Universal topological marker
Wei Chen

TL;DR
This paper introduces a universal topological marker for topological insulators and superconductors, enabling lattice site mapping of topological order across various models and symmetry classes, with implications for understanding phase transitions.
Contribution
It develops a universal topological operator and marker applicable to all symmetry classes and dimensions, connecting momentum-space invariants to real-space lattice site characterization.
Findings
Topological marker explicitly constructed for all symmetry classes from 1D to 3D.
Nonlocal topological marker decays with a correlation length diverging at phase transitions.
Demonstrated on multiple models including SSH, Majorana chain, and 3D topological insulators.
Abstract
We elaborate that for topological insulators and topological superconductors described by Dirac models in any dimension and symmetry class, the topological order can be mapped to lattice sites by a universal topological marker. Deriving from a recently discovered momentum-space universal topological invariant, we introduce a topological operator that consists of alternating projectors to filled and empty lattice eigenstates and the position operators, multiplied by the Dirac matrices that are omitted in the Hamiltonian. The topological operator projected to lattice sites yields the topological marker, whose form is explicitly constructed for every topologically nontrivial symmetry class from 1D to 3D. The off-diagonal elements of the topological operator yields a nonlocal topological marker, which decays with a correlation length that diverges at topological phase transitions, and…
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Taxonomy
TopicsTopological Materials and Phenomena · Atomic and Subatomic Physics Research · Physics of Superconductivity and Magnetism
