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].

Figure 1
figure 1

Stanene film grown on Bi2Te3 substrate. (a) STM topography of single-layer stanene film on Bi2Te3. (b) Atomically resolved STM image of single-layer stanene on Bi2Te3. (c) ARPES spectra of single-layer stanene on Bi2Te3. Blue dotted lines mark the bands of stanene on Bi2Te3. Green dashed lines mark the bands of Bi2Te3 substrate. (d) Band structure of stanene on Bi2Te3 acquired by DFT calculations. Reproduced from Ref [13]

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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.

Figure 2
figure 2

Stanene film grown on PbTe(111) substrate. (a) STM image of single-layer stanene on PbTe(111). The inset of (a) shows the line profile along the red line. Reproduced from Ref [16]. (b) Atomic-resolution STM of single-layer stanene on PbTe(111). The inset of (b) shows the Fourier transformation image. Reproduced from Ref [16]. (c) ARPES spectra of single-layer stanene on PbTe(111) around \(\overline{\boldsymbol{\Gamma}} \) point. Reproduced from Ref [16]. (d) Transport measurement of superconductivity of few-layer stanene on PbTe(111). Reproduced from Ref [17]. (e) Calculated band structure of trilayer stanene on PbTe(111). The inset of (e) compares the calculated bands with the ARPES data. Reproduced from Ref [17] (f) Color-coded resistance of trilayer stanene on PbTe(111) as a function of in-plane magnetic field at a set of temperature points. Reproduced from Ref [18]

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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.

Figure 3
figure 3

Stanene film grown on InSb(111) substrate. (a) STM image of single-layer stanene on InSb(111). Reproduced from Ref [22]. (b) STM dI/dV spectra in the bulk and at the edge of single-layer stanene on InSb(111). Reproduced from Ref [22]. (c) STM dI/dV mapping of edge state of single-layer stanene on InSb(111). Reproduced from Ref [22]. ARPES spectra of single-layer stanene on InSb(111) before (d) and after (e) K doping. Reproduced from Ref [23]. (f) ARPES spectra of 6-layer stanene on InSb(111). Reproduced from Ref [24]

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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.

Figure 4
figure 4

Stanene film grown on Cu(111) substrate. (a) STM image of single-layer stanene on Cu(111). (b) Atomic-resolution STM of single-layer stanene on Cu(111). (c) ARPES spectra of single-layer stanene on Cu(111). (d) STM dI/dV spectra in the bulk and at the edge of single-layer stanene on Cu(111). Reproduced from Ref [25]

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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.

Figure 5
figure 5

Stanene film grown on Bi(111) substrate. (a) STM image of a four-layer stanene island on Bi(111). (b) STM dI/dV spectra taken at bulk and edges of four-layer stanene on Bi(111). (c) STM dI/dV mapping of edge states (∼185 meV) for the same island in (a). (d) Layer dependence of superconducting gap of stanene on Bi(111). Reproduced from Ref [26]

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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.

Figure 6
figure 6

Stanene films grown on Ag(111) and Sb(111) substrates. (a) STM image of single-layer stanene on Ag(111). Reproduced from Ref [27]. (b) Atomic-resolution STM of single-layer stanene on Ag(111). Reproduced from Ref [27]. (c) ARPES spectra of 0.5-layer stanene on Ag(111). Reproduced from Ref [27]. (d) STM image of 0.5 layer stanene grown on Sb(111). Reproduced from Ref [28]. (e) STM image of stanene nanoribbon on Sb(111). Reproduced from Ref [28]. (f) STM dI/dV map obtained along the line indicated by the black arrow in (e). Reproduced from Ref [28]

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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.

Table 1 Comparison of stanene films grown on different substrates
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