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In two-dimensional topological insulators, a disorder-induced topological phase transition is typically identified with an Anderson localization transition at the Fermi energy. However, in ${\mathbb{Z}}_2$trivial, spin-resolved topological insulators it is the spectral gap of the spin spectrum, in addition to the bulk mobility gap, which protects the nontrivial topology of the ground state. In this work, we show that these two gaps, the bulk electronic and spin gap, can evolve distinctly on the introduction of quenched short-ranged disorder and that an odd-quantized spin Chern number topologically protects states below the Fermi energy from localization. This decoupling leads to a unique situation in which an Anderson localization transition occurs below the Fermi energy at the topological transition. Furthermore, the presence of topologically protected extended bulk states nontrivial bulk topology typically implies the existence of protected boundary modes. We demonstrate the absence of protected boundary modes in the Hamiltonian and yet the edge modes in the eigenstates of the projected spin operator survive. Our work thus provides evidence that a nonzero spin-Chern number, in the absence of a nontrivial ${\mathbb{Z}}_2$index, does not demand the existence of protected boundary modes at finite or zero energy. Published by the American Physical Society2024 

Abstract Transition metal dichalcogenides (TMDs) are known for their layered structure and tunable functional properties. However, a unified understanding on other transition metal chalcogenides (i.e. M 2 X) is still lacking. Here, the relatively new class of copper-based chalcogenides Cu 2 X (X = Te, Se, S) is thoroughly reported. Cu 2 X are synthesized by an unusual vapor–liquid assisted growth on a Al 2 O 3 /Cu/W stack. Liquid copper plays a significant role in synthesizing these layered systems, and sapphire assists with lateral growth and exfoliation. Similar to traditional TMDs, thickness dependent phonon signatures are observed, and high-resolution atomic images reveal the single phase Cu 2 Te that prefers to grow in lattice-matched layers. Charge transport measurements indicate a metallic nature at room temperature with a transition to a semiconducting nature at low temperatures accompanied by a phase transition, in agreement with band structure calculations. These findings establish a fundamental understanding and thrust Cu 2 Te as a flexible candidate for wide applications from photovoltaics and sensors to nanoelectronics. 

Abstract Chemical vapor deposition growth of metal carbides is of great interest as this method provides large area growth of MXenes. This growth is mainly done using a melted diffusion based process; however, different morphologies in growth process is not well understood. In this work, we report deterministic synthesis of layered (non-uniform c -axis growth) and planar (uniform c -axis growth) of molybdenum carbide (Mo 2 C) using a diffusion-mediated growth. Mo-diffusion limited growth mechanism is proposed where the competition between Mo and C adatoms determines the morphology of grown crystals. Difference in thickness of catalyst at the edge and center lead to enhanced Mo diffusion which plays a vital role in determining the structure of Mo 2 C. The layered structures exhibit an expansion in the lattice confirmed by the presence of strain. Density functional theory shows consistent presence of strain which is dependent upon Mo diffusion during growth. This work demonstrates the importance of precise control of diffusion through the catalyst in determining the structure of Mo 2 C and contributes to broader understanding of metal diffusion in growth of MXenes.