Landau quantization and the thickness limit of topological insulator thin films of Sb2Te3

A Roadmap for Controlled Production of Topological Insulator Nanostructures and Thin Films

The group V-VI chalcogenide semiconductors (Bi2 Se3 , Bi2 Te3 , and Sb2 Te3 ) have long been known as thermoelectric materials. Recently, they have been once more generating interest because Bi2 Se3 , Bi2 Te3 and Sb2 Te3 have been crowned as 3D topological insulators (TIs), which have insulating bulk gaps and metallic Dirac surface states. One big challenge in the study of TIs is the lack of high-quality materials with few defects and insulating bulk states. To manifest the topological surface states, it is critical to suppress the contribution from the bulk carriers. Controlled production of TI nanostructures that have a large surface-to-volume ratio is an efficient way to reduce the bulk conductance and to significantly enhance the topological surface conduction. In this review article, the recent progress on the preparation of TI nanostructures is highlighted. Basic production methods for TI nanostructures are introduced in detail. Furthermore, several specific production approaches to reduce the residual bulk carriers from defects are summarized. Finally, the progress and the prospects of the production of TI-based heterostructures, which hold promise in both fundamental study and novel applications are discussed.

Observation of Anderson localization in ultrathin films of three-dimensional topological insulators

Anderson localization, the absence of diffusive transport in disordered systems, has been manifested as hopping transport in numerous electronic systems, whereas in recently discovered topological insulators it has not been directly observed. Here, we report experimental demonstration of a crossover from diffusive transport in the weak antilocalization regime to variable range hopping transport in the Anderson localization regime with ultrathin (Bi_{1-x}Sb_{x})_{2}Te_{3} films. As disorder becomes stronger, negative magnetoconductivity due to the weak antilocalization is gradually suppressed, and eventually, positive magnetoconductivity emerges when the electron system becomes strongly localized. This work reveals the critical role of disorder in the quantum transport properties of ultrathin topological insulator films, in which theories have predicted rich physics related to topological phase transitions.

van der Waals epitaxial growth of atomically thin Bi₂Se₃ and thickness-dependent topological phase transition

Two-dimensional (2D) atomic-layered heterostructures stacked by van der Waals interactions recently introduced new research fields, which revealed novel phenomena and provided promising applications for electronic, optical, and optoelectronic devices. In this study, we report the van der Waals epitaxial growth of high-quality atomically thin Bi2Se3 on single crystalline hexagonal boron nitride (h-BN) by chemical vapor deposition. Although the in-plane lattice mismatch between Bi2Se3 and h-BN is approximately 65%, our transmission electron microscopy analysis revealed that Bi2Se3 single crystals epitaxially grew on h-BN with two commensurate states; that is, the (1̅21̅0) plane of Bi2Se3 was preferably parallel to the (1̅100) or (1̅21̅0) plane of h-BN. In the case of the Bi2Se3 (2̅110) ∥ h-BN (11̅00) state, the Moiré pattern wavelength in the Bi2Se3/h-BN superlattice can reach 5.47 nm. These naturally formed thin crystals facilitated the direct assembly of h-BN/Bi2Se3/h-BN sandwiched heterostructures without introducing any impurity at the interfaces for electronic property characterization. Our quantum capacitance (QC) measurements showed a compelling phenomenon of thickness-dependent topological phase transition, which was attributed to the coupling effects of two surface states from Dirac Fermions at/or above six quintuple layers (QLs) to gapped Dirac Fermions below six QLs. Moreover, in ultrathin Bi2Se3 (e.g., 3 QLs), we observed the midgap states induced by intrinsic defects at cryogenic temperatures. Our results demonstrated that QC measurements based on h-BN/Bi2Se3/h-BN sandwiched structures provided rich information regarding the density of states of Bi2Se3, such as quantum well states and Landau quantization. Our approach in fabricating h-BN/Bi2Se3/h-BN sandwiched device structures through the combination of bottom-up growth and top-down dry transferring techniques can be extended to other two-dimensional layered heterostructures.

Simultaneous electrical-field-effect modulation of both top and bottom Dirac surface states of epitaxial thin films of three-dimensional topological insulators

It is crucial for the studies of the transport properties and quantum effects related to Dirac surface states of three-dimensional topological insulators (3D TIs) to be able to simultaneously tune the chemical potentials of both top and bottom surfaces of a 3D TI thin film. We have realized this in molecular beam epitaxy-grown thin films of 3D TIs, as well as magnetic 3D TIs, by fabricating dual-gate structures on them. The films could be tuned between n-type and p-type by each gate alone. Combined application of two gates can reduce the carrier density of a TI film to a much lower level than with only one of them and enhance the film resistance by 10,000%, implying that Fermi level is tuned very close to the Dirac points of both top and bottom surface states without crossing any bulk band. The result promises applications of 3D TIs in field effect devices.

Strong magneto-optical effects due to surface states in three-dimensional topological insulators

We show that a thin film of a three-dimensional topological insulator such as Bi(2)Se(3)or Bi(2)Te(3) can exhibit strong linear and nonlinear magneto-optical effects in a transverse magnetic field. In particular, one can achieve an almost complete circular polarization of an incident terahertz or mid-infrared radiation and an efficient four-wave mixing.

Intrinsic topological insulator Bi(1.5)Sb(0.5)Te(3-x)Se(x) thin crystals

The quaternary topological insulator (Bi,Sb)₂(Te,Se)₃ has demonstrated topological surface states with an insulating bulk. Scientists have identified an optimized composition of Bi_1.5Sb_0.5Te_1.7Se_1.3 with the highest resistivity reported. But the physics that drive to this composition remains unclear. Here we report the crystal structure and the magneto-transport properties of Bi_1.5Sb_0.5Te_3-xSe_x (BSTS) series. A correlation between the structure and the physical properties has been revealed. We found out that within the rhombohedral structure, the composition with most Te substituting Se has the highest resistivity. On the other hand, segregation of other composition phases will introduce much higher bulk concentration.

Scanning tunneling microscopy studies of topological insulators

Scanning tunneling microscopy (STM), with surface sensitivity, is an ideal tool to probe the intriguing properties of the surface state of topological insulators (TIs) and topological crystalline insulators (TCIs). We summarize the recent progress on those topological phases revealed by STM studies. STM observations have directly confirmed the existence of the topological surface states and clearly revealed their novel properties. We also discuss STM work on magnetic doped TIs, topological superconductors and crystalline symmetry-protected surface states in TCIs. The studies have greatly promoted our understanding of the exotic properties of the new topological phases, as well as put forward new challenges. STM will continue to play an important role in this rapidly growing field from the point view of both fundamental physics and applications.

Atomic and electronic structure of an alloyed topological insulator, Bi1.5Sb0.5Te1.7Se1.3

Bi2-xSbxTe3-ySey has been argued to exhibit both topological surface states and insulating bulk states, but has not yet been studied with local probes on the atomic scale. Here we report on the atomic and electronic structures of Bi1.5Sb0.5Te1.7Se1.3 studied using scanning tunnelling microscopy (STM) and spectroscopy (STS). Although there is significant surface disorder due to alloying of constituent atoms, cleaved surfaces of the crystals present a well-ordered hexagonal lattice with 10 Å high quintuple layer steps. STS results reflect the band structure and indicate that the surface state and Fermi energy are both located inside the energy gap. In particular, quasi-particle interference patterns from electron scattering demonstrate that the surface states possess linear dispersion and chirality from spin texture, thus verifying its topological nature. This finding demonstrates that alloying is a promising route to achieve full suppression of bulk conduction in topological insulators whilst keeping the topological surface state intact.

Observation of quantum-tunnelling-modulated spin texture in ultrathin topological insulator Bi2Se3 films

Understanding the spin-texture behaviour of boundary modes in ultrathin topological insulator films is critically essential for the design and fabrication of functional nanodevices. Here, by using spin-resolved photoemission spectroscopy with p-polarized light in topological insulator Bi2Se3 thin films, we report tunnelling-dependent evolution of spin configuration in topological insulator thin films across the metal-to-insulator transition. We report a systematic binding energy- and wavevector-dependent spin polarization for the topological surface electrons in the ultrathin gapped-Dirac-cone limit. The polarization decreases significantly with enhanced tunnelling realized systematically in thin insulating films, whereas magnitude of the polarization saturates to the bulk limit faster at larger wavevectors in thicker metallic films. We present a theoretical model that captures this delicate relationship between quantum tunnelling and Fermi surface spin polarization. Our high-resolution spin-based spectroscopic results suggest that the polarization current can be tuned to zero in thin insulating films forming the basis for a future spin-switch nanodevice.

Thermoelectric properties of an ultra-thin topological insulator

Thermoelectric coefficients of an ultra-thin topological insulator are presented here. The hybridization between top and bottom surface states of a topological insulator plays a significant role. In the absence of a magnetic field, the thermopower increases and thermal conductivity decreases with an increase in the hybridization energy. In the presence of a magnetic field perpendicular to the ultra-thin topological insulator, thermoelectric coefficients exhibit quantum oscillations with inverse magnetic field, whose frequency is strongly modified by the Zeeman energy and whose phase factor is governed by the product of the Landé g-factor and the hybridization energy. In addition to the numerical results, the low-temperature approximate analytical results for the thermoelectric coefficients are also provided. It is also observed that for a given magnetic field these transport coefficients oscillate with hybridization energy, at a frequency that depends on the Landé g-factor.

Warping effect-induced optical absorbance increment of topological insulator films for THz photodetectors with high signal-to-noise ratio

Strong optical absorbance makes topological insulator (TI) surfaces a promising high-performance photodetector in the terahertz (THz) to infrared frequency range. Here, we study the optical absorbance of more realistic TI films with hexagonal warping effect using the Fermi's golden rules. It was found that when the warping term is λ ≠ 0, the absorbance is no longer a universal value as that of graphene or ideal Dirac cone, but increases monotonously with the photon energy. The increment is positively correlated with the parameter λ/vF(3) where vF is the Fermi velocity. The relative signal-to-noise ratio (SNR) of the TI film working as a photoresistor-type photodetector is significantly enhanced by the warping effect-induced absorbance increment. These investigations provide useful information for developing TI-based photodetectors with high SNR in the range of THz to infrared frequency.

Dirac electron states formed at the heterointerface between a topological insulator and a conventional semiconductor

Topological insulators are a class of semiconductor exhibiting charge-gapped insulating behaviour in the bulk, but hosting a spin-polarized massless Dirac electron state at the surface. The presence of a topologically protected helical edge channel has been verified for the vacuum-facing surface of several topological insulators by means of angle-resolved photoemission spectroscopy and scanning tunnelling microscopy. By performing tunnelling spectroscopy on heterojunction devices composed of p-type topological insulator (Bi1−xSbx)2Te3 and n-type conventional semiconductor InP, we report the observation of such states at the solid-state interface. Under an applied magnetic field, we observe a resonance in the tunnelling conductance through the heterojunction due to the formation of Landau levels of two-dimensional Dirac electrons at the interface. Moreover, resonant tunnelling spectroscopy reveals a systematic dependence of the Fermi velocity and Dirac point energy on the composition x. The successful formation of robust non-trivial edge channels at a solid-state interface is an essential step towards functional junctions based on topological insulators.

Identifying magnetic anisotropy of the topological surface state of Cr(0.05)Sb(1.95)Te(3) with spin-polarized STM

The surface magnetic property plays a key role in determining magnetic related quantum phenomena of magnetic topological insulators. Using spin-polarized scanning tunneling microscopy, we investigate the surface magnetism and anisotropy of a Cr doped topological insulator: Cr(0.05)Sb(1.95)Te(3). It is found that the topological surface state of Cr(0.05)Sb(1.95)Te(3) is spin polarized in the surface plane while the bulk shows a ferromagnetism with an out-of-plane easy axis. The upper and lower branch of the helical Dirac cone harbors the opposite spin polarization and the polarization at the Dirac point is zero. Our results show the complexity of surface magnetism of magnetic doped topological insulators.

Interplay between different magnetisms in Cr-doped topological insulators

Breaking the time-reversal-symmetry of topological insulators through magnetic doping has led to exotic physical discoveries. Here, we report the gate-dependent magneto-transport measurements on the Cr-doped (BixSb1-x)2Te3 thin films. With effective top-gate modulations, we demonstrate the presence of both the hole-mediated RKKY coupling and carrier-independent van Vleck magnetism in the magnetic TI systems. Most importantly, by varying the Cr doping concentrations from 2% to 20%, we unveil the interplay between the two magnetic orders and establish the valid approach to either enhance or suppress each individual contribution. The electric-field-controlled ferromagnetisms identified in the Cr-doped TI materials will serve as the fundamental step to further explore the TRS-breaking TI systems, and it may also help to expand the functionality of TI-based device for spintronics applications.

Manipulating surface-related ferromagnetism in modulation-doped topological insulators

A new class of devices based on topological insulators (TI) can be achieved by the direct engineering of the time-reversal-symmetry (TRS) protected surface states. In the meantime, a variety of interesting phenomena are also expected when additional ferromagnetism is introduced to the original topological order. In this Letter, we report the magnetic responses from the magnetically modulation-doped (Bi(z)Sb(1-z))2Te3/Cr(x)(Bi(y)Sb(1-y))2Te3 bilayer films. By electrically tuning the Fermi level across the Dirac point, we show that the top TI surface carriers can effectively mediate the magnetic impurities and generate robust ferromagnetic order. More importantly, such surface magneto-electric effects can be either enhanced or suppressed, depending on the magnetic interaction range inside the TI heterostructures. The manipulation of surface-related ferromagnetism realized in our modulation-doped TI device is important for the realization of TRS-breaking topological physics, and it may also lead to new applications of TI-based multifunctional heterostructures.

Electric-field tuning of the surface band structure of topological insulator Sb2Te3 thin films

We measured the response of the surface state spectrum of epitaxial Sb(2)Te(3) thin films to applied gate electric fields by low temperature scanning tunneling microscopy. The gate dependent shift of the Fermi level and the screening effect from bulk carriers vary as a function of film thickness. We observed a gap opening at the Dirac point for films thinner than four quintuple layers, due to the coupling of the top and bottom surfaces. Moreover, the top surface state band gap of the three quintuple layer films was found to be tunable by a back gate, indicating the possibility of observing a topological phase transition in this system. Our results are well explained by an effective model of 3D topological insulator thin films with structure inversion asymmetry, indicating that three quintuple layer Sb(2)Te(3) films are topologically nontrivial and belong to the quantum spin Hall insulator class.

Memory effect in a topological surface state of Bi2Te2Se

We demonstrate the controllable local manipulation of the Dirac surface state in a topological insulator, Bi2Te2Se, which has suppressed bulk carrier density. Using scanning tunneling microscopy/spectroscopy under magnetic fields, we observe Landau levels of the Dirac surface state in the conductance spectra. The Landau levels start to shift in their energy once the bias voltage between the tip and the sample exceeds a threshold value. The amount of shift depends on the history of bias ramping. As a result, conductance spectra show noticeable hysteresis, giving rise to a memory effect. The conductance images exhibit spatially inhomogeneous patterns which can also be controlled by the bias voltage in a reproducible way. On the basis of these observations, we argue that the memory effect is associated with the tip-induced local charging effect which is pinned by the defect-generated random potential. Our study opens up a new avenue to controlling the topological surface state.

Thin films of magnetically doped topological insulator with carrier-independent long-range ferromagnetic order

Thin films of magnetically doped topological insulators Cr(0.22) (Bi(x) Sb(1-x) )(1.78) Te(3) are found to possess carrier-independent long-range ferromagnetic order with perpendicular magnetic anisotropy. The anomalous Hall resistance is greatly enhanced, up to one quarter of quantum Hall resistance, by depletion of the carriers. The results demonstrate this material as a promising system to realize the quantized anomalous Hall effect.

Quantum capacitance of an ultrathin topological insulator film in a magnetic field

We present a theoretical study of the quantum magnetocapacitance of an ultrathin topological insulator film in an external magnetic field. The study is undertaken to investigate the interplay of the Zeeman interaction with the hybridization between the upper and lower surfaces of the thin film. Determining the density of states, we find that the electron-hole symmetry is broken when the Zeeman and hybridization energies are varied relative to each other. This leads to a change in the character of the magnetocapacitance at the charge neutrality point. We further show that in the presence of both Zeeman interaction and hybridization the magnetocapacitance exhibits beating at low and splitting of the Shubnikov de Haas oscillations at high perpendicular magnetic field. In addition, we address the crossover from perpendicular to parallel magnetic field and find consistency with recent experimental data.

Visualizing Landau levels of Dirac electrons in a one-dimensional potential

Using scanning tunneling spectroscopy, we study a 3D topological insulator Bi(2)Te(3) with a periodic structural deformation (buckling). The buckled surface allows us to measure the response of Dirac electrons in a magnetic field to the presence of a well-defined potential variation. We find that while the n=0 Landau level exhibits a 12 meV energy shift across the buckled structure at 7 T, the amplitude of this shift changes with the Landau level index. Modeling these effects reveals that the Landau level behavior encodes information on the spatial extent of their wave functions. Our findings have important implications for transport and magnetoresistance measurements in Dirac materials with engineered potential landscapes.

Fermi-level tuning of epitaxial Sb2Te3 thin films on graphene by regulating intrinsic defects and substrate transfer doping

High-quality Sb2Te3 films are obtained by molecular beam epitaxy on a graphene substrate and investigated by in situ scanning tunneling microscopy and spectroscopy. Intrinsic defects responsible for the natural p-type conductivity of Sb2Te3 are identified to be the Sb vacancies and Sb(Te) antisites in agreement with first-principles calculations. By minimizing defect densities, coupled with a transfer doping by the graphene substrate, the Fermi level of Sb2Te3 thin films can be tuned over the entire range of the bulk band gap. This establishes the necessary condition to explore topological insulator behaviors near the Dirac point.