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Institut 3 E,LT,MNTCCmu,DP,1 u e atr 85 Gre 38054 martyrs des rue 17 DOPT, Campus, MINATEC LETI, CEA, ad spitdoti eea seminal several in out pointed As band. 4 h oooia ufc ttso tandHT aebe me been have HgTe strained of states surface topological The 5 ´ preetd hsqeT´oiu,Uiested Gen`e Th´eorique, Universit´e de Physique D´epartement de Cl´ement Bouvier, aoaor ePyiu,EoeNraeSpeiued Lyon Sup´erieure de Normale Ecole Physique, de Laboratoire 8 , HH 2 ycrto OEL an-ui P4,F912Gif-sur-Yv F-91192 48, BP Saint-Aubin SOLEIL, Synchrotron ad h o afo h ia oei nietesrs-a w stress-gap the inside is cone Dirac the of half top the band: 1 ohyk Ohtsubo, Yoshiyuki 8 1 adi yn . eV 0.3 lying is band rsa Meunier, Tristan Dtd uy2,2013) 22, July (Dated: 2 hlpeBallet, Philippe 1 mn Taleb-Ibrahimi, Amina 10 desbtaewihltiecntn ( constant from lattice chamber which Vacuum substrate CdTe Molecular Ultra-High [100] temperature a a low in by Epitaxy grown Beam strained were The slabs studies. insulator HgTe are topological energy spectrometer to low meV) suited (few well which resolution synchrotron[14], high and SOLEIL photons the at line applications Telluride. spintronic Mercury interpretation to strained the and using experiments to transport new critical of These are states. findings surface the experimental from coming dichroism no tangpadteohrhl nietebl Γ bulk the inside half other the and gap strain aesae hs ia on iscoet h o fthe of top the to close sur- sits strong point Γ very Dirac reveal whose states substrates face CdTe [100] epitaxially on slabs HgTe grown thick nm 100 strained mogenously the within insulating gap. truly strain is topo- which bulk three-dimensional which this states insulator to logical surface character topological metallic a are give left states ducting ev oe(Γ hole heavy togcrua ihos ftebl Γ cir- bulk find the We the measured of bands. dichroism also bulk have circular and We from strong surface way a the point. the of X dichroism all the cular enough, linear to Surprisingly is Γ dispersion point. the states Γ 8-bands the surface the to the of close in analysis discrete model found a Kane feature observa- by These confirmed unique are material. a tions insulating is the topological and band other point bulk no Dirac a the of between extremum degeneracy near This 2 e)btenteΓ the between meV) (26 6 h gei xaddhmgnul,a a hce by checked was as homogenously, θ expanded is HgTe the oe ape t10 indium- at ARPES: samples in doped observed are states electronic cupied sln steHT hcns osntexceed not does thickness HgTe the as long As . 8 − 48 h RE-aawr bando h CASSIOPEE the on obtained were ARPES-data The nti etr h xeietlAPSsetao ho- of spectra ARPES experimental the letter, this In , HH 2 )i .%lre hnbl ge( HgTe bulk than larger 0.3% is A) ˚ θ 3 enmaue o l h bands. the all for measured been ad evn n afo h ia oeisd the inside cone Dirac the of half one leaving band, 6,302Geol ee ,France 9, Cedex Grenoble 38042 166, P -a cn n eirclsaemp.Ol oc- Only maps. space reciprocal and scans X-ray ireDelplace, Pierre e H11 e`v ,Switzerland Gen`eve 4, CH-1211 ve, oe hc rgni ls otetop the to close is origin which cone, h a oteXpit h circular The X-point. the to way the srduighg-eouinARPES high-resolution using asured n NSUR62 France UMR5672, CNRS and 8 , HH 2 ad ihnti a,teol con- only the gap, this Within band. ) n arn .L´evy P. Laurent and 18 ietebto aflies half bottom the hile cm ol ee ,France 9, Cedex noble te France ette, rbdb ARPES by probed 4 8 − ai Carpentier, David 3 ih oe(Γ hole light eepeae nadto to addition in prepared were 8 1 a , LH HgTe 8 , HH n h Γ the and ) 5 8 6 = ≈ , adbut band HH a 150nm, CdTe . band. 46 A). ˚ = 8 2
−1 −1 a) b) c) ky (Å ) ky (Å ) −0.10 .0 0 .1−0.10 .0 0 .1 0.1 0.1 ) 1 eV − 0.0 0.0 (Å 08 . x 0 k
−0.1 −0.1 −
0.1 0.1
Γ ) 1 eV 8hh − 0.0 0.0 (Å 16 . x 0 k
−0.1 −0.1 − Γ 6 0.1 0.1 ) 1 eV − 0.0 0.0 (Å 24 . x 0 k
−0.1 −0.1 −
0.1 0.1 ) 1 eV − 0.0 0.0 (Å 32 . x 0 k
−0.1 −0.1 − −0.10 .0 0 .1−0.10 .0 0 .1 −1 −1 ky (Å ) ky (Å )
FIG. 1: High resolution ARPES spectra for a maximally strained [100] HgTe/vacuum interface in the vicinity of the Γ-point measured at room temperature. a) Energy-momentum intensity spectrum after background substraction. b) The second derivative of the intensity data which band positions are less faithful enhances the contrast. c) Intensity spectrum at different energies. Raw data on the left and its second derivative on the right. The cone structure has a circular section up to ≈ 0.4 eV. un-doped reference samples, in order to raise the bulk gies shown on the panel c) are circular up to energies 0.4 chemical potential. eV below the Dirac point. From the experimental slope The samples surfaces were cleaned in a dedicated Ul- of the cone structure, the surface state band velocity is 5 1 tra High Vacuum preparation chamber by a low-energy found to be vF ≈ 5 × 10 m.s− . This value agrees with Ar-ion sputtering at grazing angles to remove the sur- the lowest order expansion for the energy close to the in-situ Dirac point in the Kane model (~v ≈ α P ), where the face oxide. The sharp dots observed in the LEED F √6 spectra showed that the surface was clean enough for the parameter α ≈ 0.9 for HgTe (the Kane parameters are ARPES experiments[15]. The samples were subsequently defined in the supplementary material). The same sam- transferred to the ARPES chamber in Ultra-High Vac- ple was also probed at different incident photon energies uum. The position of the Fermi level was determined hν. Varying the incident photon energy, shifts the bind- with a reference gold sample placed on the same sample ing energy of bulk bands according to their kz dispersion. holder. Here, the cone position is unaffected, emphasizing that We first present the high-resolution spectra in the this cone structure comes from a surface state with no kz vicinity of the Γ-point for an un-doped sample. On the dispersion (see supplementary material, Fig. 1S). This is panel a) of Fig. 1, the intensity of the ARPES spec- a powerful check which discriminates between 2D and 3D trum is shown for a incident photon energy hν = 20 eV. states. Surface state spectra were also collected over the We retrieve the surface projection of the two volume va- entire Brillouin zone. In the Γ-K direction, the surface lence bands Γ8,HH and Γ6 (deep blue) and, with more state spectrum becomes diffuse at energies of 0.8 eV be- intensity, a linear cone structure, which broadens as one low the Fermi level. On the other hand, in the Γ-X direc- moves away from its apex. The second derivative spec- tion, the surface state spectra remain linear all the way trum shown on panel b) enhances the contrast in the the the X point (Supplementary material Fig. 2S), where ARPES intensity. Within the experimental accuracy the its energy is 3.4 eV below the Dirac point, i.e. well below cone apex coincide with the top of the Γ8,HH band and the Γ6 band: in this direction, the surface state robust- lies 0.1 eV below the Fermi level. On the raw ARPES ness goes well beyond the usual topological protection ar- spectrum shown in panel a) the cone structure extends guments. The ARPES spectra of doped samples are quite in the gap with a decreasing intensity, as those states are similar to the one presented in Fig. 1, i.e. the electro- populated mostly through the room-temperature thermal chemical potential at the top surface appears to be little activation. The cone section for different binding ener- 3
18 3 affected at the doping level used (10 cm− -measured by an ex-situ SIMS analysis- which is equivalent to a surface 13 2 density of 10 cm− for a 100 nm thick slab). Previous theoretical studies[21, 22] of HgTe surface states do not account quantitatively with our experimen- tal findings in some of their salient features: weak hybri- dation between surface states and the Γ8,HH valence band at small k and a Dirac point which lies very close to the top of the Γ8,HH valence band. Considering the successes of the Kane model[23], for which all the parameters[24] are known for HgTe, we computed the surface and bulk states of 2D interfaces between a maximally strained HgTe slab and vacuum (resp. CdTe) within the 8 bands (Γ6, 1/2, Γ8, 3/2, 1/2 and Γ7, 1/2) Kane model. The in- terfaces± were± described± by interpolating± smoothly over a finite width w the Kane parameters between their val- ues in HgTe for 0
IR(ǫ, k) − IL(ǫ, k) the other hand if we assume that such a relationship ex- C(ǫ, k)= . (1) ists, Wang et al. [9] have shown that the dependence of IR(ǫ, k)+ IL(ǫ, k) the ARPES polarization asymmetry on the band polar- It is plotted in Fig. 3 (the geometry is specified in the izations, hSxi and hSzi is inset) as a function of ky for kx = 0 and an incident light 2 beam at ≈ 45◦ with respect to the normal to the sample. C(ǫ,k,φ)= −a cos φhSz(ǫ, k)i +4ab sin φhSx(ǫ, k)i, (2) By symmetry, the circular dichroism must cancel in the ky = 0 plane as observed for incident photon energies for a circularly polarized light beam incident in the x-z Ekin > 15.9 eV. plane at an angle φ with respect to the normal to the The most salient features of the experimental data of sample. The matrix elements a and b depends on surface Fig. 3 are (i) the absence of dichroism from the surface symmetries of the material [9]. This formula is consis- states, signaled by the white lines (no dichroism) along tent with the experimental data of Fig.3 if the coefficient 4
Left useful comments on the ARPES analysis. This work was funded by the EU contract GEOMDISS and the ANR 0 45 -0.2 grant SemiTopo. z y x Γ -0.2 8ΗΗ
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