Dual topological states in the layered titanium-based oxypnictide superconductor BaTi2Sb2O

Topological superconductors have long been predicted to host Majorana zero modes which obey non-Abelian statistics and have potential for realizing non-decoherence topological quantum computation. However, material realization of topological superconductors is still a challenge in condensed matter physics. Utilizing high-resolution angle-resolved photoemission spectroscopy and first-principles calculations, we predict and then unveil the coexistence of topological Dirac semimetal and topological insulator states in the vicinity of Fermi energy (EF) in the titanium-based oxypnictide superconductor BaTi2Sb2O. Further spin-resolved measurements confirm its spin-helical surface states around EF, which are topologically protected and give an opportunity for realization of Majorana zero modes and Majorana flat bands in one material. Hosting dual topological states, the intrinsic superconductor BaTi2Sb2O is expected to be a promising platform for further investigation of topological superconductivity.

The recent discovery of MBSs in the iron-based superconductor, combining nontrivial topological states and superconductivity in a single material, pointed out a new dimension in realizing TSC [64][65][66][67][68][69][70][71] . One later research on Li(Fe,Co)As revealed that iron-based superconductors might generically host multiple types of nontrivial topological states, e.g., both the TI and topological Dirac semimetal (TDS), together with unconventional superconductivity 72 . Thus, the surface states of these topological states near the Fermi level (E F ) would participate in the superconducting pairing, hence the possible existence of multiple types MBSs. However, the Dirac point (DP) from the TDS states of superconducting Li(Fe,Co)As with 3% Co is located above the E F , and thus the proposed one-dimensional Majorana fermion would not be expected to dominate the low-energy electronic structure 72 . Furthermore, seemingly the superconductivity would be inexorably suppressed by introducing further charge carriers in Li(Fe,Co) As 73,74 . In this regard, it is critical to search for more practical superconductors with both surface Dirac cones from TI and TDS states below E F to realize multiple MBSs in one material.
In this work, we have identified both TI and bulk DP states reminiscent of those in iron-based superconductors but with Dirac cones below E F in superconducting BaTi 2 Sb 2 O samples using angle-resolved photoemission spectroscopy (ARPES) and firstprinciples calculations. Moreover, spin-resolved ARPES measurements confirmed both of the predicted spin-helical surface TI bands and TDS bands, which are prospective to harbour Majorana zero modes and Majorana flat bands in one single material when the superconducting gap open as probed in our scanning tunneling microscopy (STM) measurement. This titanium-based oxypnictide superconductor which has the similar multiple topological states as iron-based superconductors would provide another parallel but more practical playground for comparative study on TSC.

RESULTS
The crystal structure and calculated band structure The crystal structure of BaTi 2 Sb 2 O is illustrated in Fig. 1 Fig. 1(b). Figure 1(c) displays the angle-integrated photoemission spectrum of BaTi 2 Sb 2 O over a large range of binding energy, in which we can clearly identify the Ba (4p and 4d), Ti (3p) and Sb (4d) core levels, confirming the element composition of our samples. After cleaved in the air, the sample shows typical flat and shining surface as illustrated in the inset of Fig. 1(c). The sample exhibits a metallic temperature dependence and shows zero resistance below T c = 1.05 K [the inset of Fig. 1(d)]. Temperature-dependent STS data of BaTi 2 Sb 2 O in Fig. 1(e) shows pronounced superconducting gap which is clearly visible at the lowest accessible temperature, T = 0.38 K. With increasing temperature the gap size is reduced and vanishes at about T~1.0 K. The inset of Fig. 1(e) shows an atomically resolved topographic image of the cleaved BaTi 2 Sb 2 O single crystal exhibiting homogeneous features. The cleavage plane is expected to be the Ba-termination same as that in ARPES measurements, on which there forms a 2 × 1 reconstruction since about half of the Ba atoms are lost during the cleavage leaving one half of Ba atoms on another surface 76 . More details on the sample characterizations can be found in Supplementary Note 1. Figure 1 (f) declares the calculated band structure of BaTi 2 Sb 2 O with the SOC. We concentrate on crossings of several bands around E F , which are highlighted by the enlarged image in the right panel. These three bands belong to irreducible representations Γ À 6 , Γ À 7 , and Γ þ 7 , respectively. From top to bottom, the three bands between Γ − Z connect in the following way: 1. Γ À 6 ! Z þ 6 , 2. Γ À 7 ! Z À 7 , and 3. Γ þ 7 ! Z À 7 . The crossing of the 1st and the 3rd bands at an arbitrary k z along Γ-Z features a symmetry-protected DP with parity inversion. Slightly lower in energy, the 2nd and the 3rd bands cross, leading to a small gap. The distinct behavior of these two band crossings stems from different mechanisms. BaTi 2 Sb 2 O belongs to the space group no. 123, which respects the inversion symmetryÎ . The joint operation of time-reversal (T ) and I promises the Kramer's double degeneracy everywhere in the BZ. In this case,ĉ 4 , which leaves k z invariant along Γ-Z, protects a stable DP between Γ À 6 and Γ À 7 bands. However, as Γ À 7 and Γ þ 7 share the same basis functions with the only difference on their response toÎ , the two bands will unavoidably open a gap when they cross. Such particular alignment of bands is essential for BaTi 2 Sb 2 O to resemble the electronic structure of iron-based superconductors which features a great potential to coexist two distinct types of topological superconductivity in one system, i.e., the one-dimensional Majorana fermion from topological DPs and Majorana zero modes from the topological insulator or DPs 72,77 . To better understand the different symmetry-protection and gap opening mechanisms, we present a k ⋅ p model for the DP and the gap below withĉ 4 andTÎ in Supplementary Note 2.
The surface states TISS associated with the topological insulating gap and the TDBB states can be further displayed in the surface states calculation along Γ-M. Here, two bulk bands near Γ are marked as TDBB and TIBB, respectively [ Fig. 1(g)]. By zooming in the region of the white box, we can identify two surface conelike states, as highlighted by dashed lines in Fig. 1(h). The upper one originates from the hybridization of the bulk DP and other trivial bulk bands, and the lower one should be the TI surface state. Since these two DPs are as close as~23 meV and their overlapped states have gradually merged into bulk states, it is really challenging to distinguish the dispersion between the dual states band gap from photoemission intensity plots. Therefore, we try to resolve the lower part of the surface state from TI, which can be assigned as TISS. We note that these surface states are both below E F and thus can be probed by ARPES without further carrier doping.
The ARPES results of dual topological bulk bands and related surface states Experimentally, we first revealed both the TDS and TI bulk states of BaTi 2 Sb 2 O. Due to considerable entanglement between the bulk and surface states around E F [ Fig. 1(g)], we took advantage of the matrix element effect to distinguish between them by using p-and s-polarized photons 65,78 . The detailed experiment geometry is shown in Supplementary Fig. S2 and Note 3.  Intensity (a. u.) E -E F (eV) on the k m − k z plane [the k m direction is indicated in Fig. 1(b)] taken with p-polarized photons at E F -0.5 eV, respectively. Band dispersions with apodictic periodic modulation along k z could be recognized, confirming the bulk nature of TIBB. Furthermore, we show four photoemission intensity plots taken at different k z as schematically illustrated in Fig. 2( Fig. 2(e)]. In addition, the corresponding second derivative plots in Fig. 2(d)(i)-(iv) manifest the gradual increase of the Fermi crossing and more linear dispersion when close to the DP, in accordance with the predicted TDS feature of TDBB [ Fig. 2(e)].
Next, we performed similar ARPES measurements but with s-polarized photons to identify topological surface states of BaTi 2 Sb 2 O. Figure 3(a) shows the intensity plot along Γ-M with s-polarized photons. Figure 3 Max  strong hybridization with TI surface states. Figure 3(c) displays the enlarged second derivative plot of band structure in the red box of Fig. 3(a). Together with the corresponding energy distribution curves (EDCs) [Fig. 3(d)], we can distinguish upper TDS cone and lower TI cone. The observed small gap could exclude the possibility of there being only one Dirac cone since no impurity scattering or symmetry breaking in BaTi 2 Sb 2 O. However, the lower TDS cone and upper TI cone in the gap are difficult for us to resolved. Furthermore, as exhibited by second derivative intensity plots in Fig. 3(e) and (f), detailed evolution of these surface cones along k x and k m could be recognized in evidence. The in-plane dispersion migrates apparently deviating Γ at different k x and k m positions, suggesting that both surface DPs are exactly located at Γ.
Helical spin texture of the surface states Both cones originating from TI and TDS should be spin-polarized, as suggested by our first-principles calculations [ Fig. 4(a) and the inset]. States from the upper part of TDBB, the lower part (TISS) and extension of TI cone (ETISS) all suggest the same characteristic left-hand spin helicity as Li(Fe,Co)As and most TIs, which is then further confirmed by our constant-energy spin texture calculations shown in Supplementary Fig. S3 and Note 5. We then used spinresolved ARPES to check these predictions. Here, for easy comparison, we summarized the sketch of spin nature of three surface states in Fig. 4(b) according to calculations. Figures 4(c) and (d) show our photoemission intensity plots without and withŷ direction spin-resolved measurement in the same region under more surface sensitive s-polarized photons, respectively. Evidently, for both TI and TDS cones, the left hand parts of these cones show the opposite spin direction to those of right hand parts, consistent with our calculations. Moreover, as displayed in Fig. 4(e), spinresolved MDCs taken at E B = −0.03 eV (Cut 1), −0.18 eV (Cut 2) and −0.30 eV (Cut 3) intersecting TDBB, TISS and ETISS demonstrate strong spin polarization up to 0.3. We note that the observed spin-polarized TDBB located in the energy range for the bulk Dirac bands, but is actually derived from the surface states of the bulk Dirac bands, since their unavoidably overlap on the (001) surface. Meanwhile, MDCs of partial intensities along −ŷ and +ŷ at Cut 1 to 3 in Fig. 4(f) also support the spin polarization result [see more details in Supplementary Fig. S4 and Note 6]. We note that these MDCs' peaks (marked as black arrows) indicate the exact momentum of surface bands, which are consistent with general ARPES results in Fig. 4(c).

DISCUSSION
The coexistence of spin-helical topological surface states and the bulk TDS in BaTi 2 Sb 2 O resembles that of iron-based supercoductor, such as Li(Fe,Co)As and Fe(Te,Se) [See details in Supplementary Note 7]. The DPs formed by the band inversion between Ti-d and Sb-p stay slightly below E F , which naturally forms a FS with mixing parities -a necessary ingredient for the emergent TSC in TDS 77 . On the side surface, such as (010) schematically shown in Fig. 4(g), the bulk DPs map to different surface nodes and there may exist Fermi arcs/loops between the two DPs 79 . They would be gaped by superconducting order except for the nodes along Γ-Z and Γ-X, forming four zero energy Majorana modes. More interestingly, the parity-mixing Fermi surface above the DPs, as shown by the violet sphere in Fig. 4(g), would be gaped as well. However, as long as the surface admits the mirror symmetry along y-direction, Majorana flat-bands will appear as symmetry-protected TSC. Besides the promising topological superconductivity induced by the TDBB, the TISS extending to E F and its hybridization with the bulk bands could also generate topological superconducting states similar to other iron-superconductors and TI-SC hybrid systems. Due to the proximity of the TDBB and TISS cone in BaTi 2 Sb 2 O, we cannot identify the dominant one. We actually believe both TDBB and TISS contribute to the topological superconductivity in this system. We note that our preliminary STM measurements on BaTi 2 Sb 2 O have revealed its superconducting gap of 0.135 meV which mainly tends to come from the TDSS, and the upper branch of the TISS [see more details in Supplementary Figs. S5 to S7 and Note 8]. Compared to the DPs above the E F in Fe(Te,Se), whose TSC has been confirmed after many optimizations and a long time of trying, the DPs of BaTi 2 Sb 2 O is slightly below the E F , which could dominate the low-energy electronic structure. Thus, BaTi 2 Sb 2 O, not belonging to any existing iron-based superconductor family, provides another exciting platform for exploring the proximity effect in momentum space, which will greatly enrich the potential TSC family and offer independent insights for examining the current understanding of the TSC. Furthermore, compared to Li(Fe,Co)As, as no further electron doping is required in BaTi 2 Sb 2 O, the perfect alignment of E F and DPs, namely, the DP is located slightly below E F in BaTi 2 Sb 2 O, makes it the one of the most promising candidates to detect multiple-type TSC in one system. Besides, we note that the hole doping in Ba 1−x Na x Ti 2 Sb 2 O will further enhance the superconductivity and increase the critical temperature to as high as 5.5 K while maintaining TI/TDS topology, see also Supplementary  Fig. S8 and note 9 76,80 .
In summary, we have identified the symmetry protected TDS, the TI states and their spin-momentum locking patterns in the titanium-based oxypnictide superconductor BaTi 2 Sb 2 O by ARPES measurements in association with first-principles calculations. The helical surface states of the TDS slightly below E F could naturally host both Majorana zero mode and flat band in this system. Therefore, BaTi 2 Sb 2 O is an excellent platform for studying various types of Majorana fermions and for further research of topological superconductivity.

Sample growth and characterizations
High-quality single crystals of BaTi 2 Sb 2 O were grown by using BaSb 2 as the flux. Pieces of Ba (99.95%), Sb (99.999%) and TiO (99.9%) were mixed with an atomic ratio of Ba : Sb : TiO = 10 : 20 : 1, and then placed in an alumina crucible. This crucible was later sealed into a tantalum tube, which was then sealed into a quartz tube. The assembly was heated up to 1100 ∘ C, maintained more than 30 hours, and was then slowly cooled down to 900 ∘ C at a temperature decreasing rate of 2 ∘ C/h. At 580 ∘ C the flux was immediately separated in a high speed centrifuge. BaTi 2 Sb 2 O single crystals were thus obtained in the aluminium oxide crucible.

ARPES experiments
High-resolution and spin-resolved ARPES measurements were performed at 03U and "Dreamline" beam lines of Shanghai Synchrotron Radiation Facility (SSRF), respectively. The 03U endstation is equipped with a Scienta Omicron DA30 electron analyzer. All ARPES data were taken at 15 K in an ultrahigh vacuum better than 8.0 × 10 −11 Torr. The angular and the energy resolutions were set to 0.2 ∘ and 6~20 meV (dependent on the selected probing photon energy), respectively. The spin-resolved ARPES at "Dreamline" is equipped with a Scienta Omicron DA30-L electron analyzer together with a spin detector based on the very-low-energy-electrondiffraction (VLEED).

Band calculations
First-principles calculations were performed within the framework of the projector augmented wave (PAW) method and selected the generalized gradient approximation (GGA) with Perdew-Burke-Ernzerhof (PBE) type, as encoded in the Vienna Ab initio Simulation Package (VASP). A kinetic energy cutoff of 500 eV, a Γ-centred k mesh of 12 × 12 × 6, and an energy difference criterion 10 −6 eV were utilized for all calculations. The spin-orbit coupling (SOC) was considered in a self-consistent manner. The WANNIER90 package was adopted to construct Wannier functions from the first-principles results. Topological properties calculations were carried out with our in-house code TMC.

STM/S experiments
The STM/S measurements were carried out in a scanning tunneling microscope (USM-1300, Unisoku Co., Ltd.) with the lowest temperature of 0.4 K. The samples were cleaved in an ultra-high vacuum with a base pressure about 1 × 10 −10 Torr. Pt/Ir tips were used after treatment on the