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Ring states in topological materials
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Ingap states are commonly observed in semiconductors and are often well characterized by a hydrogenic model within the effective mass approximation. However, when impurities are strong, they significantly perturb all momentum eigenstates, leading to deep-level bound states that reveal the global properties of the unperturbed band structure. In this work, we discover that the topology of band wavefunctions can impose zeros in the impurity-projected Green's function within topological gaps. These zeros can be interpreted as spectral attractors, defining the energy at which ingap states are pinned in the presence of infinitely strong local impurities. Their pinning energy is found by minimizing the level repulsion of band eigenstates onto the ingap state. We refer to these states as ring states, marked by a mixed band character and a node at the impurity site, guaranteeing their orthogonality to the bare impurity eigenstates and a weak energy dependence on the impurity strength. We show that the inability to construct symmetric and exponentially localized Wannier functions ensures topological protection of ring states. Linking ring states together, the edge or surface modes can be recovered for any topologically protected phase. Therefore, ring states can also be viewed as building blocks of boundary modes, offering a framework to understand bulk-boundary correspondence.
Forward citations
Cited by 5 Pith papers
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Topological Transitions in Orbital-Symmetry-Controlled Chemical Reactions
A Green's function topological invariant distinguishes symmetry-allowed from symmetry-forbidden 4pi electrocyclizations through crossings of poles or zeros at the chemical potential.
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Emergent superconductivity upon disordering a topological insulator
Sign-problem-free QMC simulations show that strong impurities reduce the critical interaction for superconductivity in a BHZ-Hubbard model by nucleating Cooper pairs in impurity-induced subgap ring states.
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Defect-Bound Excitons in Topological Materials
In a Chern insulator model, excitons bound to topologically protected ring-shaped defect states have lower binding energies and parameter-sensitive wave function ordering compared to trivial defect states.
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Real-Space Imaging of the Band Topology of Transition Metal Dichalcogenides
STM images of WSe2 show the valence-band electron density shift from tungsten sites near Gamma to hollow sites near K, confirming WSe2 is a topologically obstructed atomic insulator.
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Probing the Electronic Structure at the Boundary of Topological Insulators in the $\mathrm{Bi}_2\mathrm{Se}_3$ Family by Combined STM and AFM
A GW-based tight-binding model combined with Chen's derivative rule reproduces scanning tunneling spectra of Bi2Se3, Bi2Te2Se, and Bi2Te3 and reveals bulk and surface orbital contributions.
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