Abstract
Two-dimensional topological materials, especially quantum spin Hall insulators, have attracted enormous research interest owing to their potential for applications ranging from low-power electronics to fault-tolerant quantum computation. Stanene—the tin counterpart of graphene—is a promising candidate for room-temperature quantum spin Hall insulators, motivated by its simple atomic structure and considerable band-inversion gap. Nevertheless, one key challenge is to fabricate topological non-trivial stanene on insulating substrates. In this Perspective, we review recent developments in experimental routes to the creation of few-layer stanene films on various substrates. A quantitative comparison between these stanene films on different substrates is also presented.
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1 Introduction
Quantum spin Hall effect (QSHE) is a new quantum state of matter with a nontrivial topological property. Inside such a topological matter, Maxwell’s laws of electromagnetism are dramatically altered by an additional topological term with a precisely quantized coefficient [1], which gives rise to remarkable physical effects such as a quantized spin-Hall conductance and a vanishing charge-Hall conductance without an applied field. Besides its scientific important as a novel quantum state, with non-dissipative edge states and insulating bulk, QSHE has attracted great attention in solid state physics because of potential technological applications in spintronics.
In 2005, Kane and Mele first proposed the existence of QSHE in spin-orbital coupling graphene [2]. But the inverted bandgap much less than 1 meV makes graphene not a realistic QSHE system. Later, Zhang et al. proposed that QSHE should arise from HgTe/CdTe quantum wells (QWs) and hybridized InAs/GaSb QWs [3, 4]. In these two QWs, signatures of quantized conductance, regarded as the evidence for the QSHE, have been experimentally observed. However, their complicated structure and tiny bulk band gap make the evidence of QSHE less convincing [5]. Therefore, searching a new system with simpler structure and much larger bulk bandgap is the key point to the study of QSHE.
The prosperous and diverse 2D materials family constitutes an arsenal for exploring new-concept electronic devices as well as fundamental mysteries of condensed matter. A particularly interesting one of them is stanene—a single atomic layer of gray tin (α-Sn) in a honeycomb lattice structure similar to graphene. Different from graphene, stanene is characterized by its structural buckling and large atomic mass which contribute to strong spin-orbit coupling (SOC), offering an ideal platform to explore topology-related physics and electronics. Stanene and its derivatives have been predicted to be QSH insulators, with the bulk bandgap up to several hundred meV [6]. Many other exotic properties, including enhanced thermoelectricity [7], near-room-temperature quantum anomalous Hall effect [8], and topological superconductivity [9], are also expected in stanene-based materials, making them useful for various applications ranging from electronics, spintronics to quantum computation [10].
For experiments concerning 2D materials, mechanical exfoliation is usually the most straightforward approach to create atomically thin flakes [11]. However, it is difficult to obtain single-layer stanene because of the relatively high exfoliation energy of bulk tin [12]. Since it is difficult to make single-layer stanene films through“top-down” exfoliation methods, as a “bottom-up” synthesis method, molecular beam epitaxy (MBE) have been extensively studied recently.
This review will thus give an overview of making high-quality stanene films with thicknesses of few layers by using MBE method. The topological property of stanene films has been manipulated by choosing and engineering the substrates (modulating the lattice constants and the bulk bandgaps). In situ scanning tunneling microscopy (STM), angle-resolved photoemission spectroscopy (ARPES), combined with transport measurement were used to study these stanene films.
2 MBE growth of stanene on different substrates
2.1 Topological insulator substrate
The first MBE experiment that unambiguously reached the monolayer limit of stanene was the growth of stanene films on \(\text{Bi} _{2}\text{Te} _{3}(111)\) substrates, reported by Zhu et al. in 2015 [13]. In the experiment, high purity Sn (99.9999%) atoms evaporated from the effusion cells were deposited on room-temperature \(\text{Bi} _{2}\text{Te} _{3} (111)\) substrates in ultra-high vacuum. Low-temperature STM was utilized to characterize the quality of stanene films (see Fig. 1a). The atomic-resolution STM image (Fig. 1b) illustrates hexagonal arrangement of Sn atoms, consistent with the structure of the upper sub-lattice of stanene honeycomb lattice. The first experimental electronic structure of stanene was also studied by ARPES, Fig. 1c shows that, without band gaps, stanene has two metallic hole-type bands around Γ̅ point, which is consistent with the topological trivial phase in the first principles calculations (Fig. 1d). This is probably due to the compressed lattice constant of stanene grown on Bi2Te3 [14].
2.2 Semiconductor substrate
Since transport studies and electronic applications of stanene are only possible in bulk-insulating stanene films grown on insulating substrates, lattice-matched semiconductors (PbTe, InSb) have been selected as substrates to support stanene in the following experiments.
2.2.1 PbTe(111) substrate
PbTe is a normal insulator with a bandgap of ≈0.3 eV and its lattice constant in (111) plane close to that of stanene [15]. In 2018, a two-step MBE growth recipe has been developed to prepare single-layer stanene on PbTe(111) by Zang et al. [16]. In the experiment, Sn atoms were first deposited on PbTe(111) with the substrate temperature at ≈150 K, and the film was then annealed from 150 to ≈400 K, which improved the film quality (Fig. 2a). Higher annealing temperature resulted in significant change in the surface morphology and the band structure, probably due to inter-diffusion between Sn and PbTe. The atomic-resolution STM image (Fig. 2b) and the Fourier transformed image (inset of Fig. 2(b)) give a clear sight of the honeycomb-structure upper Sn atoms. Band structure of stanene/PbTe(111) was then measured by ARPES (Fig. 2c), the valence band maximum (VBM) is located at 0.32 eV below the Fermi level, which suggests that the stanene film is insulating with a bandgap of at least 0.32 eV.
Transport measurements were also performed on the stanene/PbTe(111) system. Based on previous research, β-Sn is a superconductor with critical temperature (Tc) of 3.7 K [19], while the bulk α-Sn has no superconductivity [20]. As a single layer α-Sn, stanene in principle is not a superconductor. However, the superconductivity of few-layer stanene was surprisingly discovered by a research reported by Liao et al. in 2018 [17]. Figure 2d shows that the Tc of stanene depends on film thickness, making stanene/PbTe(111) into a Tc-tunable superconductor system. More interesting, combined the first principles calculations with ARPES measurement, the trilayer stanene grown on PbTe is clarified to have a band-inversion electronic structure which results in a topological non-trivial phase (Fig. 2e). Recently, stanene/PbTe(111) system was studied at sub-kelvin temperature and in rotating magnetic field [18]. For the first time, a critical field that is several times the Pauli limit was detected (Fig. 2f), providing strong evidence for Ising superconductivity. However, this phenomena can’t be understood in the frame of the existing Ising pairing theory, considering that stanene keeps inversion symmetry [21]. Through the close experimental and theoretical collaboration, a new type of Ising pairing mechanism—type-II Ising pairing is proposed combining both SOC and crystal symmetry.
2.2.2 InSb(111) substrate
In 2019, Zheng et al. reported that single-layer stanene films can be epitaxially grown on Sb-terminated InSb(111) substrates (Fig. 3a) [22]. The STM dI/dV mapping results show that, there are highly localized edge states at the terrace edges (Fig. 3b-c), though the topological nature of these states is still unknown. Earlier than the STM study, the band structure of stanene/InSb(111) system was checked by ARPES in 2018 by Xu et al. [23]. As shown in Fig. 3d and 3e, the ARPES bandmaps reveal band gaps of 0.44 eV in the Γ̅ point of both as-grown and K doped stanene, in agreement with the first principles calculations. Even though the band inversion is absent in the calculations for the single-layer stanene/InSb(111) system, topological nontrivial phase is shown by making thicker stanene films on InSb(111). As also reported by Xu et al. in 2017 [24], by increasing the thickness up to 6 layers, stanene turns into Dirac semimetal with a pair of Dirac cones exist along kz axis near \(\overline{\boldsymbol{\Gamma}} \) point. As shown in Fig. 3f, ARPES data confirms the existence of Dirac cones in K-doped 6-layer stanene/InSb films. Furthermore, a phase transition from topological insulator (TI) to Dirac semimetal can be tuned by a slight in-plane strain (less than 1%), which offers great potential for device applications.
2.3 Metal substrate
2.3.1 Cu(111) substrates
Fabricating single-layer stanene films on Cu(111) substrates was reported by Deng et al. in 2018 [25]. By using low-temperature MBE technic, extremely flat stanene without buckling (height = 0.18 nm) uniformly forms on the top of Cu(111) (Fig. 4a). As shown in the atomic-resolution STM image (Fig. 4b), an in-plane lattice constant of 0.51 nm can be obtained, which is much larger than that of a free-standing stanene (0.47 nm). More interesting, an inversion band gap as large as 0.3 eV (Fig. 4c) and topological edge states (Fig. 4d) are observed from ARPES and STM measurements respectively, which possibly motivate stanene/Cu(111) to be the ideal system to realize QSHE.
2.3.2 Bi(111) substrates
Very recently, few-layer stanene films have also been successfully prepared through a two-step MBE growth recipe on Bi(111) substrates [26]. Figure 5a shows the typical morphology of fourth-layer stanene island sitting on a three-layer stanene platform. STM dI/dV mapping of the island shows clear edge states at the film edges (Fig. 5b-5c), signifying the potential existence of topological edge states in stanene/Bi(111) system. Moreover, superconducting properties of the stanene films have been investigated at 400 mK. As shown in Fig. 5d, clear superconducting gaps (taken along the dotted arrow in Fig. 5a) are detected on the same island where the robust edge states have been witnessed. Considering the coexistence of topological edge states and large superconducting gaps (∼0.33 meV), stanene/Bi(111) system may provide a possible platform to further study triplet pairing and Majorana modes.
2.3.3 Other metal substrates
Some other metals, such as Ag(111) and Sb(111), are also selected as substrates to grow stanene films [27, 28]. For stanene/Ag(111) system, stanene forms a nearly planar structure in large domains (Fig. 6a-6b) and its electronic structure exhibits a characteristic 2D band with parabolic dispersion (Fig. 6c) due to the non-negligible interaction with the underlying surface alloy. For stanene/Sb(111) system, stanene nanoribbons can be prepared on Sb(111) and continuous evolution of the electronic bands across the nanoribbon has been observed, which related to the strain field gradient in stanene. These results indicate that, with plentiful physics, stanene-based systems are worth further investigation.
3 Summary and perspective
In this Perspective, we have reviewed experimental approaches that have successfully created few-layer stanene films on various substrates (see Table 1 for the comparison between these stanene films grown on different substrates). As a candidate for realizing QSHE, massive research in both experiment and theory have been performed. However, the smoking-gun evidence, the quantized edge conductance in transport measurement, has not yet been observed in stanene-based systems. As a claimed QSH insulator, trilayer stanene shows band-inversion structure on PbTe(111) substrate, while single-layer (four-layer) stanene shows topological edge states on Cu(111) (Bi(111)) substrate. Nevertheless, all these systems have their disadvantages: stanene films grown on PbTe(111) are heavily P doped; Cu(111) and Bi(111) substrates are pristine metallic, which hinder the further transport study of the quantized edge channels. Therefore, choosing a suitable insulating substrate to grow stanene is the main problem waiting to be solved in the future research. All in all, taking the advantage of the simple atomic structure, large band-inversion gap, as well as abundant tuning methods, stanene-based system is still an intriguing system for basic scientific research and real-world applications.
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Funding
The authors thank the National Natural Science Foundation of China (Grant No. 92065206, No. 62204016) and the Beijing Natural Science Foundation (Grant No. 1222034). Open Access funding provided by Shanghai Jiao Tong University.
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YZ and KH wrote the manuscript. All authors read and approved the final manuscript. All data generated or analyzed during this study are included in this article and the references. All authors confirm that the work described has not been published before. All authors read and approved the final manuscript.
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Zang, Y., Zhu, K., Li, L. et al. Molecular beam epitaxy growth of few-layer stanene. Quantum Front 1, 11 (2022). https://doi.org/10.1007/s44214-022-00012-y
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DOI: https://doi.org/10.1007/s44214-022-00012-y