Session Y42: Topological Crystalline Insulators

Higher-order topological insulators

The discovery of topological insulators has rejuvenated band theory and led to fruitful collaboration between theory and experiment. Capitalizing on their inherent insensitivity to local noise, the (d-1)-dimensional surface states of d-dimensional first-order topological insulators remain gapless as long as their protecting symmetries are preserved. In my talk, I will review higher-order topological insulators (HOTIs), which comprise the most recent chapter of topological band theory. They are d-dimensional materials with (d-n)-dimensional gapless boundary states where n > 1. Using minimal examples, I will explain the fundamental types of HOTIs and their symmetry protection. I will also recount some of the exciting experimental results on HOTI (meta-)materials. My talk will be a pedagocical invitation to the field, directed at a broad audience, rather than a comprehensive technical review.   

Two-atom-thin topological crystalline insulators lacking out of plane inversion symmetry

A two-dimensional topological crystalline insulator (TCI) with a single unit cell (u.c.) thickness is demonstrated here. The chiral nature of the bulk TCI Hamiltonian from Fu [1] permits creating a 2x2 square Hamiltonian, whose topological properties hold invariant at both the bulk and at the single u.c.~thickness limits. The identical topological characterization for bulk and u.c.-thick phases is further guaranteed by a calculation involving Pfaffians.

[1]. L. Fu. Phys. Rev. Lett. 106, 106802 (2011).   

Metal-Organic Molecular Beam Epitaxy of WTe2

Monolayer transition metal dichalcogenides (TMDs) are strong candidates for future technological applications. Such applications require controlled means of ultra-high purity synthesis, as provided by molecular  beam epitaxy (MBE). So far, MBE-synthesized TMD monolayers have been limited to islands with lateral sizes on the order of tens of nanometers, due to the large difference of surface diffusivity of the transition metal and chalcogen species. Here, we introduce a molecular beam epitaxy method, based on the metal-organic precursor W(CO)₆, for growing monolayer WTe₂ [1]. We characterize our growth using x-ray photoelectron spectroscopy, scanning electron microscopy, and atomic force microscopy. We observe one-dimensional nanostructures of non-stoichiometric WTe_x localized at the substrate step edges, and two-dimensional islands on the substrate terraces.

[1] S. Tiefenbach et. al., Surf Sci. 318, L1161 (1994)

    

Tuning topological properties in Bi2Se3/VSe2 heterostructures

Topological materials have drawn great attention due to their exotic physical properties and various applications in quantum information science. Central to the fundament research and practical applications are the control and tunability of the topological states through material engineering, such as doping, strain and stacking of different 2D van der Waals materials. Here we  present a combined angle-resolved photoemission spectroscopy (ARPES) and first-principles study of the topological properties of few-layer 1T VSe₂ on few-quintuple layer Bi₂Se₃ heterojunctions. ARPES measurements show that details of the topological band structure of the heterojunction strongly depend on the thickness of the quintuple layers of Bi₂Se₃. Density functional theory is used to interpret the ARPES measurement and understand the evolution of the topological states. This study gains insights into the topological properties of VSe₂/ Bi₂Se₃ heterojunctions, which have important implications on tunability of the topological materials.    

Weak antilocalization in selective-area grown Pb1-xSnxTe nanowire networks

Lead Tin Telluride (Pb_1-xSn_xTe) is predicted to be a topological crystalline insulator (TCI) [1], meaning that the surface states are protected by crystal symmetries. The topological phase transition from a trivial narrow bandgap semiconductor to a TCI can be controlled through the Pb/Sn ratio, and has been observed experimentally at Sn concentrations of 30-40% [2][3].

Hybrid TCI/superconductor nanowire networks are of interest for applications in quantum computation, as these are predicted to host non-abelian quasiparticles, such as Majorana fermions or parafermions [4]. Towards this goal, we use a pre-patterned SiNx mask on a InP(111) substrate for selective area growth of Pb_1-xSn_xTe by molecular beam epitaxy [5], and define Hall bar devices with side gates that allow for simultaneous Hall and field-effect measurements.

By investigating the low-temperature (magneto-)transport properties, a Hall mobility (135 cm²/Vs) and carrier density (4.7·10²⁰ cm^-3, similar to [2]) are obtained for pure SnTe nanowires. Moreover, a cusp is observed in the magnetoresistance which we attribute to weak antilocalization; hinting at a contribution of the surface states to the overall transport, despite the high bulk conductivity.

[1] Hsieh, T., et al. Nat Commun 3, 982 (2012)

[2] Volobuev V.V., et al. Adv. Mat. 23, 3, 1604185 (2016)

[3] Safdar, M., Wang, Q., et al. Nano Lett. 15, 2485-2490 (2015)

[4] Xiao, J., Yan, B. Nat Rev Phys 3, 283–297 (2021).

[5] Jung, J. Schellingerhout, A.G. ArXiv:2209.09758v1 (2022)   

Close-to-Dirac point shift of large-area MOCVD-grown Bi2Te3’s Fermi level following growth on Sb2Te3

We developed a Metal Organic Chemical Vapour Deposition (MOCVD) process to grow the bi-layered Bi₂Te₃(top)/Sb₂Te₃ topological insulator on top of 4’’ Si(111). In single-phase Bi₂Te₃/Si(111), we have previously demonstrated clear topologically-protected surface states (TSS) by angle-resolved photoemission spectroscopy (ARPES) and magnetotransport, but a strong bulk contribution was still present with the Fermi level (E_F) crossing the conduction band at ~0.5 eV above the Dirac point [1]. Following the growth of 90 nm Bi₂Te₃ in direct contact with 30 nm Sb₂Te₃, we observed by ARPES a remarkable shift of E_F towards the Dirac point, totally suppressing the bulk states’ contribution. This was confirmed by magnetotransport, where, within the Hikami-Larkin-Nagaoka model, we measured an ideal α=-0.5 due to the optimized topologically-protected surface states. We will also present the first attempts in making use of such close-to-ideal positioning of the Bi₂Te₃’s Fermi level to manipulate magnetic figures in 2D-ferromagnet CrTe₂ grown on top of the developed Bi₂Te₃/Sb₂Te₃/Si(111) heterostructure.

[1] L. Locatelli, A. Kumar, P. Tsipas, A. Dimoulas, E. Longo, R. Mantovan, "Magnetotransport and ARPES studies of the topological insulators Sb₂Te₃ and Bi₂Te₃ grown by MOCVD on large-area Si substrates" Scientific Reports 12, 3891 (2022).

    

Exploration of topological electronic structures in bismuth halide series

Quasi-one-dimensional bismuth halides, Bi₄X₄ (X = I, Br), constitute a promising material platform to realize various non-trivial topological phases. Bi₄X₄ can be categorized by its stacking along c axis. Weak topological insulators (TIs) in single-layer stacking, high-order TI in double stacking, and topological phases transitions opportunities in between are on the table. In addition, discovery of gate-tunable Josephson supercurrent as well as existence of electronic instabilities driven by topological surface states (TSS) bring Bi₄X₄ a fertile candidate to study topological many-body physics and emergent quantum physics. In this talk, I will present experimental characterizations for electronic structures among the Bi₄X₄ series in terms of angle-resolved photoemission spectroscopy (ARPES), which is smoking-gun evidence to identify TSS and instabilities in them. State-of-the-art ARPES at synchrotrons enable us to explore (001) and (100) surfaces distinguishably, thus can provide reliable topological characterizations among the series. Taking advantages of it, we discovered a room-temperature topological phase transition between weak TI and high-order TI, an ideal weak TI with spin-polarized electronic instabilities derived from TSS within bulk gap, and gapped TSS due to hinge states in high-order TI. Future efforts to induce topological phase transitions will be also discussed.   

Shubnikov-de Haas oscillations in Pb1-xSnxTe epitaxial films

Topological crystalline insulators (TCIs) are a class of materials prized in recent years for their ability to form symmetry-protected massless surface states. SnTe is a TCI while PbTe is a trivial insulator, but Pb1-xSnxTe shows a topological phase transition at X~0.4. Higher Pb concentrations yield a trivial insulator while lower concentrations yield a TCI. Characterizing the surface states at Sn rich side of the transition remains elusive due to parasitic transport from. We grew high quality Pb1-xSnxTe heterostructures in a chalcogenide molecular beam epitaxy system. XRD measurements confirm single crystal thin films grown epitaxially on BaF2 (111) substrates. High field magnetoresistance measurements were carried out at various temperatures (10mK-700mK) and angles. We analyzed Shubnikov de-Haas (SdH) oscillations in samples with various Sn concentrations at various temperatures and field angles. The summed frequencies contained in the SdH oscillations elucidate the nature of topological surface states.   

g-factor of topological states from magnetooptical spectroscopy and quantum oscillations in Pb1-xSnxSe quantum well

Large g-factors in system with strong spin-orbit coupling are ideal for spintronic and quantum computing devices. Here, we report the high g-factor of the surface state in Pb_1-xSn_xSe quantum wells. We successfully grow high quality Pb_0.85Eu_0.15Se/Pb_0.7Sn_0.3Se/ Pb_0.85Eu_0.15Se single quantum wells with mobility larger than 4000cm²V^-1s^-1.  The high carrier mobility allows us to reach the quantum limit at reasonably achievable magnetic fields. We exploit this advantage to combine magnetooptical Landau level spectroscopy, Shubnikov-de-Haas transport measurement and consistent modelling of the two experiments to precisely extract the band parameters of the topological states of this system along with their spin and orbital g-factor. The obtained effective g-factor (g~80 at 1T for index n=1) is comparable with what is found for the InSb system, and is much larger than the InAs system (~15). This information is vital to the realization and understanding of novel quantized Hall effect stemming from this material family, and also shed light onto their future applications to quantum devices utilizing topological surface states.

    

Highly Tunable Band Inversion in AB2X4 (A=Ge, Sn, Pb; B=As, Sb, Bi; X=Se, Te) Compounds

Topological materials have been discovered so far largely by searching for existing compounds in crystallographic databases, but there are potentially new topological materials with desirable features that have not been synthesized. One of the desirable features is high tunability resulted from the band inversion with a very small direct band gap, which can be tuned by changes in pressure or strain to induce a topological phase transition. Using density functional theory (DFT) calculations, we have studied the septuple layered AB₂X₄ series compounds, where A=(Ge, Sn and Pb), B=(As, Sb and Bi) and X=(Se and Te). With the DFT thermodynamic stability validated by the already reported compounds in these series, we predict new stable Se compounds, which are not found in crystallographic database. Among them, we find that GeBi₂Se₄ and GeSb₂Se₄ having a small direct band gap at the Z point are very close to a strong topological insulator, which can be tuned by a moderate pressure to induce the band inversion. Importantly, the topological features with the small direct band gap are well isolated in both momentum and energy windows, which offers high tunability for studying the topological phase transition.   

Reducing the 3D-2D crossover thickness in Bi2Se3 by heterostructure engineering

The 3D topological insulator Bi2Se3 crosses over to the 2D limit usually as layer thickness is reduced past 6 Bi2Se3 quintuple layers (QL), as can be measured by the opening of a hybridization gap from its two surface states. In common Bi2Se3 heterostructures with a band-bending-induced potential gradient, the separation of the two surface states in real space and in energy both decreases as layer thickness is reduced, yielding the typical 6QL crossover thickness. Here, a combined first-principles theory and experimental study shows that an energy separation of the two surface states can be sustained to prevent surface state hybridization until 3 QLs. This is achieved by allowing the lower surface state to interact with a BiSe substrate (on top of NbSe2), which relieves the upper surface state from hybridizing with it. We further show that the 3QL Bi2Se3/BiSe system behaves similar to an asymmetric 4QL Bi2Se3 system, where Rashba-type quantum well bands are induced by a compositional gradient perpendicular to the layers.

    

molecular beam epitaxy and characterization of Bi2Se3 and Sb2Te3 on In2Se3 layers via selenium passivation of non-vicinal InP(111)B substrates

Topological Insulators (TI) have gained much attention due to their non-trivial topology facilitating a wide variety of applications. However, there is a large unintentional background doping that conceals their surface channels, and crystal defects such as twin domains are frequently observed. Although these are van der Waals materials, the influence of the substrate on the molecular beam epitaxy (MBE) material properties has been shown to be non-negligible. Non-vicinal InP(111)B has been used before and reported by some to produce good material properties, yet it has been challenging to completely suppress the twin domains. In this study, we explore the quality of epitaxial Bi₂Se₃ and Sb₂Te₃ on 5 nm ultra-thin In₂Se₃ layers grown by a selenium passivation technique during the oxide desorption of the InP(111)B substrates, without the use of an indium source. AFM shows the formation of a smooth In₂Se₃ layer and the HR-XRD shows its high crystallinity, with the presence of satellite peaks from which the thickness could be extracted. Morphology of Bi₂Se₃ exhibits smooth surfaces with large terraces. AFM of Sb₂Te₃ show planes with steps, with a larger roughness than Bi₂Se_3. Φ scans of the (015) plane of both the Bi₂Se₃ and Sb₂Te₃ layers show complete suppression of twin domains. Further investigation showed that the direction of the twin suppression is sometimes parallel to the (311) plane of the InP(111)B substrates and other times it is in the opposite direction. In either case we observe full twin suppression.   

Quantum Interference in SnTe nanowires

SnTe is a topological crystalline insulator (TCI) [1] and is predicted to undergo a phase transition to a higher-order topological state [2] by breaking crystal symmetry. These higher-order topological insulators (HOTI) have not been experimentally realized; they host hinge states on the boundary of two gapped surfaces, leading to conducting hinges. When combined with a superconductor, this system could host parafermions on a pair of hinge states due to the one-dimensional character of these states. Detecting the 2D surface and 1D hinge states in this material is therefore a key objective.

To this end, we perform transport measurements on SnTe nanowires. However, probing the topological surface states of SnTe is challenging due to a high bulk carrier density (~10²¹ cm^-3) and electrostatic gating therefore has a negligible effect. Nevertheless, conductance oscillations are observed as function of source-drain and backgate voltage which we attribute to Fabry-Pérot oscillations, a coherent transport behaviour indicating a (quasi-) ballistic transport channel [3]. The period of the oscillation corresponds to a characteristic length closely resembling the physical length of the device. Furthermore, the conductance variation on top of the background signal has a magnitude corresponding to one ballistic transport channel, hinting towards transport through a SnTe surface state.

 

[1] Nature Phys 8, 800–803 (2012).

[2] Nat Rev Phys 3, 283–297 (2021).

[3] Nano Letters 10 (9), 3439-3445 (2010).