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Experimental Evidence of the Topological Surface States in Mg3Bi2 Films Grown by Molecular Beam Epitaxy

Type-II nodal line semimetal (NLS) is a new quantum state hosting one-dimensional closed loops formed by the crossing of two bands which have the same sign in their slopes along the radial direction of the loop. According to the theoretical prediction, Mg3Bi2 is an ideal candidate for studying the type-II NLS by tuning its spin-orbit coupling (SOC). In this paper, high quality Mg3Bi2 films are grown by molecular beam epitaxy (MBE). By in-situ angle resolved photoemission spectroscopy (ARPES), a pair of surface resonance bands (SRBs) around Gamma point is clearly seen. It shows that Mg3Bi2 films grown by MBE is Mg(1)-terminated by comparing the ARPES data with the first principles calculations results. And, the temperature dependent weak anti-localization (WAL) effect in Mg3Bi2 films is observed under low magnetic field, which shows a clear two dimensional (2D) e-e scattering characteristics by fitting with the Hikami-Larkin-Nagaoka (HLN) model. Combining with ARPES, magneto-transport measurements and the first principles calculations, this work proves that Mg3Bi2 is a semimetal with topological surface states TSSs, which paves the way for Mg3Bi2 as an ideal materials platform for studying the exotic features of type-II nodal line semimetals (NLSs) and the topological phase transition by tuning its SOC.

They eliminate 180 backscattering under the protection of time-reversal symmetry and prevent to be fully gapped when perturbed due to the odd number of band crossing. Besides, due to the time-reversal symmetry, there are two closed electrons scattering paths for surface states. One path accumulates a Berry phase of π when across single Dirac cone and induces a destructive quantum interference with the other path, leading to the enhancement of the conductivity. That is the origination of weak antilocalization effect which only exists under low magnetic field for the time-reversal symmetry reason. 11,12 NLSs are novel proposed topological solid-state phases which host one-dimensional closed loops or line degeneracies formed by the intersection of two bands. It is proposed as type-II NLSs when the linear spectrum at every point of the nodal line is strongly tilted and tipped over along one transverse direction, which may lead to different magnetic, optical, and transport properties compared with conventional nodal loops. To date, only K4P3 was theoretically predicted as a type-II NLS, but no candidate material has been experimentally reported. Therefore, it is highly desirable to experimentally realize and study topological materials with clear type-II NLS signature. [13][14][15] Here we investigate Mg3Bi2, which is predicted as owning TSSs and is an ideal materials platform for studying type-II NLSs. 14,15 Previous studies of Mg3Bi2 mainly focused on its good thermoelectric properties as one of Mg3Sb2-class materials. 16 To realize novel topological materials-based devices, such as spin transistors, topological quantum computation, or even to achieve the quantum anomalous Hall effect (QAHE), wellcontrolled thickness of ultrathin films are inevitable. 18 In this work, we have grown Mg3Bi2 films by MBE which allows us to control the thickness of Mg3Bi2 film layer by layer. In-situ reflection high energy electron diffraction (RHEED) and ex-situ X-ray diffraction (XRD) measurements were performed to confirm the high quality of our Mg3Bi2 films. First principles calculations and in-situ ARPES measurements were performed to study the band structure of Mg3Bi2. The ARPES spectra are consistent with our first principles calculations, and we confirmed that the natural surface of our films is type-I Mg-terminated, the definition of which will be given below.
To further confirm the topology of its surface states, magneto-transport measurements were performed. We observed clear 2D weak anti-localization (WAL) effect which is the hallmark of topological protected surface states. Therefore, we have provided direct experimental evidences for the existence of TSSs in Mg3Bi2 film and paved the way to study type-II NLSs.

Structure characterization of Mg 3 Bi 2 film
Mg3Bi2 crystalizes in a layered Kagome lattice structure with a space group of P3m1 (No.164).
As shown in Figure 1a, the unit cell contains five atomic layers with a stacking sequence of Mg(1)-Bi-Mg(2)-Bi-Mg(1) along the (001) crystallographic orientation, which could be defined as a quintuple layer (QL), similar to that of A2B3-type topological insulators. Figure   To directly confirm the TSSs of Mg3Bi2 films, we performed in-situ ARPES measurements at 12 K. Figure 3a shows the experimental band structure in the K--K  direction. A Rashba-type splitting structure could be clearly identified, as shown by the guidelines in Figure 3a, indicating an Mg-termination sample surface. What is more, the sharply dispersive bands marked as S matches well with the theoretical calculation for Mg(1)-termination, as shown in Figure 3(b).
The constant energy contour (CEC) at Fermi energy for the experimental and theoretical calculation are compared in Figure 3c and d, in which they match quite well with each other, despite the fact that the bulk continuum of the valence bands dominates the spectra weight in Figure 3d. Therefore, we have preliminarily confirmed that our Mg3Bi2 films are with the Mg(1)termination which is different from the reported Bi-termination for single crystal Mg3Bi2. 15 ARPES spectrum near Fermi level is shown in Figure 3e, in which the SRB and S band are more pronounced. Figure 3f depicts its corresponding Momentum Distribution Curves (MDCs). A Lorentzian-type peak fit procedure was applied to each curve between -0.08~-0.22eV of the energy to find the peak position of SRB1 and SRB2. Their peaks position was forward linear fitted and thus we obtained the slope of SRB1 and SRB2 which are C1=4.91 and C2=-4.91, respectively. The detailed fitting result is shown in Figure S1. Figure 3g and   Magneto-transport is another way to study the TSSs. For transport measurements, we grew Mg3Bi2 films on Al2O3(0001) substrate to eliminate the substrate effect. The characterization of Mg3Bi2 films on Al2O3 is shown in Figure S2. The temperature dependent longitudinal resistivity ρxx of the Mg3Bi2 film is shown in Figure 4a, in which the applied magnetic field (9 T) is perpendicular to the electrical field. ρxx keeps decreasing from room temperature to 8 K, which is consistent with the behavior of semimetals. As the temperature drops below 8 K, ρxx experiences an upturn (inset). This phenomenon was also observed in other topological materials and was Theoretically, the WAL phenomena for perpendicular magnetic field could be explained by Hikami-Larkin-Nagaoka (HLN) model. 26 To confirm the magneto-transport behaviors under perpendicular field, we adopt the HLN model to fit the transport data. The HLN model can be described as

Weak anti-localization effects
where G(B) is the magneto-conductance (i.e., inverse of R(B)), A is the coefficient of WAL, e is the electronic charge, ћ is the reduced Planck constant, Ψ is the digamma function, Bϕ=ћ/(4elϕ) is a characteristic magnetic field and lϕ is the phase coherence length. Figure 4c depicts the evolution of ΔGxx versus temperature, together with the fitting results by the HLN model. The extracted coherence length lϕ as a function of T is shown in Figure 4d. lϕ decreases from 210.9 nm at 2 K to 62.5 nm at 15 K, following a power law dependence on T as lϕ∝T -0.51 . This monotonic decrease behavior was also observed in other topological aterials, 27 where lϕ∝T -0.5 and lϕ∝T -0.75 for 2D and 3D systems, respectively. The power factor of -0.51 for our Mg3Bi2 system indicates that the WAL mainly originated from the 2D topological surface states at low temperature. The WAL coefficient A at different temperatures is also shown in Figure 4d (right axis), where A=N and  equals to -0.5 for the TSSs of symplectic universality class and N is the number of independent conducting channels. 26,28 Multiple channels could be involved in the transport due to the existence of different surface states, as well as possible conducting channels from bulk states. [29][30][31] The value A is between -0.87 and -0.47 for different temperatures which means N=1 or 2 indicating one or two TSS contributes as the conducting channel.

Conclusion
In summary, we report the growth of high quality Mg3Bi2 crystalline films on Graphene/6H- The methods on sample preparation, measurements detail, the detailed fitting procedure on SRB slope and characterization of Mg3Bi2 on Al2O3. Supporting information is available free of charge.

Author Contributions
The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. †These authors contributed equally to this paper.

Notes
The authors declare no competing financial interest.

Sample preparation
The Mg3Bi2 films were grown on 2×10 mm 6H-SiC(0001) substrate with epitaxially grown Graphene by MBE. The base pressure was maintained at 3×10 -11 mbar and the vacuum was better than 2×10 -10 mbar during growth. Mg (3N) and Bi (5N) sources were thermally evaporated from standard Knudsen cells. Mg and Bi were kept at 380C and 540C and with the flux rate of 0.661Å/s and 0.112Å/s (measured by Quartz crystal micro-balance), respectively. The flux ratio between Mg and Bi should be at least ~5:1 to minimize Mg vacancies and ensure the high quality of the as-grown films. The substrate was kept at 350C during the growth and the quality of the film was monitored by in-situ RHEED.

Measurements
For the ARPES measurements, the spectra are excited by the He I (21.2 eV) resonance line of a commercial Helium gas discharge lamp. The light is guided to the analysis chamber by a quartz capillary. In virtue of the efficient three-stage differential pumping system, the pressure in the analysis chamber is better than 2.0×10 -10 mbar during our experiments. A VG Scienta DA30L energy analyzer is used to collect the photoelectrons. Mg3Bi2 film with the thickness of 50nm was transferred in-situ into the ARPES chamber and measurements were done at 12K. The magneto-transport measurements were performed with the standard four-probe technique using silver paint as contacts by Physical Property Measurement System (PPMS-9). The samples for transport measurements is about 50 nm thick in a rectangular shape (5 mm × 6 mm) grown on Al2O3(0001) substrate.
The detailed fitting procedure on SRB slope

21
Considering the symmetry of SRB1 and SRB2 around  , we fit the band by the equation of y=a×|x|+b, where |x| represent the absolute value of x. From Figure S1 we can see that the SRB band between -0.08~-0.22eV of the energy fits well by y=-4.908×|x|+0.191, and we thus conclude that the slope of SRB band is C=4.91.