Material design of TI nanostructures

The development of nanostructured topological insulator materials and electronic devices is very relevant to practical applications (see the Introductory article). A major challenge to utilize the surface properties of these materials in charge transport processes is associated with the excessive bulk carriers arising from crystal defects^{Reference Navrátil, Horák, Plecháček, Kamba, Lošt’ák, Dyck, Chen and Uher19–Reference Jiang, Sun, Chen, Wang, Li, Song, He, Wang, Chen, Xue, Ma and Zhang21} and environmental doping.^{Reference Analytis, Chu, Chen, Corredor, McDonald, Shen and Fisher10,Reference Analytis, McDonald, Riggs, Chu, Boebinger and Fisher11,Reference Kong, Cha, Lai, Peng, Analytis, Meister, Chen, Zhang, Fisher, Shen and Cui22–Reference Chen, He, Weng, Zhang, Zhao, Liu, Jia, Mou, Liu, He, Peng, Feng, Xie, Liu, Dong, Zhang, Wang, Peng, Wang, Zhang, Yang, Chen, Xu, Dai, Fang and Zhou24} Compared with the bulk crystals, TI nanostructures are promising systems for investigating the surface states due to the large surface-to-volume ratio. The HgTe/CdTe quantum well is the first TI with a 2D form, with metallic edges wrapping around the quantum well.^{Reference Kane and Mele25–Reference König, Wiedmann, Brüne, Roth, Buhmann, Molenkamp, Qi and Zhang27} The observation of the quantum spin Hall effect in this system demonstrated the feasibility of accessing the exotic properties of TIs in low-dimensional electronic devices.^{Reference König, Wiedmann, Brüne, Roth, Buhmann, Molenkamp, Qi and Zhang27} Extensive research efforts have led to the extension of the concepts of 2D TIs into 3D TIs with metallic states on the crystal surface protected by time-reversal symmetry.^{Reference Fu, Kane and Mele28–Reference Roy30} This largely expands the pool of TI materials. It is worth mentioning that non-trivial surface states, which are protected by crystal symmetry, have also recently been observed on the topological crystalline insulators (TCIs), Pb_1–xSn_xSe, Pb_1–xSn_xTe, and SnTe.^{Reference Fu31–Reference Hsieh, Lin, Liu, Duan, Bansil and Fu35}

The most widely studied TIs are the binary chalcogenides of Bi₂Se₃, Bi₂Te₃, and Sb₂Te₃,^{Reference Zhang, Liu, Qi, Dai, Fang and Zhang4–Reference Chen, Analytis, Chu, Liu, Mo, Qi, Zhang, Lu, Dai, Fang, Zhang, Fisher, Hussain and Shen6} which possess a single Dirac cone of the surface states residing in a relatively large bulk bandgap (∼0.2 to 0.3 eV), compared to the early example of the HgTe/CdTe quantum well structure (10 meV).^{Reference König, Wiedmann, Brüne, Roth, Buhmann, Molenkamp, Qi and Zhang27} These compounds share similar tetradymite-type structures that are formed by stacking covalently bonded molecular layers with weak van der Waals interactions. Their TI nature is further identified in their solid solution Bi_2–xSb_xTe_3–ySe_y for a wide range of compositions^{Reference Xiong, Petersen, Qu, Hor, Cava and Ong12,Reference Ren, Taskin, Sasaki, Segawa and Ando13,Reference Kong, Chen, Cha, Zhang, Analytis, Lai, Liu, Hong, Koski, Mo, Hussain, Fisher, Shen and Cui16, Reference Ren, Taskin, Sasaki, Segawa and Ando36–Reference Zhang, Chang, Zhang, Wen, Feng, Li, Liu, He, Wang, Chen, Xue, Ma and Wang39} —a layered crystalline system with tunable composition to optimize the properties (see Figure 1a).

Figure 1.

Topological insulator nanomaterials. (a) Tetradymite-type crystal structure of Bi_2–xSb_xTe_3–ySe_y consisting of molecular layers bonded by van der Waals interactions, with Bi/Sb atoms in orange and Se/Te atoms in purple. (b) Optical micrograph of Bi₂Se₃ thin flakes produced by mechanical exfoliation. The overlaid numbers indicate the number of quintuple layers of Bi₂Se₃.^{Reference Checkelsky, Hor, Cava and Ong40} (c) Scanning electron microscope (SEM) image of Bi₂Se₃ nanoribbons synthesized by a nanoparticle-catalyzed vapor transport process.^{Reference Peng, Lai, Kong, Meister, Chen, Qi, Zhang, Shen and Cui14} (d) SEM image of Bi₂Te₃ nanoplates formed by a catalyst-free vapor transport.^{Reference Kong, Dang, Cha, Li, Meister, Peng, Liu and Cui45} (e) Optical image of Bi₂Se₃ films grown on mica by van der Waals epitaxy.^{Reference Peng, Dang, Cao, Chen, Wu, Zheng, Li, Shen and Liu47}

As shown in Figure 1b, the weak interlayer coupling allows facile preparation of ultrathin flakes by mechanical exfoliation of bulk crystals using Scotch tape^{Reference Checkelsky, Hor, Cava and Ong40}—the technique widely adopted to produce graphene from graphite.^{Reference Novoselov, Geim, Morozov, Jiang, Zhang, Dubonos, Grigorieva and Firsov41} The process essentially offers convenient access to TI nanomaterials with excellent quality. We further demonstrated that the concept can be generalized to exfoliate Bi₂Se₃ nanostructures by using an atomic force microscopy tip.^{Reference Hong, Kundhikanjana, Cha, Lai, Kong, Meister, Kelly, Shen and Cui42} Alternatively, the top-down exfoliation can also be performed through a solution process, which allows the preparation of large quantities of thin flakes from bulk crystals.^{Reference Coleman, Lotya, O’Neill, Bergin, King, Khan, Young, Gaucher, De, Smith, Shvets, Arora, Stanton, Kim, Lee, Kim, Duesberg, Hallam, Boland, Wang, Donegan, Grunlan, Moriarty, Shmeliov, Nicholls, Perkins, Grieveson, Theuwissen, McComb, Nellist and Nicolosi43}

Bottom-up synthesis is also routinely employed to prepare TI nanostructures with well-defined morphologies. Quasi-1D nanoribbons of Bi₂Se₃ are often prepared in a horizontal tube furnace by a gold nanoparticle-catalyzed vapor transport process, in which the gold nanoparticle promotes 1D growth via the vapor-liquid-solid process^{Reference Peng, Lai, Kong, Meister, Chen, Qi, Zhang, Shen and Cui14,Reference Kong, Randel, Peng, Cha, Meister, Lai, Chen, Shen, Manoharan and Cui15} (Figure 1c). Solution synthesis is also employed to grow 1D nanoribbons by using a solvothermal process.^{Reference Xiu, He, Wang, Cheng, Chang, Lang, Huang, Kou, Zhou, Jiang, Chen, Zou, Shailos and Wang44} Two-dimensional TI nanoplates are typically produced by catalyst-free vapor transport (see Figure 1d) or solvothermal synthesis.^{Reference Kong, Dang, Cha, Li, Meister, Peng, Liu and Cui45,Reference Kong, Koski, Cha, Hong and Cui46} Two-dimensional nanostructures of TIs in the form of thin films are synthesized using van der Waals epitaxy (see Figure 1e). The technique is highly tolerant of large lattice mismatch, allowing the growth of high-quality films on different substrates with triangle/hexagonal lattices.^{Reference Peng, Dang, Cao, Chen, Wu, Zheng, Li, Shen and Liu47–Reference Kou, He, Xiu, Lang, Liao, Wang, Fedorov, Yu, Tang, Huang, Jiang, Zhu, Zou and Wang51} Nanostructures of non-layered crystals, on the other hand, are primarily obtained through bottom-up synthesis. For example, quasi-1D nanowires of SnTe, a TCI with a rock-salt structure, can be synthesized through a catalyst-free vapor transport process,^{Reference Safdar, Wang, Mirza, Wang, Xu and He52} whereas their films are generated by molecular beam epitaxy.^{Reference Assaf, Katmis, Wei, Satpati, Zhang, Bennett, Harris, Moodera and Heiman53}

The presence of non-trivial surface states in solid solutions and doped crystals allows for the compositional engineering of TIs. Low-dimension nanostructures, with their large surface-to-volume ratios, provide excellent geometries to probe the surface states. A significant fraction of conductivity, however, still comes from bulk carriers in most non-doped nanomaterials. Accordingly, various dopants are frequently employed to reduce the number of bulk carriers through compensational doping. In addition, the alloying approach of parent compounds in the form of a solid solution, for example in (Bi_xSb_1–x)₂Te₃, is also used to manipulate carrier type and density through compositional tuning (Figure 2a–c).^{Reference Kong, Chen, Cha, Zhang, Analytis, Lai, Liu, Hong, Koski, Mo, Hussain, Fisher, Shen and Cui16,Reference Zhang, Chang, Zhang, Wen, Feng, Li, Liu, He, Wang, Chen, Xue, Ma and Wang39} These efforts allow access to TIs with suppressed bulk conductivity, in which the charge transport is dominated by surface states.^{Reference Kong, Chen, Cha, Zhang, Analytis, Lai, Liu, Hong, Koski, Mo, Hussain, Fisher, Shen and Cui16,Reference Hong, Cha, Kong and Cui17} The suppression of bulk carrier density is further confirmed by observing pronounced ambipolar field effects (see Figure 2d), in which the Fermi level is electrostatically manipulated with gate voltage.^{Reference Kong, Chen, Cha, Zhang, Analytis, Lai, Liu, Hong, Koski, Mo, Hussain, Fisher, Shen and Cui16,Reference Hong, Cha, Kong and Cui17} The minimum carrier density of ∼2 × 10¹¹ cm^–2 achieved in the Sb-doped Bi₂Se₃ nanoribbon is much lower than for (Bi_0.5Sb_0.5)₂Te₃, presumably due to the exposed Dirac point within the bulk bandgap accessible by gating.^{Reference Hong, Cha, Kong and Cui17}

Figure 2.

Compositional tuning and ambipolar field effect in a (Bi_xSb_1–x)₂Te₃ nanoplate.^{Reference Kong, Chen, Cha, Zhang, Analytis, Lai, Liu, Hong, Koski, Mo, Hussain, Fisher, Shen and Cui16} (a–b) Transmission electron microscope (TEM) image and high-resolution TEM image, respectively, of a (Bi_0.5Sb_0.5)₂Te₃ nanoplate revealing the single crystalline nature. (c) Nanoplate area carrier density is chemically modulated by adjusting the composition. Inset: Bismuth, antimony, and tellurium elemental maps. Overlaying the elemental maps (bottom right panel) reveals the morphology of the nanoplate with uniform color, indicating that the elements are homogeneously distributed. (d) Ambipolar field effect observed in an ultrathin (Bi_0.5Sb_0.5)₂Te₃ nanoplate (thickness ∼5 nm). Top: typical dependence of resistance, R, on gate voltage, V _G, exhibiting a sharp peak. Bottom: corresponding Hall coefficient, R _H, versus V _G reverses sign when R approaches its maximum, suggesting a change in carrier type.

Electronic transport in topological insulator nanostructures

Enhanced surface electron contribution in TI nanostructures provides an ideal platform for probing electron transport of the topological surface states. We review a few examples of electronic transport studies of TI nanostructures. More specifically, Shubnikov-de Haas (SdH) oscillations (i.e., quantum oscillations in magneto-resistance observed at high magnetic field) from TI nanostructures have been reported, following the initial observations from TI bulk crystals.^{Reference Analytis, McDonald, Riggs, Chu, Boebinger and Fisher11–Reference Ren, Taskin, Sasaki, Segawa and Ando13} The unique morphology and dimensions comparable to the phase coherence length/mean free path of the surface electrons have led to observations of quantum interference and 1D states. Finally, proximity-induced superconductivity (i.e., the superconducting transition of non-superconducting materials in contact with a superconductor) has also been observed in TI nanostructures.

Aharonov–Bohm effect and 1D topological states

The Aharonov-Bohm (AB) effect is a quantum phenomenon that originates from the electromagnetic potential difference between two separate electron paths, which results in a periodic modulation of the electron propagation probability by changing the magnetic field enclosed by the paths. Since the earliest demonstration of the AB effect in solid state systems—metallic ring structures, h/e or h/2e periodicity in magnetoresistance has been understood as evidence of coherent electron transport (e.g., in carbon nanotubes [CNTs]).^{Reference Webb, Washburn, Umbach and Laibowitz57,Reference Bachtold, Strunk, Salvetat, Bonard, Forro, Nussbaumer and Schonenberger58} In a topological insulator nanowire device exposed to a magnetic flux along the long axis, all surface electrons will gain identical phase from the magnetic flux Φ, while bulk carriers experiencing an external magnetic field would generate no regular periodicity. The first AB oscillations in topological insulator nanowires were reported in Bi₂Se₃ nanowires,^{Reference Peng, Lai, Kong, Meister, Chen, Qi, Zhang, Shen and Cui14} providing strong evidence of topological surface electron conduction in a coherent manner (Figure 3). Subsequently, many other nanowires of candidate topological insulators also manifest AB oscillations, for example, Bi₂Te₃, β–Ag₂Te, and SnTe nanowires.^{Reference Xiu, He, Wang, Cheng, Chang, Lang, Huang, Kou, Zhou, Jiang, Chen, Zou, Shailos and Wang44,Reference Safdar, Wang, Mirza, Wang, Xu and He52,Reference Lee, In, Yoo, Jo, Park, Kim, Koo, Kim, Kim and Wang59}

Figure 3.

Aharonov–Bohm effect in topological insulator nanowires.^{Reference Peng, Lai, Kong, Meister, Chen, Qi, Zhang, Shen and Cui14} (a) Scanning electron microscope image of a Bi₂Se₃ nanoribbon device under a parallel magnetic field B. (b) Normalized magnetoresistance showing periodic oscillations matching the magnetic flux h/e.

In addition, AB oscillations in TI nanowires suggest a different type of electronic band structure made of the surface electrons—1D states of the topological surface states.^{Reference Bardarson, Brouwer and Moore60,Reference Zhang and Vishwanath61} When the surface electrons’ mean free path exceeds the circumference of the nanowire cross-section, momentum quantization brings one-dimensional subband formation out of 2D surface electrons. Interestingly, these 1D subbands can be periodically modulated by a magnetic flux, giving magneto-oscillations in conductance (Figure 4a–b). Unlike the 1D subband formation in the “graphene to CNT transition,” the surface electrons on TI nanowires have an additional phase factor (π) from the spin-momentum interlocking nature, which is known as the spin Berry phase (spins of the surface electrons make a 2π rotation along the nanowire circumference and acquire π phase due to electrons’ fermionic nature, spin = 1/2). Thus, all the 1D subbands of surface electrons are gapped at zero magnetic field. However, the magnetic half quantum flux (Φ = h/2e) restores a gapless 1D mode. A recent experiment by Hong et al. indeed showed such a gap closing transition tuned by a magnetic field (Figure 4c).^{Reference Hong, Zhang, Cha, Qi and Cui18} A more detailed study of the gapless state at Φ = h/2e revealed that it is robust against additional impurities, strong enough to suppress most quantum interferences, but it can be easily destroyed under time-reversal symmetry breaking (i.e., perpendicular magnetic field).

Figure 4.

One-dimensional band evolution in topological insulator (TI) nanowires.^{Reference Hong, Zhang, Cha, Qi and Cui18} (a) Schematic band structure of a bulk topological insulator (Bi₂Se₃). Surface states (red) exist in parallel with bulk conduction/valence bands (purple). (b) Left: band structure of a TI nanowire (with no magnetic field). Topological surface band transforms to discrete 1D subbands (black bands) with spin degeneracy. Right: band structure of a TI nanowire (with magnetic flux Φ = ±h/2e). The gapless bands (red and blue) are not spin degenerate. The bottom cartoons summarize additional π Berry’s phase from a 2π rotation of electrons (red to blue color transition), resulting in spin-degenerate 1D channels (black) at zero magnetic field (left) and helical 1D channels (blue and red) with magnetic flux Φ = ±h/2e (right). (c) Resistance (R) versus gate voltage (V _G) graph from a Bi₂Se₃ nanowire device, with Φ = 0 (black, gapped) and Φ = h/2e (red, gapless). The resistance maximum indicates the Fermi level close to the Dirac point.

Applications and future perspective

Spin-textured surface states are attractive for novel electronics. The spin-momentum locking nature of the surface electrons suggests an electrical manipulation of spin currents, which is naturally desirable for spintronics applications. One of the practical challenges is spin injection from ferromagnetic contact to TI materials, requiring further experimental efforts in interface engineering. TI materials (i.e., Bi₂Te₃) are also well known for their superior thermoelectric properties.^{Reference Hor, Richardella, Roushan, Xia, Checkelsky, Yazdani, Hasan, Ong and Cava68} The thermoelectric figure of merit is expected to be improved by making use of surface states decoupling with electronic heat conduction. In particular, TI nanowires and nanoplates are ideal material forms for thermal transport measurements in suspended geometries (Figure 5a) and are expected to enhance thermoelectric performance.^{Reference Pettes, Maassen, Jo, Lundstrom and Shi69,Reference Xu, Gan and Zhang70}

Figure 5.

Applications of topological insulator nanostructures. (a) A suspended Bi₂Te₃ nanoplate device for thermal transport measurement.^{Reference Pettes, Maassen, Jo, Lundstrom and Shi69} The scale bar indicates 10 μm. (b) Flexible, transparent electrodes of Bi₂Se₃ 10 nm nanosheet on a mica substrate.^{Reference Peng, Dang, Cao, Chen, Wu, Zheng, Li, Shen and Liu47} (c) Bi₂Se₃ nanoribbons before Cu intercalation (left) and after Cu intercalation (right, 60 at.%).^{Reference Koski, Cha, Reed, Wessells, Kong and Cui72}

The layered structure of Bi₂Se₃, Bi₂Te₃, and their alloys imply that TI nanostructures can be broadly defined as 2D materials. Combined with many other 2D atomic crystals, TI nanostructures provide building blocks for 2D van der Waals heterostructures^{Reference Geim and Grigorieva71} with unique electronic states. A few examples of transparent electrodes demonstrate how TI nanomaterials can be used for applications like many other 2D layered materials (Figure 5b). For example, the surface states in Bi₂Se₃ will enhance the electrical conductivity of the electrode material, while the thin film of Bi₂Se₃ maintains high optical transmittance over a wide range of wavelengths.^{Reference Peng, Dang, Cao, Chen, Wu, Zheng, Li, Shen and Liu47} The layered structure with van der Waals gaps is an interesting playground for intercalation. Chemical intercalation of metal atoms and organic molecules into TI nanomaterials has been reported;^{Reference Koski, Cha, Reed, Wessells, Kong and Cui72–Reference Cha, Koski, Huang, Wang, Luo, Kong, Yu, Fan, Brongersma and Cui74} some metal atoms/ions (i.e., zero-valence copper) can be intercalated up to 60% in atomic percentage, modifying electronic and optical properties (Figure 5c). The chemistry and electrochemistry of TI nanomaterials has not been fully developed yet, but more in-depth studies are expected in the future.

Here, we briefly reviewed the progress in TI nanostructures over the last few years. Despite their short history, TI nanostructures have provided many intriguing examples of both fundamental studies and applications. As more device applications of TIs develop, TI nanostructures will gain more interest. This field is fertile ground for both physics and applications for years to come.