Materials discovery acceleration by using conditional generative methodology

1D topological systems for next-generation electronics

Topological insulators represent unusual topological quantum states, typically with gapped bulk band structure but gapless surface Dirac fermions protected by time-reversal symmetry. Recently, a distinct kind of topological insulator resulting from nonsymmorphic crystalline symmetry was proposed in the KHgX ($X=\mathrm{As}$, Sb, Bi) compounds. Unlike regular topological crystalline insulators, the nonsymmorphic glide-reflection symmetry in KHgX guarantees the appearance of an exotic surface fermion with hourglass shape dispersion (where two pairs of branches switch their partners) residing on its (010) side surface, contrasting to the usual two-dimensional Dirac fermion form. Here, by using high-resolution angle-resolved photoemission spectroscopy, we systematically investigate the electronic structures of KHgSb on both (001) and (010) surfaces and reveal the unique in-gap surface states on the (010) surface with delicate dispersion consistent with the ``hourglass Fermion'' recently proposed. Our experiment strongly supports that KHgSb is a nonsymmorphic topological crystalline insulator with hourglass fermions, which serves as an important step to the discovery of unique topological quantum materials and exotic fermions protected by nonsymmorphic crystalline symmetry.

[EN]In three-dimensional topological Insulators, the topological protected helical surface conducting states exist along with the bulk insulating states. In a class of topological insulators, namely topological crystalline insulators, the protection role of surface states is taken by crystalline symmetry instead of time-reversal symmetry. These exotic characteristics bring about potential applications in logic devices, thermoelectricity or quantum computers. However, due to some critical challenges (like their compatibility with the existing devices, their fabrication processes as well as their compatibility with topological or quantum behavior under external stimuli, working temperature range, cost efficiency, practical structure and ease of use), topological materials are still lagging in device applications. In this regard, this thesis aims at investigating the fundamental properties of a topological crystalline insulator, 𝑃𝑏0.77𝑆𝑛0.23𝑆𝑒, based on Raman characterization at different temperature ranges and low magnetic fields as well as magneto-transport of its Hall bar devices at low temperatures, albeit with meeting challenges in fabrication and characterization. The Raman response of this material at relaxed conditions confirms the presence of topological surface states. Moreover, temperature-dependent Raman characterizations indicate that both surface states and their bulk counterparts contribute to the Raman response considering the interplay of electrons and phonons. Furthermore, our findings based on magnetic-field dependent Raman characterization demonstrate that the surface states are topologically protected by symmetry. These Raman results are also corroborated with magneto-transport characterizations, revealing the prominent role of an inherent attribute of this material based on strong spin-orbit coupling. Our results pave the way for electron studies in field-effect transistors based on topological phase transitions

In this review, we discuss recent progress in the explorations of topological materials beyond topological insulators; specifically, we focus on topological crystalline insulators and bulk topological superconductors. The basic concepts, model Hamiltonians, and novel electronic properties of these new topological materials are explained. The key role of the symmetries that underlie their topological properties is elucidated. Key issues in their materials realizations are also discussed.

Topological materials in crystal solids, including topological insulators (TIs), topological crystalline insulators (TCIs), topological Dirac semimetals (DSMs), topological Weyl semimetals (WSMs), topological Dirac or Weyl nodal line semimetals (NLSMs) and beyond, are mainly featured with topological, protected non-trivial surface states, and their bulk phases are insulators or semimetals with the proper presence of Dirac cones, Weyl nodes or Dirac nodal lines around the Fermi level. The author suggests a two-step computational screening strategy of 3D topological materials by mixing chemistry with physics with the considerations of fully filled bands and band inversion.

Based on first-principles calculations, we study electronic structure of interfaces between a topological insulator (TI) SnBiTe and a topological crystalline insulator (TCI) SnTe. We consider two interface models characterized by the different atomic structure on the contact of the SnTe(111) and SnBiTe(0001) slabs: the model when two materials are connected without intermixing (abrupt type of interface) and the interface model predicted to be realized at epitaxial immersion growth on topological insulator substrates (smooth interface). We find that a strong potential gradient at the abrupt interface leads to the redistribution of the topological states deeper from the interface plane which prevents the annihilation of the Dirac states, predicted earlier. In contrast, a smooth interface is characterized by minor charge transfer, which promotes the strong interplay between TI and TCI Dirac cones leading to their complete annihilation.The topologically protected Dirac state of SnTe(111) survives irrespective of the interface structure.

Dual topological materials are unique topological phases that host coexisting surface states of different topological nature on the same or on different material facets. Here, we show that Bi2TeI is a dual topological insulator. It exhibits band inversions at two time reversal symmetry points of the bulk band, which classify it as a weak topological insulator with metallic states on its 'side' surfaces. The mirror symmetry of the crystal structure concurrently classifies it as a topological crystalline insulator. We investigated Bi2TeI spectroscopically to show the existence of both two-dimensional Dirac surface states, which are susceptible to mirror symmetry breaking, and one-dimensional channels that reside along the step edges. Their mutual coexistence on the step edge, where both facets join, is facilitated by momentum and energy segregation. Our observation of a dual topological insulator should stimulate investigations of other dual topology classes with distinct surface manifestations coexisting at their boundaries.

Bismuth is gaining importance as a key element of functional quantum materials. The effects of spin-orbit coupling (SOC) are at the heart of many exciting proposals for next-generation quantum technologies, including topological materials for efficient information transmission and energy-saving applications. The "heavy" element bismuth and its compounds are predestined for SOC-induced topological properties, but materials design is challenged by a complex link between them and the chemical composition and crystal structure. Nevertheless, a lot can be learned about a certain property by testing its limits with compositional and/or structure modifications. We survey a handful of topological bismuth-based materials that bear structural and chemical semblance to the early topological insulators, antimony-doped elemental bismuth, Bi2Se3 and Bi2Te3. Chemical bonding via p orbitals and modular structure underlie all considered bismuth chalcogenides, subhalides, and chalcogenide halides and allow us to correlate the evolution of chemical bonding and structure with variability of the topological properties, although materials design should not be regarded as a building blocks set. Over the past decade, material discoveries have unearthed a plethora of topological properties, and bismuth is very fertile as a progenitor of a rich palette of exotic quantum materials, ranging from strong and weak 3D and crystalline topological insulators over topological metals and semimetals to magnetic topological insulators, while preserving the general layered structure motif.

We predict planar Sb/Bi honeycomb to harbor a two-dimensional (2D) topological crystalline insulator (TCI) phase based on first-principles computations. Although buckled Sb and Bi honeycombs support 2D topological insulator (TI) phases, their structure becomes planar under tensile strain. The planar Sb/Bi honeycomb structure restores the mirror symmetry, and is shown to exhibit non-zero mirror Chern numbers, indicating that the system can host topologically protected edge states. Our computations show that the electronic spectrum of a planar Sb/Bi nanoribbon with armchair or zigzag edges contains two Dirac cones within the band gap and an even number of edge bands crossing the Fermi level. Lattice constant of the planar Sb honeycomb is found to nearly match that of hexagonal-BN. The Sb nanoribbon on hexagonal-BN exhibits gapped edge states, which we show to be tunable by an out-of-the-plane electric field, providing controllable gating of edge state important for device applications.

Electronic structures of topological quantum materials studied by ARPES

In addition to novel surface states, topological insulators can also exhibit robust gapless states at crystalline defects. Step edges constitute a class of common defects on the surface of crystals. In this work we establish the topological nature of one-dimensional (1D) bound states localized at step edges of the (001) surface of a topological crystalline insulator Pb<sub>0.7</sub>Sn<sub>0.3</sub>Se, both theoretically and experimentally. We show that the topological stability of the step-edge states arises from an emergent particle-hole symmetry of the surface low-energy physics, and demonstrate the experimental signatures of the particle-hole symmetry breaking. We also reveal the effects of an external magnetic field on the 1D bound states. Furthermore, our work suggests the possibility of similar topological step-edge modes in other topological materials with a rocksalt structure.

The properties that distinguish topological crystalline insulator (TCI) and topological insulator (TI) rely on crystalline symmetry and time-reversal symmetry, respectively, which encodes different bulk and surface/edge properties. Here, we predict theoretically that electron-doped TlM (M = S and Se) (110) monolayers realize a family of two-dimensional (2D) TCIs characterized by mirror Chern number CM = -2. Remarkably, under uniaxial strain (≈ 1%), a topological phase transition between 2D TCI and 2D TI is revealed with the calculated spin Chern number CS = -1 for the 2D TI. Using spin-resolved edge states analysis, we show different edge-state behaviors, especially at the time reversal invariant points. Finally, a TlBiSe2/NaCl quantum well is proposed to realize an undoped 2D TCI with inverted gap as large as 0.37 eV, indicating the high possibility for room-temperature observation.

Topological crystalline insulators (TCIs) can exhibit unusual, quantized electric phenomena such as fractional electric polarization and boundary-localized fractional charge1-6. This quantized fractional charge is the generic observable for identification of TCIs that lack clear spectral features5-7, including ones with higher-order topology8-11. It has been predicted that fractional charges can also manifest where crystallographic defects disrupt the lattice structure of TCIs, potentially providing a bulk probe of crystalline topology10,12-14. However, this capability has not yet been confirmed in experiments, given that measurements of charge distributions in TCIs have not been accessible until recently11. Here we experimentally demonstrate that disclination defects can robustly trap fractional charges in TCI metamaterials, and show that this trapped charge can indicate non-trivial, higher-order crystalline topology even in the absence of any spectral signatures. Furthermore, we uncover a connection between the trapped charge and the existence of topological bound states localized at these defects. We test the robustness of these topological features when the protective crystalline symmetry is broken, and find that a single robust bound state can be localized at each disclination alongside the fractional charge. Our results conclusively show that disclination defects in TCIs can strongly trap fractional charges as well as topological bound states, and demonstrate the primacy of fractional charge as a probe of crystalline topology.

Discovery of exotic phases of matter from the topologically non-trivial systems not only makes the research on topological materials more interesting but also enriches our understanding of the fascinating physics of such materials. Pb0.6Sn0.4Te was recently shown to be a topological crystalline insulator. Here, we show that by forming a mesoscopic point-contact using a normal non-superconducting elemental metal on the surface of Pb0.6Sn0.4Te, a superconducting phase is created locally in a confined region under the point-contact. This happens when the bulk of the sample remains to be non-superconducting, and the superconducting phase emerges as a nano-droplet under the point-contact. The superconducting phase shows a high transition temperature Tc that varies for different point-contacts and falls in a range between 3.7 K and 6.5 K. Therefore, this Letter presents the discovery of a superconducting phase on the surface of a topological crystalline insulator, and the discovery is expected to shed light on the mechanism of induced superconductivity in topologically non-trivial systems in general.

Average symmetry protects the topological surface states of topological (crystalline) insulators with time-reversal symmetry from disorder-induced localization. However, the nature of such average symmetry for magnetic topological insulators and, in particular, its connection to surface transport await inspection. Here, we investigate the impact of imperfect magnetic order on an antiferromagnetic topological insulator, which is a solid with a bulk axion field $\ensuremath{\theta}=\ensuremath{\pi}$. We find that the disordered topological surfaces of an antiferromagnetic topological insulator can be generally gapped and localized. The behavior of topological surfaces is now controlled by a mesoscopic average time-reversal symmetry that requires a magnetically imperfect system to be divisible into finite and magnetically neutral slabs. In the presence of this mesoscopic average time-reversal symmetry, the topological surface states will be gapless in the thermodynamic limit and tend to delocalize at a single energy similar to the delocalization transition in the chiral universality class. The notion of average-symmetry-induced delocalization is thus extended to account for magnetic topological insulators, and the spectroscopic and transport signatures clarified herein are relevant to future experimental investigations.