Large spin-orbit coupling and helical spin textures in 2D heterostructure [Pb2BiS3][AuTe2]

Two-dimensional heterostructures with strong spin-orbit coupling have direct relevance to topological quantum materials and potential applications in spin-orbitronics. In this work, we report on novel quantum phenomena in [Pb2BiS3][AuTe2], a new 2D strong spin-orbit coupling heterostructure system. Transport measurements reveal the spin-related carrier scattering is at odds with the Abrikosov-Gorkov model due to strong spin-orbit coupling. This is consistent with our band structure calculations which reveal a large spin-orbit coupling gap of εso = 0.21 eV. The band structure is also characterized by helical-like spin textures which are mainly induced by strong spin-orbit coupling and the inversion symmetry breaking in the heterostructure system.


I. The cleaved surface morphology of [Pb 2 BiS 3 ][AuTe 2 ]
The c-axis length of [Pb 2 BiS 3 ][AuTe 2 ] is 9.34Å. Previous structure determinations [S1-S3] have shown that weak chemical bonds Pb(Bi)-Te connects the building blocks of [Pb 2 BiS 3 ] and [AuTe 2 ]. Sample cleavage breaks the interlayer bonds and leaves either the [Pb 2 BiS 3 ] layer or the [AuTe 2 ] layer exposed to the ambient environment with equal probability. AFM measurements were conducted to investigate the surfaces morphology, shown in (c) and (d).
The AFM equipped with a peak-force tapping mode has a vertical resolution up to 50 pm. (e) summarizes the depth information of the cleaved surfaces shown in (d). 80% of the surface is 1.08 nm deep and the rest is 1.5 nm deep. Comparing with the structure of [Pb 2 BiS 3 ][AuTe 2 ], we conclude that the 1.08 nm deep surfaces are one-unit-cell thick films and the 1.5 nm thick surfaces correspond to one and half unit cell. It is worth mentioning that the cleaved surfaces are stable in ambient environment although surface oxidation could happen.

Weak antilocalization and spin-orbit scattering fields of different systems
For systems with small effective atomic numbers such as GaAs [S4] and silver [S5], the cusplike WAL curves disappear quickly with increasing magnetic field. For example, WAL of silver only occurs in small fields between ±0.02 T. By contrast, heavy element Bismuth [S6] and TIs [S7-S8] show more pronounced WAL effects. The SOC characteristic fields B so of different systems increase with increasing (effective) atomic numbers with an exception for the TIs. The strong SOC and the Berry's phase in TIs lead to a remarkably large B so , for example B so >8T has been reported in reference S9.

Qualitative analysis of the WAL
For 2D, non-magnetic and strong SOC systems, fitting WAL using the HLN equation (Eq.2) requires three unknown parameters B e , B so and B φ , which are the characteristic fields of elastic scattering, spin-orbit scattering and phase coherence, respectively. Three fitting parameters normally can generate large uncertainties. To bear this in mind, fitting parameters need to be well consistent with experimental results and known properties of materials. We focus on the WAL data at 1.6 K because that τ φ much longer than both τ so and τ e is still satisfied at this temperature. Using Eq. 1, the best fit leads to B φ =0.004 T, corresponding to a phase coherence length lφ≈200 nm. The 200 nm long lφ is reasonable because that Bi 2 Te 3 demonstrates a similar WAL curvature with that of [Pb 2 BiS 3 ][AuTe 2 ] and Bi 2 Te 3 possesses a similar lφ≈300 nm at 2 K.   Eq. 2 is an excellent approximation to Eq. 1 and no significant improvement in the fitting is obtained by using Eq. 2.

IV. Two-dimensionality WAL in [Pb 2 BiS 3 ][AuTe 2 ]
The 2D characteristic can be determined not only by the field dependence, but also by the temperature dependent phase coherence length lφ. It is known that, for electron-electron scattering in two-dimensional systems, the inelastic scattering diffusion length as a function of temperature follows a power-law dependence T −n with exponent n≈1/2 [S10]. Assuming the inelastic scattering diffusion length is approximately equal to the phase coherence length lφ [S11], lφ should also follow the T −1/2 relation. Below is the experimental data of the temperature

V. Spin-orbit gap in bulk and one-unit-cell film [Pb 2 BiS 3 ][AuTe 2 ]
Unlike the electronic structure of [