events [7–10]. Recent observations haverevealed that the spin-order of the TSS is not the only as-set of TIs in spintronic engineering. The unoccupied partof the Dirac cone [11–13] and the induced Rashba split-ting may open new routes for innovative devices [14–16].In addition, latest studies have reported the existenceof surface resonance (SR) states with preferential spincharacter [17–20]. SR could explain the complex inter-action between TSS and bulk states, as already observedin the mixing of TSS with bulk bands (BBs) [9, 21, 22].However, previous studies did not distinguish betweenthe sub-picosecond electron dynamics of SRs and of thenearby BBs [19, 20, 23, 24].When a TI is optically perturbed, excited electronsdecay through normally unoccupied states, including theportion of the Dirac cone above the Fermi level which isspin polarized. Thus, the electronic dynamics can be sig-nificantly affected by the spin constraints. This has moti-vated out-of-equilibrium experiments on TIs. In particu-lar, time- and angle-resolved photoemission spectroscopy(trARPES) provides valuable information on electron in- teractions [23, 25–30] as it gives access to the time evo-lution of excited carriers in the reciprocal space [31–33].However, detecting the spin degrees of freedom requiresa more sophisticated method [18, 34, 35]. One experi-mental approach is to employ circular dichroism (CD).CD-ARPES is based on the coupling between the helic-ity of the incident photons and the (total) angular mo-mentum of electrons. Here, we define CD as the nor-malized difference of the ARPES intensities measuredwith probe beams of opposite circular polarization, CD= ( I CR − I CL ) / ( I CR + I CL ), where the subscripts CR andCL refer to right and left photon helicity, respectively. Aproper interpretation of CD-ARPES can disclose relevantinformation on the spin of image potential states [36],magnetic doped TIs [37], Berry curvature in 2D materi-als [38] and on the evolution of surface localization [39].The relation between CD and spin / orbital angular mo-mentum (OAM) is highly complex [15, 24, 40–47] anda number of investigations reported that the CD signalmight be affected by other factors, e.g. the final state ef-fect and the experimental geometry [48–50]. Therefore,the definitive link between spin-orbital texture and CDrequires a comprehensive analysis and it is beyond thepurpose of this work.Here, we exploit CD-trARPES to disentangle bulk andTSS photocurrents. The separation of bulk, TSS and SRdynamics in the trARPES signal is required in order toexplain the experimental observations. We present CD-trARPES of the nonequilibrium electron and spin statesin Bi Te where only the TSS crosses the Fermi leveland the insulating bulk restricts the number of relaxationchannels. Our results demonstrate femtosecond decay ofunpolarized BBs to TSSs and SRs followed by an elec-tronic accumulation in TSS lasting several ps. The sameapproach can be generalized to study the bulk and sur-face electron dynamics in a wide class of TIs and open a a r X i v : . [ phy s i c s . a pp - ph ] F e b FIG. 1. (a)-(c) TrARPES maps of Bi Te along the ¯Γ ¯ K for selected pump-probe delays: (a) Negative (unperturbed), (b)+0 .
25 ps, (c) +1 ps. Inset (a) shows the LEED pattern. Panels (d) and (e) show the circular dichroism (CD) correspondingthe same delays of panels (b) and (c), respectively. route towards their advanced engineering for innovativeopto-electronic and spintronics applications.
2. Results and discussion
Figures 1a-c show the trARPES measurements of afreshly cleaved Bi Te sample recorded along the ¯Γ ¯ K di-rection of the Surface Brillouin Zone (SBZ) in equilibrium(a), 250 fs (b) and 1 ps (c) after excitation by linearly p-polarized pump pulses with 1.85 eV photon energy. Thelow energy electron diffraction (LEED) pattern of thesample, reported in the upper inset of Fig. 1a, confirmedthe high quality of the cleaved surface and the absenceof surface reconstruction. The Dirac-cone is clearly vis-ible in all three panels. At 250 fs delay (Fig. 1b), twounoccupied bands (B1 and B2) can be seen: one is lo-cated 0.8 eV above the Fermi level, the other at lower en-ergy has parabolic dispersion and is well-separated fromthe TSS. These unoccupied states have been widely in-vestigated in TIs, and predicted theoretically [23, 51].However, their nature is still under debate: while somestudies considered them as bulk states [23, 24], otherinvestigations suggested that these bands are SRs [20].We will demonstrate that the photoemission (PE) sig-nal is detected from both SRs and BBs, therefore, B1and B2 bands in Figs. 1b,c are the superposition of BBsand SRs. At 1 ps delay, electrons in the higher energyB1 states have almost completely relaxed, while the twobands at lower energy (B2 and TSS) are still populated,in line with the electronic dynamics of Bi Te previously reported [20, 23]. Figures 1d,e show the non-equilibriumCD measured at the same delays as in panels b and cobtained as the difference between the trARPES mapsmeasured with CR and CL light. The dichroic signal ispresent in all three excited bands, revealing the followingfeatures: (i) a nearly perfect anti-symmetric CD behav-ior with respect to the ¯Γ point, in agreement with theexpected spin symmetry of the Dirac cone [52]; (ii) theCD decreases approaching the center of the SBZ, con-sistent with the previous reports on the spin structureof the TSSs [40, 41, 53]; (iii) the opposite sign of CD inB1 and B2 with respect to the one in TSS: the signs ofCD for different bands corresponds to the time dependentone-step PE model calculation and spin-resolved ARPESmeasurements of the Bi Te unoccupied spin structure[20].We also measured CD-ARPES at several azimuthal an-gles α (see Fig. 2a and Supplementary Information [54]).Previous static spin-resolved ARPES and CD-ARPESmeasurements reported a strong hexagonal warping ofthe Dirac-cone in Bi Te [55]. The distortion of the Diraccone is amplified at larger k || and eventually creates asnowflake-shape. The warped Dirac cone leads to anout-of-plane spin component which follows a three-foldsymmetry and is maximum along ¯Γ ¯ K [53], as schemati-cally reported in Fig. 2a. The sign-reversal of CD follow-ing a sin(3 α ) law was observed experimentally [40, 41]and supported theoretically [42]. We rotated the sam-ple by α = 60 ◦ (see Fig. 2a), checked the orientationby LEED and repeated the CD-trARPES measurementsalong the direction D2 (azimuthal rotation of 60 ◦ rela-tive to D1). Figure 2c shows the results at 250 fs de- B2 [0.45 eV] B2 [0.05 eV] IRF I n t en s i t y ( no r m . ) - TSS [0.05 eV] B2 [0.25 eV] (e) CD Delay (ps) B1 [0.8 eV] + (a) (c)D2(b)D1 E - E F ( e V ) -0.70.7 ++ - K || (10 -2 ¯ -1 ) -0.50.5 -- + E F D E K ||, G-K D1 K || , G - M E - D2 a Figure 1: A network graph.This is an .EPS to .PDF converter, using a minimal L A TEX document. Placethe .EPS file in the same folder as this converter. Insert the .EPS figure nameinside the curly brackets (in this case rnetwork2).Copy and paste the following code to convert more images at the same time:1
FIG. 2. (a) Schematic representation of the out-of-plane component of spin-OAM texture [20, 41]. Red (green) color indicatesthe outward (inward) spin direction. The colored symbols mark relevant energy-momentum frame whose dynamics is shown inpanels (d)-(e). Inset displays the rotation angles α and θ . Panels (b) and (c) show the CD-ARPES map of the sample orientedalong D1 and D2 at 250 fs delay (D1 and D2 are depicted in panel (a)). Panel (d) shows the normalized electronic dynamicsof the corresponding symbols in (a). Solid lines represent best exponential fits. IRF is the instrumental response function,corresponding to the cross-correlation of pump and probe pulses. Panel (e) shows the evolution of CD for B1, B2 and TSSstates extracted from areas shown in (a). Solid lines represent linear or exponential fits. lay and should be compared side-by-side with the D1map (Fig. 2b): the sign reversal is clear. Additionalmeasurements along other directions show consistent re-sults according to the sin(3 α ) factor and the absence ofCD along ¯Γ ¯ M or when the mirror plane of the crystalmatches the incidence plane (see Supplementary Infor-mation [54]). We observed a similar behaviour not onlyfor TSSs but also for B1 and B2. This observation indi-cates the three-fold symmetry of the CD signal of corre-sponding SR states, SR1 and SR2, since unpolarized BBsdo not contribute to the CD signal of B1 and B2. TheCD of SRs are anti-correlated with the one of the TSS,that has been predicted theoretically [17] and our investi-gation confirmed it experimentally. We deduced the CDof SRs and TSS schematically shown in Fig. 2a. In thefollowing, we elucidate the effect of photoexcitation onthe total CD. By excluding the effect of the pump pulseon the CD signal, since the other factors influencing thematrix elements remain constant, we are able to resolvethe photoemitted electrons from different bands.We will introduce the following notation: X [ En ] rep-resents the band X at a chosen binding energy En.The electronic dynamics of B1 [0 . , B2 [0 .
25 eV] andTSSs [0 .
05 eV] are extracted from the specified points ofthe band structure shown in Fig. 2a marked by squares,circles and triangles, respectively. The symbols ”+” and” × ” indicates the dynamics in the upper and lower partsof B2 (B2 [0 .
45 eV] and B2 [0 .
05 eV] ). Since all bands are symmetric with respect to the ¯Γ point, we extract theelectronic dynamics of each band by referring to the en-ergy of states, i.e. B1 [0 . is the B1 electronic statesat 0 . > .
05 eV. To fit the rise-time of TSS [0 .
05 eV] andB2 [0 .
05 eV] , we use an additional exponential componentwith larger time constants of 0 . ± . . ± . / scattering channels for electron and hole recombi-nation in an intrinsic TI [20, 59–61]. Despite the similarrise-times of TSS [0 .
05 eV] and B2 [0 .
05 eV] , the decay oc-curs on significantly different time scales of 7 . ± . . ± .
26 ps, respectively. We note that B2 [0 .
05 eV] is spin unpolarized and consequently has more scatteringchannels for relaxation with respect to TSS [0 .
05 eV] .Figure 2e shows the time evolution of CD for B1 [0 . ,B2 [0 .
25 eV] and TSSs [0 .
05 eV] . While the CD signals of W B2TSSDE (a) B2 [0.3 eV] (CD) fit B2 [0.3 eV] (CD) TSS [0.3 eV] (CD) fit TSS [0.3 eV] (CD) CD Delay(ps) I n t en s i t y ( no r m . ) Delay(ps)
Sum B2 [0.3 eV]
Dif B2 [0.3 eV]
Sum TSS [0.3 eV]
Dif TSS [0.3 eV] fit Bulk fit Surface
Bulk Surface
Figure 2: Another network graph.2
FIG. 3. Panel (a) schematically represents two angles of θ (brown) and θ (blue) where the data of (b)-(d) were measured.The black dashed window (W) shows the important energy-momentum region where B2 [0 . (red circle) and TSS [0 . (green triangle) are in the same energy level (see ∆E in Fig. 2a ). Panel (b) shows the logarithmic EDCs of θ (brown) and θ (blue) taken with circular right (thin) and circular left (thick) probe polarization. (c) The time dependent CD of B2 [0 . andTSS [0 . . Solid lines are corresponding exponential fits. (d) The dynamics of sum circular light (S) and difference circularlight (D). Solid line is corresponding fit to S and dashed line to D. the dotted Gaussian profile represents the instrumentalresponse function. B1 [0 . and TTS [0 .
05 eV] is essentially unaffected by thepump, the CD of B2 [0 .
25 eV] shows a clear rise-time. Astationary CD is consistent with the electronic dynam-ics of a spin-polarized band, since only electrons withthe proper spin orientation can occupy these states, re-sulting in a constant dichroic signal, regardless of theirnumber. Note that the experimental geometry, the sym-metry of initial and final states, the probe polarizationand photon energy remain constant during the time evo-lution. We explored various factors which can influencethe time-dependent CD induced by a linearly polarizedpump pulse in order to determine the most plausibleone. We first repeated the experiment with s-polarizedpump beam and the results confirmed similar CD dynam-ics of B2 [0 .
25 eV] (see Supplementary Information [54]).Therefore, the pump induced modification of matrix el-ements is excluded. In addition, the effect cannot beattributed to any change of the electronic population inthe B2 [0 .
25 eV] . This can be ruled out considering that,after reaching its maximum value within 600 fs from pho-toexcitation, the CD signal remains constant despite thealmost complete loss of spectral weight (compare red cir-cles in Fig. 2d and 2e at large delays). Another pos-sibility is a transient pump-induced spin polarization inB2 [0 .
25 eV] , as reported in Refs. [18, 24, 62]. However,such a photoinduced effect should be pump-polarization dependent and also appear in B1 [0 . , where the directoptical population is stronger. Therefore, we can excludesuch effect. One other scenario is the accumulation ofspin-polarized electrons in unpolarized BB due to spin-dependent decay channels. Only electrons with specificspin orientation can decay from B1 to TTS. The oppo-site spins accumulate in B2 [0 .
25 eV] which rises from B1decay. However, owing to the depolarization and scat-tering channels of BBs, a long-lived spin population inthe unpolarized B2 [0 .
25 eV] states (see Fig. 2e, red cir-cles at long delays) is improbable. The last hypothesis isthat in the probed region, we detect the superposition ofun-polarized B2 [0 .
25 eV] and polarized SR2 [0 .
25 eV] pho-toelectrons giving rise to the variations of CD.In order to confirm the last hypothesis, we analyzedCD at two specific photoemission angles θ ≈ ◦ and θ ≈ ◦ as depicted in Fig. 3a (see Fig. 2a for geometryof θ rotation). Note that B2 at θ and TSS at θ havethe same binding energy 0 . θ and θ with both CR and CL probepolarization. We emphasize that, due to energy and k || overlap, the PE signal from the surface localized SR2states is mixed with the PE signal of B2 states. The un-polarized background (i.e. the helicity-independent spec- E E F K z S S Photoexcitation (a)
Bulk to SurfaceTransport Surface IntrabandDecay e-h Recombination (b) (c) (d)
SR2TSS
BB2 e-h e-e K | e-e | phonons FIG. 4. The schematic representation of the electronic distribution after excitation of Bi Te by a linearly polarized pulse.Each panel shows the dominant process. (a) First, upon the photoexcitation, the 1.85 eV pump promotes electrons above theFermi level, hot electrons fill mainly the unoccupied BBs. (b) Electrons of BBs are rapidly scattered or transported to thesurface. (c) Intraband scaterring process in TSSs and SRs. (d) Bottom of B2 and TSS relax by electron-hole recombinationand energy transfer to phonons. tral weight) is the contribution of B2: at angle θ , it ismostly overlapped with SR2 and at θ , it overlaps withTSS [0 . . TSS [0 . is in contrast with TSS [0 .
05 eV] of Figs. 2d-e which are taken at lower energies and arewell separated from B2. Fig. 3b shows the TSS [0 . and SR2 [0 . which display opposite CD (see the differ-ent intensities of CR and CL for each EDC in the blackdashed window W). Figure 3c reports the dynamics ofCD signal for B2 [0 . and TSS [0 . . Interestingly,the CD dynamics of TSS [0 . is different with respectto the dynamics of TSS [0 . reported in Fig. 2e. Thisis because TSS at higher energies (i.e. TSS [0 . ) isstrongly superimposed to B2 [0 . . Presumably, thepresence of B2 [0 . electrons in the PE signal causes theinitial variations of the CD of TSS [0 . . To clarify thispoint, we compare the dynamics of CDs of B2 [0 . andTSS [0 . . The B2 electrons are present in both casesand we must detect a common dynamics. We fit CDsfrom B2 [0 . and TSS [0 . by an exponential func-tion obtaining similar rise-times of 93 ± [0 . un-polarized electrons since surface and bulk bands overlap.In fact, the constant CDs after about 600 fs show thatthe predominant PE signal comes from TSS [0 . andSR2 [0 . at longer delays. Therefore, the relaxation dy-namics is mostly a surface mechanism in the picosecond regime. Figure 3d compares the dynamics of B2 [0 . and TSS [0 . when taking the sum of opposite helici-ties, S= I CR + I CL , and the difference between oppositehelicities D= I CR − I CL . ”S” contains information aboutthe dynamics of B2 [0 . (i.e. the unpolarized back-ground). Fig. 3d shows that the dynamics of S is similarfor B2 [0 . and TSS [0 . (see solid symbols). Thisevidence suggests the presence of B2 electrons, a com-mon spin-degenerate dynamics in both cases. Instead,D is mainly related to the spin-polarized SR2 and TSS.The 50 fs delay between S (B2 [0 . ) and D (SR2 [0 . or TSS [0 . ) indicates that the photoexciation pre-dominantly involves bulk states. Furthermore, we findexact match between the dynamics of SR2 [0 . andTSS [0 . (open symbols). Figures 3c and 3d show thatthe unpolarized B2 can be disentangled from SRs andTSSs on the femtosecond regime. Indeed, when electronsrelax from bulk bands into the surface states, the effectof B2 in the probed region becomes less detectable. Ourresults suggest that in the measured energy-momentumwindow W, the spin-polarized surface electrons of TSSand SR2 appear with a delay after perturbation, thendwell at the surface for the entire relaxation process.These findings allow us to differentiate the complexdynamics of TSSs, SRs and BBs. Although some re-cent studies focused on the spin decay behavior in TIs, acomplete dynamical view of the electronic redistributionupon photoexcitation cannot be achieved without consid-ering the role of TSSs, SRs and BBs. Experimentally, weobserved a much faster decay of B2 states with respect toSRs and TSSs which is attributed to the 3D unpolarizednature of bulk bands with larger number of available de-cay channels. This agrees with previous studies in whichthe electron-electron scattering rate of the bulk bandsof TIs has been suggested to be an order of magnitudelarger than that of the TSSs [24]. The electronic tran-sition between states with opposite spins requires a spinflip event. As a result, some transitions are hindered.This is in line with our observation that the B2 and TSSremain almost isolated from each other apart from thezone center, where the decay channel from the bottomof B2 becomes effective. Thus, our analysis provide amore comprehensive picture of the spin-based relaxationmechanisms. In this context, Fig. 4 sketches the time-dependent electronic population and relaxation dynam-ics of Bi Te . At zero delay (Fig. 4a) the pump pulsepromotes electrons from the occupied valence bands toempty bulk states. Then, electrons of unpolarized bulkbands migrate to surface (-resonant) bands according tothe available spin states of each one. The oposite spintexture of the TSS and SR favors inter-band scatter-ing for one spin direction and forbids it for the oppo-site direction. Consequently, intra-band electron decayis enhanced with respect to inter-band relaxation andexplains the lack of interaction between SR2 and TSSduring the relaxation time (Fig. 4c). Our results demon-strate that in an intrinsic TI, Bi Te , the picosecond re-laxation process is mainly due to surface (resonant) stateswith strongly limited scattering channels. The completerelaxation occurring at long delays is explained by the en-ergy transfer from the bottom of the TSS to low energyphonons [56–58] and electron-hole recombination [30] atthe surface (Fig. 4d).
3. Conclusions
In summary, we have investigated the ultrafast elec-tronic dynamics of Bi Te combining circular dichroismwith trARPES. The results showed that the excitationwith 1.85 eV pump photon energy takes place in bulkstates, with a consequent ultrafast transport and redis-tribution of electrons in the surface. SR acts as a reser-voir to accommodate the electrons with spins opposite tothose in the TSS and plays a key role in re-establishingequilibrium. Distinguishing between bulk and surface dy-namics has a fundamental importance for TI-based spin-tronic devices. In this context, our technique directlymaps the unoccupied band structure and extracts thefemtosecond light-induced dynamics resolving differentunoccupied bands. Our study opens a new route to studythe time-dependent electronic behavior in the bulk andsurface of other TIs. We believe our results will triggerfuture theoretical and experimental studies on the SRs and their contribution to the electronic relaxation of awide class of TI compounds.
4. Methods
Single crystals of Bi Te were grown using the self-flux method. The stoichiometric mixture of high purityelements was heated to 1000 ◦ C for 12 hours and thengradually cooled down to 500 ◦ C over 100 hours beforereaching room temperature. The samples were cleaved in situ and measured in ultrahigh vacuum conditions atpressure < × − mbar and at room temperature.TrARPES experiments were conducted using a Yb-based regeneratively amplified laser system with repe-tition rate of 100 kHz. The pump (1.85 eV photon en-ergy, 30 fs pulse duration and p-polarization) and probe(6.05 eV, 65 fs) pulses, impinging on the sample at anincidence angle of about 45 ◦ , were focused to spot sizesof about 100 and 50 µ m, respectively [63]. The timeresolution of the experiment (width of the instrumen-tal response function) is about 80 fs, and the pump flu-ence ∼ µ J/cm . Photoemission (PE) spectra wererecorded using a time-of-flight (ToF) analyzer with an en-ergy resolution of about 50 meV and angular acceptanceof ∼ ◦ [64]. The angle-resolved maps were acquiredby rotating the sample’s normal with respect to the an-alyzer axis by 3 ◦ steps. CD data were obtained using a λ /4 waveplate on the probe beam to generate circularlypolarized light. The sample orientation was checked in-situ by LEED. References ∗ Current address: Institute of Physics II, University ofCologne, D-50937 Cologne, Germany † [email protected][1] A. Kirilyuk, A. V. Kimel, and T. Rasing, Ultrafast opti-cal manipulation of magnetic order, Reviews of ModernPhysics , 2731 (2010).[2] J. Mentink, J. Hellsvik, D. Afanasiev, B. Ivanov, A. Kiri-lyuk, A. Kimel, O. Eriksson, M. Katsnelson, and T. Ras-ing, Ultrafast spin dynamics in multisublattice magnets,Physical Review Letters , 057202 (2012).[3] E. Carpene, H. Hedayat, F. Boschini, and C. Dallera, Ul-trafast demagnetization of metals: Collapsed exchangeversus collective excitations, Physical Review B ,174414 (2015).[4] T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. M¨ahrlein,T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, andR. Huber, Coherent terahertz control of antiferromag-netic spin waves, Nature Photonics , 31 (2011).[5] J. E. Moore, The birth of topological insulators, Nature , 194 (2010).[6] D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, A topological dirac insulator ina quantum spin hall phase, Nature , 970 (2008).[7] P. Roushan, J. Seo, C. V. Parker, Y. S. Hor, D. Hsieh,D. Qian, A. Richardella, M. Z. Hasan, R. J. Cava, andA. Yazdani, Topological surface states protected frombackscattering by chiral spin texture, Nature , 1106(2009).[8] Z. Alpichshev, J. Analytis, J.-H. Chu, I. R. Fisher,Y. Chen, Z.-X. Shen, A. Fang, and A. Kapitulnik, Stmimaging of electronic waves on the surface of Bi Te :topologically protected surface states and hexagonalwarping effects, Physical Review Letters , 016401(2010).[9] T. Zhang, P. Cheng, X. Chen, J.-F. Jia, X. Ma, K. He,L. Wang, H. Zhang, X. Dai, Z. Fang, X. Xie, and Q.-K.Xue, Experimental demonstration of topological surfacestates protected by time-reversal symmetry, Physical Re-view Letters , 266803 (2009).[10] C. Pauly, G. Bihlmayer, M. Liebmann, M. Grob,A. Georgi, D. Subramaniam, M. R. Scholz, J. S´anchez-Barriga, A. Varykhalov, S. Bl¨ugel, O. Rader, andM. Morgenstern, Probing two topological surface bandsof sb te by spin-polarized photoemission spectroscopy,Physical Review B , 235106 (2012).[11] J. A. Sobota, S.-L. Yang, A. F. Kemper, J. J. Lee, F. T.Schmitt, W. Li, R. G. Moore, J. G. Analytis, I. R. Fisher,P. S. Kirchmann, T. P. Devereaux, and Z.-X. Shen, Directoptical coupling to an unoccupied dirac surface state inthe topological insulator Bi Se , Physical Review Letters , 136802 (2013).[12] D. Bugini, F. Boschini, H. Hedayat, H. Yi, C. Chen,X. Zhou, C. Manzoni, C. Dallera, G. Cerullo, andE. Carpene, Ultrafast spin-polarized electron dynamics inthe unoccupied topological surface state of Bi Se , Jour-nal of physics. Condensed matter: an Institute of Physicsjournal (2017).[13] D. Niesner, T. Fauster, S. V. Eremeev, T. V. Men-shchikova, Y. M. Koroteev, A. P. Protogenov, E. V.Chulkov, O. E. Tereshchenko, K. A. Kokh, O. Alekperov,A. Nadjafov, and N. Mamedov, Unoccupied topologicalstates on bismuth chalcogenides, Physical Review B ,205403 (2012).[14] Z.-H. Zhu, G. Levy, B. Ludbrook, C. N. Veenstra, J. A.Rosen, R. Comin, D. Wong, P. Dosanjh, A. Ubaldini,P. Syers, N. P. Butch, J. Paglione, I. S. Elfimov, andA. Damascelli, Rashba spin-splitting control at the sur-face of the topological insulator Bi Se , Physical ReviewLetters , 186405 (2011).[15] M. S. Bahramy, P. King, A. de la Torre, J. Juul Chang,M. Shi, L. Patthey, G. Balakrishnan, P. Hofmann,R. Arita, N. Nagaosa, and F. Baumberger, Emergentquantum confinement at topological insulator surfaces,Nature Communications , 1159 (2012).[16] L. A. Wray, S.-Y. Xu, Y. Xia, D. Hsieh, A. V. Fe-dorov, Y. San Hor, R. J. Cava, A. Bansil, H. Lin, andM. Z. Hasan, A topological insulator surface under strongcoulomb, magnetic and disorder perturbations, NaturePhysics , 32 (2011).[17] M. Nurmamat, E. E. Krasovskii, K. Kuroda, M. Ye,K. Miyamoto, M. Nakatake, T. Okuda, H. Namatame,M. Taniguchi, E. V. Chulkov, K. A. Kokh, O. E.Tereshchenko, and A. Kimura, Unoccupied topologicalsurface state in Bi Te Se, Physical Review B , 081301(2013). [18] C. Cacho, A. Crepaldi, M. Battiato, J. Braun, F. Cilento,M. Zacchigna, C. Richter, O. Heckmann, E. Springate,Y. Liu, S. Dhesi, H. Berger, P. Bugnon, K. Held, M. Gri-oni, H. Ebert, K. Hricovini, J. Minar, and F. Parmigiani,Momentum-resolved spin dynamics of bulk and surfaceexcited states in the topological insulator Bi Se , Physi-cal Review Letters , 097401 (2015).[19] C. Jozwiak, J. A. Sobota, K. Gotlieb, A. F. Kemper,C. R. Rotundu, R. J. Birgeneau, Z. Hussain, D.-H. Lee,Z.-X. Shen, and A. Lanzara, Spin-polarized surface reso-nances accompanying topological surface state formation,Nature Communications , 13143 (2016).[20] J. S´anchez-Barriga, M. Battiato, M. Krivenkov, E. Go-lias, A. Varykhalov, A. Romualdi, L. V. Yashina,J. Min´ar, O. Kornilov, H. Ebert, K. Held, and J. Braun,Subpicosecond spin dynamics of excited states in thetopological insulator Bi Te , Physical Review B ,125405 (2017).[21] Y. Ishida, H. Kanto, A. Kikkawa, Y. Taguchi, Y. Ito,Y. Ota, K. Okazaki, W. Malaeb, M. Mulazzi, M. Okawa,S. Watanabe, C.-T. Chen, M. Kim, C. Bell, Y. Kozuka,H. Y. Hwang, Y. Tokura, and S. Shin, Common origin ofthe circular-dichroism pattern in angle-resolved photoe-mission spectroscopy of SrTiO and Cu x Bi Se , PhysicalReview Letters , 077601 (2011).[22] C. Seibel, H. Bentmann, J. Braun, J. Min´ar, H. Maaß,K. Sakamoto, M. Arita, K. Shimada, H. Ebert, andF. Reinert, Connection of a topological surface state withthe bulk continuum in Sb Te (0001), Physical ReviewLetters , 066802 (2015).[23] M. Hajlaoui, E. Papalazarou, J. Mauchain, G. Lantz,N. Moisan, D. Boschetto, Z. Jiang, I. Miotkowski,Y. Chen, A. Taleb-Ibrahimi, L. Perfetti, and M. Marsi,Ultrafast surface carrier dynamics in the topological in-sulator Bi Te , Nano Letters , 3532 (2012).[24] J. S´anchez-Barriga, E. Golias, A. Varykhalov, J. Braun,L. Yashina, R. Schumann, J. Min´ar, H. Ebert, O. Ko-rnilov, and O. Rader, Ultrafast spin-polarization controlof dirac fermions in topological insulators, Physical Re-view B , 155426 (2016).[25] J. Reimann, J. G¨udde, K. Kuroda, E. Chulkov, andU. H¨ofer, Spectroscopy and dynamics of unoccupied elec-tronic states of the topological insulators Sb Te andSb Te s, Physical Review B , 081106 (2014).[26] J. A. Sobota, S. Yang, J. G. Analytis, Y. Chen, I. R.Fisher, P. S. Kirchmann, and Z.-X. Shen, Ultrafast opti-cal excitation of a persistent surface-state population inthe topological insulator Bi Se , Physical Review Letters , 117403 (2012).[27] M. Hajlaoui, E. Papalazarou, J. Mauchain, L. Per-fetti, A. Taleb-Ibrahimi, F. Navarin, M. Monteverde,P. Auban-Senzier, C. Pasquier, N. Moisan, D. Boschetto,M. Neupane, M. Z. Hasan, T. Durakiewicz, Z. Jiang,Y. Xu, I. Miotkowski, Y. Chen, S. Jia, and M. Marsi,Tuning a schottky barrier in a photoexcited topologicalinsulator with transient dirac cone electron-hole asym-metry, Nature Communications (2014).[28] Y. Wang, D. Hsieh, E. Sie, H. Steinberg, D. Gard-ner, Y. Lee, P. Jarillo-Herrero, and N. Gedik, Measure-ment of intrinsic dirac fermion cooling on the surface ofthe topological insulator Bi Se using time-resolved andangle-resolved photoemission spectroscopy, Physical Re-view Letters , 127401 (2012).[29] A. Crepaldi, B. Ressel, F. Cilento, M. Zacchigna, C. Grazioli, H. Berger, P. Bugnon, K. Kern, M. Grioni,and F. Parmigiani, Ultrafast photodoping and effectivefermi-dirac distribution of the dirac particles in Bi Se ,Physical Review B , 205133 (2012).[30] F. Freyse, M. Battiato, L. Yashina, and J. S´anchez-Barriga, Impact of ultrafast transport on the high-energystates of a photoexcited topological insulator, PhysicalReview B , 115132 (2018).[31] H. Hedayat, A. Ceraso, G. Soavi, S. Akhavan, A. Cadore,C. Dallera, G. Cerullo, A. Ferrari, and E. Carpene, Non-equilibrium band broadening, gap renormalization andband inversion in black phosphorus, arXiv:2007.09754(2020).[32] H. Hedayat, C. J. Sayers, D. Bugini, C. Dallera,D. Wolverson, T. Batten, S. Karbassi, S. Friedemann,G. Cerullo, J. van Wezel, et al. , Excitonic and latticecontributions to the charge density wave in 1 t -TiSe re-vealed by a phonon bottleneck, Physical Review Research , 023029 (2019).[33] H. Hedayat, C. J. Sayers, A. Ceraso, J. van Wezel,S. R. Clark, C. Dallera, G. Cerullo, E. Da Como,and E. Carpene, Investigation of the non-equilibriumstate of strongly correlated materials by complemen-tary ultrafast spectroscopy techniques, arXiv preprintarXiv:2012.02660 (2020).[34] X. Zhou, C. Fang, W.-F. Tsai, and J. Hu, Theory ofquasiparticle scattering in a two-dimensional system ofhelical dirac fermions: Surface band structure of a three-dimensional topological insulator, Physical Review B ,245317 (2009).[35] W.-C. Lee, C. Wu, D. P. Arovas, and S.-C. Zhang, Quasi-particle interference on the surface of the topological in-sulator Bi Te , Physical Review B , 245439 (2009).[36] T. Nakazawa, N. Takagi, M. Kawai, H. Ishida, andR. Arafune, Rashba splitting in an image potential stateinvestigated by circular dichroism two-photon photoe-mission spectroscopy, Physical Review B , 115412(2016).[37] T. Yilmaz, G. D. Gu, E. Vescovo, K. Kaznatcheev, andB. Sinkovic, Photon energy and polarization-dependentelectronic structure of Cr-doped Bi Se , Phys. Rev. Ma-terials , 024201 (2020).[38] M. Sch¨uler, U. De Giovannini, H. H¨ubener, A. Rubio,M. A. Sentef, and P. Werner, Local berry curvature sig-natures in dichroic angle-resolved photoelectron spec-troscopy from two-dimensional materials, Science Ad-vances , eaay2730 (2020).[39] T. Kondo, Y. Nakashima, Y. Ishida, A. Kikkawa,Y. Taguchi, Y. Tokura, and S. Shin, Visualizing theevolution of surface localization in the topological stateof Bi Se by circular dichroism in laser-based angle-resolved photoemission spectroscopy, Physical Review B , 241413 (2017).[40] Y. Wang, D. Hsieh, D. Pilon, L. Fu, D. Gardner,Y. Lee, and N. Gedik, Observation of a warped helicalspin texture in Bi Se from circular dichroism angle-resolved photoemission spectroscopy, Physical ReviewLetters , 207602 (2011).[41] W. Jung, Y. Kim, B. Kim, Y. Koh, C. Kim,M. Matsunami, S.-i. Kimura, M. Arita, K. Shimada,J. H. Han, et al. , Warping effects in the band andangular-momentum structures of the topological insula-tor Bi Te , Physical Review B , 245435 (2011).[42] H. Mirhosseini and J. Henk, Spin texture and circu- lar dichroism in photoelectron spectroscopy from thetopological insulator Bi Te : first-principles photoemis-sion calculations, Physical Review Letters , 036803(2012).[43] S. R. Park, J. Han, C. Kim, Y. Y. Koh, C. Kim, H. Lee,H. J. Choi, J. H. Han, K. D. Lee, N. J. Hur, et al. , Chi-ral orbital-angular momentum in the surface states ofBi Se , Physical Review Letters , 046805 (2012).[44] M. Scholz, J. S´anchez-Barriga, D. Marchenko,A. Varykhalov, A. Volykhov, L. Yashina, and O. Rader,High spin polarization and circular dichroism oftopological surface states on Bi Te , arXiv preprintarXiv:1108.1053 (2011).[45] H. Hedayat, D. Bugini, H. Yi, C. Chen, X. Zhou,G. Cerullo, C. Dallera, and E. Carpene, Femtosecond dy-namics of spin-polarized electrons in topological insula-tors, IEEE Magnetics Letters , 1 (2018).[46] K. Sumida, T. Natsumeda, K. Miyamoto, I. V. Silkin,K. Kuroda, K. Shirai, S. Zhu, K. Taguchi, M. Arita,J. Fujii, A. Varykhalov, O. Rader, V. A. Golyashov, K. A.Kokh, O. E. Tereshchenko, E. V. Chulkov, T. Okuda, andA. Kimura, Enhanced surface state protection and bandgap in the topological insulator PbBi Te S , PhysicalReview Materials , 104201 (2018).[47] C.-Z. Xu, Y. Liu, R. Yukawa, L.-X. Zhang, I. Mat-suda, T. Miller, and T.-C. Chiang, Photoemission cir-cular dichroism and spin polarization of the topologicalsurface states in ultrathin Bi Te films, Physical ReviewLetters , 016801 (2015).[48] M. Mulazzi, G. Rossi, J. Braun, J. Min´ar, H. Ebert,G. Panaccione, I. Vobornik, and J. Fujii, Understand-ing intensities of angle-resolved photoemission with cir-cularly polarized radiation from a cu (111) surface state,Physical Review B , 165421 (2009).[49] Z.-H. Zhu, C. Veenstra, G. Levy, A. Ubaldini, P. Syers,N. Butch, J. Paglione, M. Haverkort, I. Elfimov, andA. Damascelli, Layer-by-layer entangled spin-orbital tex-ture of the topological surface state in Bi Se , PhysicalReview Letters , 216401 (2013).[50] J. S´anchez-Barriga, A. Varykhalov, J. Braun, S.-Y.Xu, N. Alidoust, O. Kornilov, J. Min´ar, K. Hummer,G. Springholz, G. Bauer, R. Schumann, L. V. Yashina,H. Ebert, M. Z. Hasan, and O. Rader, Photoemissionof Bi Se with circularly polarized light: Probe of spinpolarization or means for spin manipulation?, PhysicalReview X , 011046 (2014).[51] G. Zhou and D. Wang, Few-quintuple Bi Te nanofilmsas potential thermoelectric materials, Scientific Reports , 8099 (2015).[52] S. Basak, H. Lin, L. Wray, S.-Y. Xu, L. Fu, M. Hasan,and A. Bansil, Spin texture on the warped dirac-conesurface states in topological insulators, Physical ReviewB , 121401 (2011).[53] J. S´anchez-Barriga, M. Scholz, E. Golias, E. Rienks,D. Marchenko, A. Varykhalov, L. Yashina, and O. Rader,Anisotropic effect of warping on the lifetime broadeningof topological surface states in angle-resolved photoemis-sion from Bi Te , Physical Review B , 195413 (2014).[54] H. Hedayat, D. Bugini, H. Yi, C. Chen, X. Zhou,G. Cerullo, C. Dallera, and E. Carpene, Supplementaryinformation at //doi.org/xxx, Scientific Reports (2021).[55] L. Fu, Hexagonal warping effects in the surface states ofthe topological insulator Bi Te , Physical Review Letters , 266801 (2009). [56] A. Tamt¨ogl, P. Kraus, N. Avidor, M. Bremholm, E. M. J.Hedegaard, B. B. Iversen, M. Bianchi, P. Hofmann,J. Ellis, W. Allison, G. Benedek, and W. E. Ernst,Electron-phonon coupling and surface debye temperatureof Bi Te (111) from helium atom scattering, PhysicalReview B , 195401 (2017).[57] J. A. Sobota, S.-L. Yang, D. Leuenberger, A. F. Kem-per, J. G. Analytis, I. R. Fisher, P. S. Kirchmann, T. P.Devereaux, and Z.-X. Shen, Distinguishing bulk and sur-face electron-phonon coupling in the topological insulatorBi Se using time-resolved photoemission spectroscopy,Physical Review Letters , 157401 (2014).[58] C. Luo, H. J Wang, S. A Ku, H.-J. Chen, T.-T. Yeh, J.-Y.Lin, K. Wu, J.-Y. Juang, B.-L. Young, T. Kobayashi, C.-M. Cheng, C.-H. Chen, K.-D. Tsuei, R. Sankar, F. Chou,K. Kokh, O. Tereshchenko, E. V Chulkov, Y. Andreev,and G. Gu, Snapshots of dirac fermions near the diracpoint in topological insulators, Nano Letters , 5797(2013).[59] A. Sterzi, G. Manzoni, L. Sbuelz, F. Cilento, M. Zac-chigna, P. Bugnon, A. Magrez, H. Berger, A. Crepaldi,and F. Parmigiani, Bulk diffusive relaxation mechanismsin optically excited topological insulators, Physical Re-view B , 115431 (2017).[60] S. Zhu, Y. Ishida, K. Kuroda, K. Sumida, M. Ye,J. Wang, H. Pan, M. Taniguchi, S. Qiao, S. Shin, et al. ,Ultrafast electron dynamics at the dirac node of thetopological insulator Sb Te , Scientific Reports , 13213(2015).[61] H. Hedayat, D. Bugini, H. Yi, C. Chen, X. Zhou,G. Cerullo, C. Dallera, and E. Carpene, Surface state dy-namics of topological insulators investigated by femtosec-ond time-and angle-resolved photoemission spectroscopy,Applied Sciences , 694 (2018).[62] D. Hsieh, F. Mahmood, J. W. McIver, D. R. Gardner,Y. S. Lee, and N. Gedik, Selective probing of photoin-duced charge and spin dynamics in the bulk and surfaceof a topological insulator, Physical Review Letters ,077401 (2011).[63] F. Boschini, H. Hedayat, C. Dallera, P. Farinello, C. Man-zoni, A. Magrez, H. Berger, G. Cerullo, and E. Carpene,An innovative yb-based ultrafast deep ultraviolet sourcefor time-resolved photoemission experiments, Review ofScientific Instruments , 123903 (2014).[64] E. Carpene, E. Mancini, C. Dallera, G. Ghiringhelli,C. Manzoni, G. Cerullo, and S. De Silvestri, A versatile apparatus for time-resolved photoemission spectroscopyvia femtosecond pump-probe experiments, Review of Sci-entific Instruments , 055101 (2009). Acknowledgments
E. C. and H. H. acknowledge support from PRIN2017 − Author contributions
E. C., G. C. and C. D. conceived and coordinated theproject. H. H. and D. B. performed the CD and trARPESexperiments. H. Y., C. C. and X. J. Z synthesized Bi Te single crystals. H. H. and E.C. analyzed the data andwrote the manuscript with contribution from all authors.All authors reviewed the manuscript and discussed theresults. Competing interests
Te authors declare no competing interests.
Additional information
Supplementary information is available for this pa-per at https://doi.org/xxx