Zeros of Green Functions in Topological Insulators

Abstract

This study demonstrates that the zeros of the diagonal components of Green functions are key quantities that can detect non-interacting topological insulators. We show that zeros of the Green functions traverse the band gap in the topological phases. The traverses induce the crosses of zeros, and the zeros' surface in the band gap, analogous to the Fermi surface of metals. By calculating the zeros of the microscopic models, we show the traverses of the zeros universally appear in all six classes of conventional non-interacting topological insulators. By utilizing the eigenvector-eigenvalue identity, which is a recently rediscovered relation in linear algebra, we prove that the traverses of the zeros in the bulk Green functions are guaranteed by the band inversions, which occur in the topological phases. The relevance of the zeros to detecting the exotic topological insulators such as the higher-order topological insulators is also discussed. For the Hamiltonians with the nearest-neighbor hoppings, we also show that the gapless edge state guarantees the zeros' surfaces in the band gap. The analysis demonstrates that the zeros can be used to detect a wide range of topological insulators and thus useful for searching new topological materials.

21 pages, 1 table, 14 figures

References in corpus (13)

• Topological Insulators with Inversion Symmetry
• Topological Field Theory of Time-Reversal Invariant Insulators
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Classification of stable three-dimensional Dirac semimetals with nontrivial topology
• Topological Anderson Insulator
• Simplified topological invariants for interacting insulators
• Doped high-Tc cuprate superconductors elucidated in the light of zeros and poles of electronic Green's function
• Absence of Luttinger's Theorem due to Zeros in the Single-Particle Green Function
• Topological interpretation of Luttinger theorem
• In-gap impurity states as the hallmark of the Quantum Spin Hall phase
• Multicriticality of Two-dimensional Class D Disordered Topological Superconductors
• Topological Green function of interacting systems
• Note on eigenvectors from eigenvalues

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• Unified role of Green's function poles and zeros in topological insulators
• Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants
• The Algebraic Structure Underlying Pole-Skipping Points
• Bulk Spacetime Encoding via Boundary Ambiguities
• Correlated Zak insulator in organic antiferromagnets
• Impurity-induced Mott ring states and Mott zeros ring states in the Hubbard operator formalism