Topological Crystalline Insulator Research Articles

Topological disclination mode in photonic Chern insulators

Topological defects in topological materials offer novel routes for creating topological modes and probing bulk topology. Disclination, a class of topological defects, has been recently shown to host fractional charges in topological crystalline insulators with well-defined Wannier centers. Here, we study the effects of disclinations in gyromagnetic photonic crystals with non-zero Chern numbers that prohibit the Wannier center picture. We find the emergence of topological disclination modes carrying orbital angular momentum from the interplay between the Chern-type topology and the effective flux induced by the disclination. When the Chern number changes its sign, the chirality of the disclination mode also flips, revealing the bulk-disclination correspondence. Furthermore, we perform numerical experiments to probe the disclination mode. Our results expand the study of disclination physics in photonic crystals to time-reversal-broken systems.

Catalyst-free MBE growth of PbSnTe nanowires with tunable aspect ratio

Topological crystalline insulators (TCIs) are interesting for their topological surface states, which hold great promise for scattering-free transport channels and fault-tolerant quantum computing. A promising TCI is SnTe. However, Sn-vacancies form in SnTe, causing a high hole density, hindering topological transport from the surface being measured. This issue could be relieved by using nanowires with a high surface-to-volume ratio. Furthermore, SnTe can be alloyed with Pb reducing the Sn-vacancies while maintaining its topological phase. Here we present the catalyst-free growth of monocrystalline PbSnTe in molecular beam epitaxy. By the addition of a pre-deposition stage before the growth, we have control over the nucleation phase and thereby increase the nanowire yield. This facilitates tuning the nanowire aspect ratio by a factor of four by varying the growth parameters. These results allow us to grow specific morphologies for future transport experiments to probe the topological surface states in a Pb1–x Sn x Te-based platform.

Application of femtosecond mode-locked SnTe thin films and generation of bound-state solitons

In the realm of ultrafast laser technology, the exploration of two-dimensional materials as saturable absorbers (SA) has garnered significant research interest. Our research investigates the characteristics of SnTe thin films, a topological crystalline insulator material, as a potential saturable absorber for ultrafast lasers. Using the molecular beam epitaxy (MBE) technique, we analyze the films’ morphology and composition through atomic force microscopy (AFM) and successfully deposit SnTe epilayers on Au(111)/mica substrates. Through the utilization of SnTe-SA, an erbium-doped fiber laser is fabricated, demonstrating a pulse output with a width of 276 fs and a center wavelength of 1560 nm, highlighting the potential of SnTe films in manufacturing ultrafast optical devices. Additionally, tightly bound solitons with a soliton interval of 1.01 ps are observed, contributing to the exploration of soliton nonlinear dynamics.

Density Functional Theory Study of the Spin-Orbit Insulating Phase in SnTe Cubic Nanowires: Implications for Topological Electronics.

We investigate the electronic, structural, and topological properties of the SnTe and PbTe cubic nanowires using ab initio calculations. Using standard and linear-scale density functional theory, we go from the ultrathin limit up to the nanowire thicknesses observed experimentally. Finite-size effects in the ultrathin limit produce an electric quadrupole and associated structural distortions; these distortions increase the band gap, but they get reduced with the size of the nanowires and become less and less relevant. Ultrathin SnTe cubic nanowires are trivial band gap insulators; we demonstrate that by increasing the thickness, there is an electronic transition to a spin-orbit insulating phase due to trivial surface states in the regime of thin nanowires. These trivial surface states with a spin-orbit gap of a few meV appear at the same k-point of the topological surface states. Going to the limit of thick nanowires, we should observe the transition to the topological crystalline insulator phase with the presence of two massive surface Dirac fermions hybridized with the persistent trivial surface states. Therefore, we have the copresence of massive Dirac surface states and trivial surface states close to the Fermi level in the same region of the k-space. According to our estimation, the cubic SnTe nanowires are trivial insulators below the critical thickness tc1 = 10 nm, and they become spin-orbit insulators between tc1 = 10 nm and tc2 = 17 nm, while they transit to the topological phase above the critical thickness of tc2 = 17 nm. These critical thickness values are in the range of typical experimental thicknesses, making the thickness a relevant parameter for the synthesis of topological cubic nanowires. Pb1-xSnxTe nanowires would have both these critical thicknesses tc1 and tc2 at larger values depending on the doping concentration. We discuss the limitations of density functional theory in the context of topological nanowires and the consequences of our results on topological electronics.

Spin-resolved topology and partial axion angles in three-dimensional insulators

Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- (T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{{\\mathcal{T}}}}}}}}$$\\end{document}-) invariant (helical) 3D TCIs—termed higher-order TCIs (HOTIs)—the boundary signatures can manifest as a sample-dependent network of 1D hinge states. We here introduce nested spin-resolved Wilson loops and layer constructions as tools to characterize the intrinsic bulk topological properties of spinful 3D insulators. We discover that helical HOTIs realize one of three spin-resolved phases with distinct responses that are quantitatively robust to large deformations of the bulk spin-orbital texture: 3D quantum spin Hall insulators (QSHIs), “spin-Weyl” semimetals, and T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{{\\mathcal{T}}}}}}}}$$\\end{document}-doubled axion insulator (T-DAXI) states with nontrivial partial axion angles indicative of a 3D spin-magnetoelectric bulk response and half-quantized 2D TI surface states originating from a partial parity anomaly. Using ab-initio calculations, we demonstrate that β-MoTe2 realizes a spin-Weyl state and that α-BiBr hosts both 3D QSHI and T-DAXI regimes.

Axially lattice-matched wurtzite/rock-salt GaAs/Pb1−xSnxTe nanowires

We investigate the full and half-shells of Pb1−xSnxTe topological crystalline insulator deposited by molecular beam epitaxy on the sidewalls of wurtzite GaAs nanowires (NWs). Due to the distinct orientation of the IV–VI shell with respect to the III–V core the lattice mismatch between both materials along the nanowire axis is less than 4%. The Pb1−xSnxTe solid solution is chosen due to the topological crystalline insulator properties above some critical concentrations of Sn (x ≥ 0.36). The IV–VI shells are grown with different compositions spanning from binary SnTe, through Pb1−xSnxTe with decreasing x value down to binary PbTe (x = 0). The samples are analysed by scanning transmission electron microscopy, which reveals the presence of (110) or (100) oriented binary PbTe and (100) Pb1−xSnxTe on the sidewalls of wurtzite GaAs NWs.

Pentagonal nanowires from topological crystalline insulators: a platform for intrinsic core-shell nanowires and higher-order topology.

We report on the experimental realization of Pb1-xSnx Te pentagonal nanowires (NWs) with [110] orientation using molecular beam epitaxy techniques. Using first-principles calculations, we investigate the structural stability of NWs of SnTe and PbTe in three different structural phases: cubic, pentagonal with [001] orientation and pentagonal with [110] orientation. Within a semiclassical approach, we show that the interplay between ionic and covalent bonds favors the formation of pentagonal NWs. Additionally, we find that this pentagonal structure is more likely to occur in tellurides than in selenides. The disclination and twin boundary cause the electronic states originating from the NW core region to generate a conducting band connecting the valence and conduction bands, creating a symmetry-enforced metallic phase. The metallic core band has opposite slopes in the cases of Sn and Te twin boundaries, while the bands from the shell are insulating. We finally study the electronic and topological properties of pentagonal NWs unveiling their potential as a new platform for higher-order topology and fractional charge. These pentagonal NWs represent a unique case of intrinsic core-shell one-dimensional nanostructures with distinct structural, electronic and topological properties between the core and the shell region.

Fractional disclination charge as a probe in acoustical topological crystalline insulators

The body–boundary correspondence refers to the relationship between the body and boundary states of topological insulators (TIs). In TIs, the presence of boundary states is connected to the bulk topological properties of the material. The topology can be identified by studying the energy of the topological modes within the bulk bandgap. However, not all topological materials exhibit boundary states within the insulating energy gap. In many cases, the presence of boundary states can be hidden or masked by the bulk energy bands, making it difficult to measure TIs. Recent experiments have shown that defects, which are commonly found in crystalline materials, can be used as probes to explore higher-order topologies that have been recently realized on various platforms. These defects can generate fractional charges and stable bound states in the dispersion region, allowing us to observe the clear body–disclination correspondence. We have performed simulations using a coupled acoustic cavity system with C3 and C5 symmetries to investigate the body–disclination correspondence in topological crystal insulators (TCIs) in the field of acoustics. Simulation and theoretical results have demonstrated that defects such as disclinations can be used to probe higher-order topologies that were previously unobservable in three-dimensional structures. This approach allows us to detect fractional mode charges and stable bound states, which are crucial for understanding the topological nature of TCIs. Our work demonstrates the potential of using disclination defects to study the intricate relationship between the body and boundary states in topological materials, particularly in the context of acoustics.

Persistence of Structural Distortion and Bulk Band Rashba Splitting in SnTe above Its Ferroelectric Critical Temperature.

The ferroelectric semiconductor α-SnTe has been regarded as a topological crystalline insulator, and the dispersion of its surface states has been intensively measured with angle-resolved photoemission spectroscopy (ARPES) over the past decade. However, much less attention has been given to the impact of the ferroelectric transition on its electronic structure, and in particular on its bulk states. Here, we investigate the low-energy electronic structure of α-SnTe with ARPES and follow the evolution of the bulk-state Rashba splitting as a function of temperature, across its ferroelectric critical temperature of about Tc ≈ 110 K. Unexpectedly, we observe a persistent band splitting up to room temperature, which is consistent with an order-disorder contribution of local dipoles to the phase transition that requires the presence of fluctuating dipoles above Tc. We conclude that no topological surface state can occur under these conditions at the (111) surface of SnTe, at odds with recent literature.

Observation of interplay between phonon chirality and electronic band topology

The recently demonstrated chiral modes of lattice motion carry angular momentum and therefore directly couple to magnetic fields. Notably, their magnetic moments are predicted to be strongly influenced by electronic contributions. Here, we have studied the magnetic response of transverse optical phonons in a set of Pb 1− x Sn x Te films, which is a topological crystalline insulator for x > 0.32 and has a ferroelectric transition at an x -dependent critical temperature. Polarization-dependent terahertz magnetospectroscopy measurements revealed Zeeman splittings and diamagnetic shifts, demonstrating a large phonon magnetic moment. Films in the topological phase exhibited phonon magnetic moment values that were larger than those in the topologically trivial samples by two orders of magnitude. Furthermore, the sign of the effective phonon g -factor was opposite in the two phases, a signature of the topological transition according to our model. These results strongly indicate the existence of interplay between the magnetic properties of chiral phonons and the topology of the electronic band structure.

Spintronic Quantum Phase Transition in a Graphene/Pb0.24Sn0.76Te Heterostructure with Giant Rashba Spin‐Orbit Coupling

AbstractMechanical stacking of two dissimilar materials often has surprising consequences for heterostructure behavior. In particular, a 2D electron gas (2DEG) is formed in the heterostructure of the topological crystalline insulator Pb0.24Sn0.76Te and graphene due to contact of a polar with a nonpolar surface and the resulting changes in electronic structure needed to avoid polar catastrophe. The spintronic properties of this heterostructure with non‐local spin valve devices are studied. This study observes spin‐momentum locking at lower temperatures that transitions to regular spin channel transport only at ≈40 K. Hanle spin precession measurements show a spin relaxation time as high as 2.18 ns. Density functional theory calculations confirm that the spin‐momentum locking is due to a giant Rashba effect in the material and that the phase transition is a Lifshitz transition. The theoretically predicted Lifshitz transition is further evident in the phase transition‐like behavior in the Landé g‐factor and spin relaxation time.

Observation of Topologically Distinct Corner States in “Bearded” Photonic Kagome Lattices

AbstractKagome lattices represent an archetype of intriguing physics, attracting a great deal of interest in different branches of natural sciences, recently in the context of topological crystalline insulators. Here, two distinct classes of corner states in breathing Kagome lattices (BKLs) with “bearded” edge truncation are demonstrated, unveiling their topological origin. The in‐phase corner states are found to exist only in the topologically nontrivial regime, characterized by a nonzero bulk polarization. In contrast, the out‐of‐phase corner states appear in both topologically trivial and nontrivial regimes, either as bound states in the continuum or as in‐gap states depending on the lattice dimerization conditions. Furthermore, the out‐of‐phase corner states are highly localized, akin to flat‐band compact localized states, and they manifest both real‐ and momentum‐space topology. Experimentally, both types of corner states are observed in laser‐written photonic bearded‐edge BKLs, corroborated by numerical simulations. The results not only deepen the current understanding of topological corner modes in BKLs but also provide new insight into their physical origins, which may be applied to other topological BKL platforms beyond optics.

Light-Induced Nonthermal Phase Transition to the Topological Crystalline Insulator State in SnSe.

Femtosecond pulses have been used to reveal hidden broken symmetry states and induce transitions to metastable states. However, these states are mostly transient and disappear after laser removal. Photoinduced phase transitions toward crystalline metastable states with a change of topological order are rare and difficult to predict and realize experimentally. Here, by using constrained density functional perturbation theory and accounting for light-induced quantum anharmonicity, we show that ultrafast lasers can permanently transform the topologically trivial orthorhombic structure of SnSe into the topological crystalline insulating rocksalt phase via a first-order nonthermal phase transition. We describe the reaction path and evaluate the critical fluence and possible decay channels after photoexcitation. Our simulations of the photoexcited structural and vibrational properties are in excellent agreement with recent pump-probe data in the intermediate fluence regime below the transition with an error on the curvature of the quantum free energy of the photoexcited state that is smaller than 2%.

Complex coincidence of superconducting and inverse proximity in quasi 2D nanostructured SnTe

The induction of superconductivity in topological insulators and topological crystalline insulators is being investigated rigorously as a promising strategy for taking quantum spintronic applications to the next level. In this work, the complex interplay between topological and superconducting components is carefully tuned in such a way that an unusual coincidence of superconducting and inverse proximity is captured for the first time in the electrical transport properties of quasi two-dimensional nanostructured SnTe contacted using ‘s-wave’ superconducting electrodes. Ultralow temperature measurements in the complex superconducting proximity phase reveal two critical fields (H c2) of 0.9 T and 510 Oe. The lower H c2 is identified to be from the superconducting electrode while the higher one is attributed to the interface. The presence (absence) of coincidence between the upper critical field (H C2) extracted from Ginzburg–Landau theory and the Werthamer–Helfand–Hohenberg plot in the normal (inverse) superconducting proximity region and concurrent crossover in correlation lengths ξ(T) and L φ(T) are observed to be the manifestation of robust competition between the mutual domination of different mechanisms such as topological surface states and Cooper pair correlations. The current-dependent magnetoresistance measurements clearly demonstrate the dominant role of the interplay between the superconducting correlations and spin–orbit coupling. Interestingly, mere doubling of the contact area of the superconductor is observed to simultaneously enhance the critical field to ∼4 T and the transition temperature to ∼4.1 K in the interface region, suggesting the possibility of opening up a new gateway into nano-topological superconducting spintronic applications.

Transport and thermoelectric properties of the Pb1-xSnxTe topological crystalline insulator in the vicinity of the band inversion

Semiconductor solid solutions Pb1-xSnxTe are well known as promising materials widely used in the IR electronics, thermoelectricity and other fields of science and technology. Recently, it has been found that these alloys in certain concentration ranges exhibit the properties characteristic of the new quantum objects of solid-state physics – topological crystalline insulators (TCIs), whose unique properties define new possibilities for practical use of these materials in spintronics, quantum computing and thermoelectricity. The fact that in Pb1-xSnxTe the band inversion near some composition xc, leads to the emergence of the TCI states stimulates a detailed study of the behavior of transport and thermoelectric properties near xc. In this work, for the Pb1-xSnxTe solid solutions in the composition range x = 0.59–0.68, we obtained the dependences of electrical conductivity, the Hall coefficient, charge carrier mobility, the Seebeck coefficient, and thermoelectric power factor on x at fixed temperatures in the interval (77–300) K. In the isotherms of all studied properties, we observed peaks at x ∼0.62 and attributed them to the band inversion and transition into the TCI state, which are accompanied by the self-organization processes in the crystal lattice.

In‐Plane Nanowire Growth of Topological Crystalline Insulator Pb1 − xSnxTe

AbstractPredicted topological crystalline insulators such as Pb1 − xSnxTe are an interesting candidate for applications in quantum technology, as they can host spin‐polarized surface states. Moreover, in the nanowire geometry, a quasi‐1D system can be realized with potential applications exploiting Majorana fermions. Herein, the selective area growth of Pb1 − xSnxTe islands and nanowires over the full range of x is demonstrated, and their in‐depth growth dynamics and faceting are analyzed. By transmission electron microscopy, the single‐crystalline and defect‐free nature of the grown material and the homogeneous, controllable Pb/Sn ratio in the nanowires is confirmed. With support of phase‐field growth simulations, it is shown that the crystal faceting mainly follows the driving force of surface energy minimization, favoring the lowest energy {200} surfaces. A kinetic enhancement of adatom incorporation on {110} facets is recognized to limit their extension with respect to {200} and {111} facets. After inspecting all possible in‐plane orientations, we identify the 〈110〉 directions as the optimal candidate for the growth of high‐quality and perfectly straight Pb1 − xSnxTe nanowires, enabling the design of complex networks due to their threefold symmetry. This work opens the way to systematic transport investigation of the carrier density in Pb1 − xSnxTe nanowires and can facilitate further optimization of the Pb1 − xSnxTe system.

Absence of Topological Protection of the Interface States in Z_{2} Photonic Crystals.

Inspired from electronic systems, topological photonics aims to engineer new optical devices with robust properties. In many cases, the ideas from topological phases protected by internal symmetries in fermionic systems are extended to those protected by crystalline symmetries. One such popular photonic crystal model was proposed by Wu and Hu in 2015 for realizing a bosonic Z_{2} topological crystalline insulator with robust topological edge states, which led to intense theoretical and experimental studies. However, a rigorous relationship between the bulk topology and edge properties for this model, which is central to evaluating its advantage over traditional photonic designs, has never been established. In this Letter, we revisit the expanded and shrunken honeycomb lattice structures proposed by Wu and Hu and show that they are topologically trivial in the sense that symmetric, localized Wannier functions can be constructed. We show that the Z and Z_{2} type classifications of the Wu-Hu model are equivalent to the C_{2}T protected Euler class and the second Stiefel-Whitney class, respectively, with the latter characterizing the full valence bands of the Wu-Hu model, indicating only a higher order topological insulator. Additionally, we show that the Wu-Hu interface states can be gapped by a uniform topology preserving C_{6} and T symmetric perturbation, which demonstrates the trivial nature of the interface. Our result reveals that topology is not a necessary condition for the reported helical edge states in many photonics systems and opens new possibilities for interface engineering that may not be constrained by topological considerations.

Native Pb vacancy defects induced p-type characteristic in epitaxial monolayer PbSe

PbSe, a predicted two-dimensional (2D) topological crystalline insulator (TCI) in the monolayer limit, possess excellent thermoelectric and infrared optical properties. Native defects in PbSe take a crucial role for the applications. However, little attention has been paid to the defect induced doping characteristics. Here, we provide an experimental and theoretical investigation of defect induced p-type characteristic on epitaxial monolayer PbSe on Au(111). Scanning tunneling microscopy (STM) measurements demonstrate an epitaxial PbSe monolayer with a fourfold symmetric lattice. Combined scanning tunneling spectroscopy (STS) and density functional theory (DFT) calculations reveal a quasi-particle bandgap of 0.8 eV of PbSe. STM results unveil that there are two types of defects on the surface, one is related the vacancies of Pb atoms and the other is the replacement of the absent Se atoms by Pb. Corresponding theoretical optimization confirms the structures of the defects. More importantly, both STS measurements and DFT calculations give evidence that the Pb vacancies move the Fermi energy inside the valence band and produce extra holes, leading to p-type characteristics of PbSe. Our work provides effective information for the future research of device performance based on PbSe films.

Secondary ion mass spectrometry characterization of matrix composition in topological crystalline insulator [formula omitted

This study explores the use of Secondary Ion Mass Spectrometry (SIMS) to accurately measure the content of Pb1−xSnxTe, a new class of electronic materials known as Topological Crystalline Insulators (TCIs). We analyzed the SIMS signal ratios of SnCs+/PbCs+ and Sn±/Pb± in thin layers and determined the calibration curves necessary to estimate the exact amount of content in this ternary compound. Additionally, we investigated the matrix effect and performed depth profiling to obtain a more precise determination of the content. These findings contribute to the understanding and development of TCIs, and highlight the potential of SIMS for accurate content determination in ternary compounds.

Fractional mode charge in Cn-symmetric higher-order topological crystalline insulators

The measurement of topological insulators is usually achieved by measuring spectra, which is inadequate in higher-order topological insulators because the separation of bandgaps may be blurred, such as body boundaries and corner state hybridization, and the above measurement requires that the energy of the topological mode must be located in the bulk bandgap to be measured. Recent experiments have shown a strong relationship between the fractional mode charge and the location of the Wannier center in the crystal body. The fractional quantization of the corner charge originates from the filling anomaly, and the fractional mode charge can be calculated from experimental measurements of the local density of states to describe the topological state of the system, which has been demonstrated in optical systems. We have achieved a similar effect in acoustics by utilizing a coupled acoustic-cavity system featuring C3, C4, and C6 symmetries for simulation. Furthermore, we extended our study to 3D third-order topological crystalline insulators to validate the fractional-corner charge approach. The simulation and theoretical results demonstrate that the fractional mode charge can clearly identify the high-order topology, even without gap states.