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Pfaffian Formalism for Higher-Order Topological Insulators
Physical Review Letters
|February 8, 2020
Summary
We generalize the Pfaffian formalism for topological insulators (TIs) to 3D chiral higher-order topological insulators (HOTIs). This new method links TIs and HOTIs, enabling generalization of key conclusions and efficient computation of topological indices.
Area of Science:
- Condensed Matter Physics
- Topological Materials Science
Background:
- Topological insulators (TIs) are crucial in condensed matter physics.
- The Pfaffian formalism is vital for studying time-reversal invariant TIs.
Purpose of the Study:
- Generalize the Pfaffian formalism to 3D chiral higher-order topological insulators (HOTIs).
- Establish a fundamental link between TIs and HOTIs.
- Extend important conclusions from TIs to HOTIs.
Main Methods:
- Generalization of the Pfaffian formalism.
- Application to 3D chiral HOTIs protected by C4 and time-reversal symmetry (T).
- Development of a method to compute the Z2 index without a global gauge.
Main Results:
- A generalized Pfaffian description for 3D chiral HOTIs.
- Demonstration of the generalization of Fu-Kane's parity criterion to HOTIs.
- An efficient method for computing the Z2 index of 3D chiral HOTIs.
Conclusions:
- The Pfaffian formalism provides a unified framework for TIs and HOTIs.
- This work facilitates deeper understanding and characterization of higher-order topological phases.
- The developed methods enable efficient topological characterization of complex topological materials.
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