Dirac cone in a non-honeycomb surface alloy
Pampa Sadhukhan, Dhanshree Pandey, Vipin Kumar Singh, Shuvam Sarkar, Abhishek Rai, Kuntala Bhattacharya, Aparna Chakrabarti, Sudipta Roy Barman
DDirac cone in a non-honeycomb surface alloy
Pampa Sadhukhan , Dhanshree Pandey , , Vipin Kumar Singh , Shuvam Sarkar ,Abhishek Rai , Kuntala Bhattacharya , Aparna Chakrabarti , and Sudipta Roy Barman UGC-DAE Consortium for Scientific Research, Khandwa Road, Indore 452001, Madhya Pradesh, India Homi Bhabha National Institute, Training School Complex,Anushakti Nagar, Mumbai 400094, Maharashtra, India Theory and Simulations Laboratory, Raja Ramanna Centre forAdvanced Technology, Indore 452013, Madhya Pradesh, India and Department of Physics, Indian Institute of Space Science and Technology, Thiruvananthapuram 695547, Kerala, India
We demonstrate unexpected occurrence of linear bands resembling Dirac cone at the zone-center ofAu Sn surface alloy with ( ) surface structure formed by deposition of about 0.9 ML Sn on Au(111)at elevated temperature. The surface exhibits an oblique symmetry with unequal lattice constantsmaking it the first two dimensional surface alloy to exhibit Dirac cone with a non-honeycomb lattice.
Since the discovery of graphene[1, 2], fabrication ofatomically thin two dimensional (2D) materials withnontrivial band topology has attracted enormous atten-tion primarily because of their dissipationless conduc-tion. This led to the discovery of a family of 2D quan-tum materials with exotic properties; for example, tomention a few are stanene[3], silicene[4], aluminene[5],borophene[6] and phosphorene[7]. In particular, the pre-diction of stanene[3], a buckled tin honeycomb layer, tobe a quantum spin Hall insulator with Dirac cone-like lin-ear energy dispersion and a large gap of 0.3 eV has stirredup efforts to realize it on substrates. The first experimen-tal synthesis of stanene was obtained by molecular beamepitaxy on Bi Te substrate[8]. Recently, stanene with aeven larger gap of 0.44 eV was reported on InSb(111)[9].Two very recent studies[10, 11] demonstrated existenceof stanene on metal substrates. Deng et al. [10] reportedepitaxial growth of flat stanene on Cu(111) and obtained s − p band inversion as well as spin-orbit coupling (soc)induced topological gap. Yuhara et al. [11] also reportedplanar stanene on Ag Sn surface alloy on Ag(111), how-ever angle resolved photoemission (ARPES) showed aparabolic band dispersion.Gold is an interesting substrate for stanene growth. Italso exhibits a Rashba spin-orbit split surface state inthe L -gap[12, 13]. However, the existing literature of Sngrowth on Au(111) presents conflicting results. A den-sity functional theory (DFT) work predicted that a pla-nar stanene is energetically favorable[14]; while anotherstudy showed that its band structure would be modi-fied due to bonding with Au substrate[15]. In contrast,there are both experimental[16, 17] as well as theoreti-cal studies[18, 19] that show occurrence of Au-Sn surfacealloy at room temperature (RT). We have studied thegrowth of Sn on Au(111) under different conditions anddemonstrate presence of perfectly linear Dirac-like bandscrossing the Fermi level ( E F ) at the zone center (Γ) withFermi velocity comparable to graphene. The Dirac-likebands occur only in a specific Au-Sn ( ) surface al-loy phase with oblique symmetry ( γ =70.9 ◦ and b : a = √ / √
3) that is formed at high temperature, but is sta-ble when cooled to RT and has a composition of Au Sn.Our DFT calculation for a model structure, namely mod-ified Lieb lattice with oblique symmetry shows presenceof linear bands for this binary alloy.Polished and oriented Au(111) crystal was cleaned in-situ by repeated cycles of 0.5 keV Ar + ion sputteringfor 15 min followed by annealing at 673 K for about 10min. Sn was deposited using a water cooled Knudsencell[20] operated at 1078 K Low energy electron diffrac-tion (LEED) was performed using a four grid rear viewoptics. The STM measurements were carried out in avariable temperature STM work station in the constantcurrent mode by applying the bias to a tungsten tip. Thecoverage has been determined from the change in slopeof the Auger electron spectroscopy signals from Sn andAu as well as by STM. The photoemission measure-ments were carried out in a separate workstation us-ing R4000 electron energy analyzer. The base pressure ofboth the workstations were better than 2 × − mbar.For ARPES, the overall energy resolution measured byfitting the Au Fermi level including RT broadening was100 meV, while the angular resolution was 1 ◦ for ac-ceptance angle of ± ◦ . The energy resolution for XPSusing monochromatized Al K α source was 0.34 eV. Thecore-level spectra have been fitted using a least square er-ror minimization procedure where Doniach- ˘ S unji´ c (DS)line shape[21] convoluted with a Gaussian function rep-resenting the instrumental broadening has been used torepresent each component.The electronic structure calculations using densityfunctional theory (DFT) have been performed by Vi-enna ab initio simulation package (VASP)[22] using theprojector augmented wave method[23]. For exchange-correlation functional, the generalized gradient approxi-mation has been employed[24]. We use an energy cutoffof 350 eV for the plane waves. The final energies havebeen calculated with a k mesh of 29 × ×
1. A vacuumregion of about 18 ˚A is considered in the z -direction.The energy and the force tolerance for our calculations a r X i v : . [ c ond - m a t . m t r l - s c i ] D ec (b)(a)(d) (e)b ac d (c) Figure 1: The low energy electron diffraction (LEED) pat-tern with 104 eV beam energy of (a) the (2113) phase ofSn/Au(111) obtained by depositing ≈ ◦ areshown by green, blue and red circles, while the white circlesrepresent their common spots that appear at (1 ×
1) position.The primitive reciprocal lattice vectors for the blue domainare marked by black dashes, while the white dashes representthose of Au(111). (d) A high resolution scanning tunnelingmicroscopy (STM) image showing one domain of the (2113)phase using tunneling current of 0.9 nA and a bias voltageof -0.3 V. The real space primitive unit cell and basis vectors(white arrows) are shown, inset shows the Fourier transformof this image. (e) Height profiles along ab (black line) and cd(red line) of (d) are compared with the height profile (greenline) along an atomic array perpendicular to the discommen-surate lines of Au(111) herringbone reconstruction. are 1 µ eV and 20 meV/˚A, respectively.The LEED pattern of ≈ T S ) of 413 K in Fig. 1(a)is completely different from the Au(111) substrate inFig. 1(b). Au(111) exhibits satellite spots around each1 × ×√ × M = ( ),the three sets of red, green and blue colored spots cor-respond to three 120 ◦ rotated domains (Fig. 1(c)). We henceforth denote this structure by (2113). The recipro-cal unit cell vectors for one of the domains and the sub-strate are shown in Fig. 1(c). If a (= a ) is the substratedirect lattice vector, the overlayer direct lattice vectorsshown by white arrows in Fig. 2(d) are b = √ × a , while b = √ × a . b ( b ) is rotated by 30 ◦ (100.9 ◦ ) withrespect to a and thus the unit cell of the overlayer isoblique with γ = 70.9 ◦ .A high resolution atomic scale STM image in Fig. 1(d)shows the oblique mesh, where the lengths of the unitcell vectors b and b are estimated to be 8.4 ± ± √ / √ γ having similar value as obtained from LEED (70 ± ◦ ).The height profiles in Fig.1(e) show that the overlayer isflat with atomic corrugation of ± D )forming a ’Λ’ shape, as shown by white dashed lines inFig. 2(a)). The bands are linear along Γ- M over a bindingenergy ( E B ) range starting from 1.5 eV at k (cid:107) = 0.2˚A − to the Fermi level ( E F ), where the two branches of ’Λ’meet at the Γ point. Its linearity is established from themomentum distribution curves (MDC) (Fig.2(b)) fromwhich E B as a function of k (cid:107) (red squares) is obtained(Fig.2(c)).The first Brillouin zone of the (2113) phase obtainedfrom the unit cell determined above is overlaid on thatof the substrate in Fig. 2(d). ARPES measured up to the M point of the substrate BZ spans the K (cid:48) and M (cid:48) pointsof the overlayer BZ when all the domains are considered,but no other linear band is observed at either K (cid:48) or M (cid:48) (see Fig. S1(a,b) of Supplementary material (SM)[27]).Similarly, ARPES spectra up to the K point of substrateBZ spans the M (cid:48) and Γ (cid:48) points of overlayer BZ, but noother linear bands are observed (see Fig. S1(c,d)[27]).The linear band is observed only at the common zonecenter Γ of the three domains. The linear bands are notobserved at Γ (cid:48) point of domain3 possibly because of over-lap with bands related to the other two domains for whichthis is an arbitrary k point and the proximity of intense s − p band of Au.The D band is also observed at a different photon en-ergy of 23 eV, the E B ( k (cid:107) ) variation from MDC (solidblack triangles in Fig. 2(c)) is very similar to 21.2 eV (b)(d) (f)(a) (e) KK’K MM ’ M ’ M ’ ’ (1 x 1) B.Z B.Zdomain1domain2domain3 (c)
Figure 2: (a) ARPES spectra of the (2113) Sn/Au(111)phase using 21.2 eV photon energy ( hν ) along the Γ- M direc-tion. The linear band D is highlighted by white dashed lines.(b) The momentum distribution (MDC) curves from E B = 0to 1.6 eV at step of 0.1 eV in (a). (c) E B as a function of k (cid:107) (red squares) for D band obtained from the MDC curvesin (b). (d) The first Brillouin zones of Au(111) (outer regu-lar hexagon) and the (2113) phase (inner elongated hexagon)with the high symmetry points indicated. ARPES spectraalong (e) Γ- M with hν = 23 eV and (f) along Γ- K with hν =21.2 eV. photon energy showing that it is surface related. More-over, as expected for a Dirac cone, D is unaffected bythe variation of the azimuthal angle e.g. from the Γ- M direction (Fig. 2(a)) to Γ- K direction (Fig. 2(f) and blackopen circles in Fig. 2(c)). The ARPES data for the inter-mediate azimuthal angles are shown in Fig. S2 of SM[27].A least square fitting obtained from MDC curvesof Fig. 2(a,e,f) with a blue straight line provides anexcellent fit. The magnitude of the slopes ( dE B / dk (cid:107) )of the left and the right branches are essentially same,6.88 ± ± v F = h dE B dk (cid:107) , the Fermi velocity ( v F ) turns out to be1.05 × m/s, which is very similar to that of graphene(1 × m/s)[26]. However, the important differenceswith graphene is that the structure is non-honeycomband a single Dirac-like cone is observed at the zone cen-ter. Theoretical studies have predicted their existence of
90 88 86 84 82binding energy (eV) expt. fit B S
Au metal Au 4f expt. fit Au A Au B Au 4f (2113) Au Sn i n t en s i t y ( a r b . un i t ) (a) (b)(c) (d)
27 26 25 24 23binding energy (eV)
Sn 4dSn metal expt. fit B expt fit Sn A Sn B surface (2113) Au Sn Sn 4d
Figure 3: (a) Au 4 f and (b) Sn 4 d core level spectra ofthe (2113) phase compared with (c) Au 4 f (d) Sn 4 d of bulkmetals Au and Sn, respectively. The residual of the leastsquare fitting (black line) is shown in the top of each panel. such single Dirac cones non-honeycomb structures. Forexample, the Lieb lattice with a square symmetry hostsa topologically nontrivial Z invariant insulating phasewith a single Dirac cone per BZ[28, 29]. A MoS al-lotrope having square-octagonal ring structure has beenshown theoretically to exhibit a single Dirac cone at E F at the zone center and its v F is comparable to that ofgraphene[30]. Graphaynes that are rectangular show twononequivalent distorted Dirac cones[31]. We have used amodified Lieb lattice model for our DFT calculations, asdiscussed latter.It is interesting to note that another weak linear band D (cid:48) in Fig. 2(a,e,f) is observed that is parallel to D with a k (cid:107) momentum offset of about 0.2 ˚A − . Both the branchesof D (cid:48) cross E F at 0.2 ˚A − . The energy offset between D and D (cid:48) is about 0.5 eV. It has been shown in an earlierstudy that Au intercalation in graphene induces largeRasbha spin orbit coupling (soc) of 0.1 eV[32]. GiantRashba effect has also been observed in a AuPb binarysurface alloy at the surface zone center with a Rashbaparameter value of 4.45 eV ˚A[33]. If we interpret D (cid:48) tobe due to Rashba soc, the Rashba parameter value hereis 5 eV˚A, which is similar to AuPb. As in case of D , the D (cid:48) band is also unaffected by change of photon energy(Fig. 2(e)) and the azimuthal angle (Fig. 2(f) and Fig.S2[27]).Before proceeding further to understand the origin ofthe Dirac-like cones discussed above, we have addressedthe question of alloying in the (2113) phase. Previ-ous studies[16, 17] using LEED and AES show forma-tion of AuSn surface alloy at RT. Au 4 f and Sn 4 d core-level spectra of the (2113) phase (Fig. 3(a,b)) arecompared with those of the corresponding bulk metals inFig. 3(c,d). In Fig. 3(c), Au 4 f shows the 4 f / bulk peakat 84 eV, while the surface component (shaded green) isshifted to lower E B at 83.6 eV[34]. In contrast, for the(2113) phase, the surface component is absent and boththe Au 4 f spin-orbit split peaks exhibit an asymmetry onthe higher E B side that cannot be accounted for by DSasymmetry. A good quality fit is obtained only when anadditional component (Au A , blue shaded) is considered,and its position is varied freely. The main peak (Au B )appears at 84 eV, while Au A appears at 0.3 eV higher E B . Au B position coincides with the bulk componentof Au metal (Fig. 3(a,c)) and thus it can be assignedto the underlying substrate. On the other hand, Au A is related to the (2113) 2D surface alloy. This is sup-ported by an earlier work, which show that the Au 4 f peak shifts to higher E B in bulk Au-Sn alloys comparedto Au metal[35].The Sn 4 d spectrum in Fig. 3(d) for Sn metal showsthe 4 d / and 4 d / peaks at 24 eV and 25 eV, respec-tively. In contrast, the corresponding peaks in the (2113)phase are both shifted to higher E B by 0.3 eV. Thisclearly indicates surface alloying since in bulk Au-Sn al-loys, such shift to higher E B is reported with respectto Sn metal[35]. It is noted that the Sn 4 d peaks arebroader and fitting with single component fails, indicat-ing presence of at least two components. This is estab-lished by the Sn 4 d spectrum recorded with higher reso-lution, where the shoulder depicting the second compo-nent is showed by an arrow (Fig. 3(b), green line). Thus,presence of two non-equivalent Sn atom positions in theAu-Sn alloy is indicated. These components (Sn A andSn B ) are separated by 0.3 eV. The composition of thesurface alloy is determined to be Au Sn, considering theareas of Au A and (Sn A + Sn B ) and their correspondingphotoemission cross-sections. Note that following simi-lar procedure for 0.9 ML Sn deposited on Au(111) at RT,we find the composition to be AuSn, in agreement withliterature[16]. Thus, clearly, besides the surface struc-ture, the composition of the surface alloy also changeswith T S .It is important to note that the occurrence of the Dirac-like linear bands in Fig. 2 is specific to the (2113) phasewith composition of Au Sn. The ARPES for the otherphases with different surface structure and compositionstudied by us do not show the linear bands (Fig. S3)[27].DFT has been extensively used to understand the elec-tronic structure of the 2D materials. However, inorder to perform DFT, a starting structural model forthe (2113) phase is required. Although we have de-termined the unit cell, the task of obtaining the atomicpositions is complicated due to surface alloying and isoutside the scope of the present work. If bare Au(111)surface is considered, the unit cell would comprise of 5Au atoms in the regular fcc positions with the latticeparameters b = 4.89˚A, b = 7.61˚A and γ = 70.9 ◦ . But,for Au Sn, a 2:1 ratio of the Au and Sn atoms is notsatisfied with 5 atoms in the unit cell. So, we have con-sidered an extra Sn atom noting that the size of the unit cell ( b = 8.4 ± b =7.61˚A. Among a few structures we have probed, wepresent here an atomic arrangement following the Lieblattice that has been shown to host a topologically non-trivial phase with a single Dirac point per unit cell alongwith a dispersionless band through it[28]. However, inorder to be consistent with experiment, we take a non-primitive Lieb lattice with 6 atoms per unit cell andmodified to be oblique with γ = 70.9 ◦ rather than be-ing rectangular[28]. To retain the inversion symmetry,we assume two Sn atoms to be at the center and cornerpositions, while the four Au atoms occupy intermediatepositions forming a parallelogram with subtended angleof γ (Fig. S4(a))[27]. The calculated band structures re-veal that only for this model, a pair of linear bandsmeet at the Γ point, but at about 2 eV above E F andshows a small gap of 130 meV (Fig. S4(b,c)[27]). Thesebands originate primarily from the Sn p states with someadmixture of Au s states. However, our experimentaldata show that the linear bands meet at E F and also thetwo shallow parabolic bands crossing the linear bandsare not observed (Fig. 2). The reasons for such qualita-tive disagreement with ARPES could be related to thefact that the (2113) phase occurs only at high tempera-ture and thus it could be a metastable phase, while DFTcalculates the lowest energy ground state at zero temper-ature. Most importantly, we have used only a notionalmodel structure consistent with the experimentally deter-mined unit cell. The disagreement may also be attributedto that. We believe that the complete structure of the(2113) phase needs to be determined experimentally andused as input to the DFT calculation for realistic deter-mination of its electronic band structure.To conclude, we have identified Dirac-like linear bandsat the zone center in Au Sn surface alloy that has anoblique unit cell described by M = ( ). This is thus anexample of Dirac cone in a non-honeycomb surface alloy.The linear bands forming the Dirac cone have Fermi ve-locity comparable to that of graphene. It is surprisingthat exotic electronic structure is possible even in compli-cated surface alloys. The present results will rejuvenatethe search for 2D quantum materials that are importantfor high speed electronic devices.D.P. and A.C. thanks P.A. Naik, A. 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Pampa Sadhukhan , Dhanshree Pandey , , VipinKumar Singh , Shuvam Sarkar , Abhishek Rai ,Kuntala Bhattacharya , Aparna Chakrabarti , andSudipta Roy Barman UGC-DAE Consortium for Scientific Research,Khandwa Road, Indore 452001, Madhya Pradesh, India Homi Bhabha National Institute, Training SchoolComplex, Anushakti Nagar, Mumbai 400094,Maharashtra, India Theory and Simulations Laboratory, Raja RamannaCentre for Advanced Technology, Indore 452013,Madhya Pradesh, India Department of Physics, Indian Institute of SpaceScience and Technology, Thiruvananthapuram 695547,Kerala, IndiaThis Supplementary material contains four figures. (a) (b)(c) (d)
Fig. S 1: ARPES spectra of the (2113) phase along Γ M direction (a) over an extended range up to M point and (b) around Γpoint. ARPES spectra along Γ K direction (c) over an extended range up to K point and (d) around Γ point. k ll (Å ̄¹) b i nd i ng ene r g y ( e V ) (a) (b)(c) (d)(e) (f)(g) (h) =22˚ =23˚ =28˚ =33˚ =38˚ =43˚ =48˚ =53˚ Fig. S 2: ARPES spectra around Γ point from Γ M to Γ K direction at azimuthal angle φ = (a) 22 ◦ , (b) 23 ◦ (Γ- M ), (c) 28 ◦ , (d)33 ◦ , (e) 38 ◦ , (f) 43 ◦ , (g) 48 ◦ and (h) 53 ◦ (Γ- K ). Au k ll (Å ̄¹) (a) (b) (c)(d) (e) (f) b i nd i ng ene r g y ( e V ) (g) Au (=0) (j) (h) (i)(l)(k) b i nd i ng ene r g y ( e V ) k ll (Å ̄¹) Fig. S 3: Low energy electron diffraction pattern and ARPES spectrum of (a, g) Au(111) and 0.9 ML Sn/Au(111) depositedat (b, h) T S = 300 K forming a p (3 × R ◦ pattern, (c, i) T S = 383 K forming a mixed phase (d, j) T S = 413 K forming the(2113) phase, (e, k) T S = 443 K forming a √ ×√ T S = 493 K forming √ ×√ M M M M Fig. S 4: (a) The structure of the oblique Lieb lattice after atom position relaxation, the unit cell is marked by black dashedline, Au and Sn atoms are shown by dark blue and red filled circles, (b) The corresponding band structure is shown along Γ- M (cid:48)(cid:48)