Krakovna et al. (2020)
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Physics research on topological insulators and condensed matter materials; not directly relevant to AI safety but may have indirect connections to hardware security and quantum computing applications.
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Abstract
We predict that a family of antiperovskite materials realize a higher order topological insulator phase, characterized by a previously introduced $\mathbb{Z}_4$ index. A tight binding model and a $k\cdot p$ model are used to capture the physics of the bulk, surface and hinge states of these materials. A phase diagram of the higher order and weak topological invariants is obtained for the tight binding model. The mirror Chern number is also discussed. In order to reveal the gapless hinge states in the presence of mirror Chern surface states, several ways of opening the surface gap are proposed and confirmed by calculation, including cleaving the crystal to reveal a low-symmetry surface, building a heterostructure, and applying strain. Upon opening the surface gap, we are able to study the hinge states by computing the momentum space band structure and real space distribution of mid-gap states.
Summary
This paper predicts that antiperovskite materials exhibit higher-order topological insulator (HOTI) phases characterized by a Z₄ topological index. Using tight-binding and k·p models, the authors map out phase diagrams of topological invariants and identify gapless hinge states as a key signature of these materials. The work proposes and validates three methods to reveal hinge states by opening surface gaps: crystal cleavage to expose low-symmetry surfaces, heterostructure engineering, and strain application. These findings provide both theoretical predictions and practical strategies for experimentally observing higher-order topological phases in antiperovskite compounds.
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# Higher-order topological insulators in antiperovskites
Yuan Fang
Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11974, USA
Jennifer Cano
Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11974, USA
Center for Computational Quantum Physics, The Flatiron Institute, New York, New York 10010, USA
###### Abstract
We predict that a family of antiperovskite materials realize a higher order topological insulator phase, characterized by a previously introduced ℤ4subscriptℤ4\\mathbb{Z}\_{4} index. A tight binding model and a k⋅p⋅𝑘𝑝k\\cdot p model are used to capture the physics of the bulk, surface and hinge states of these materials. A phase diagram of the higher order and weak topological invariants is obtained for the tight binding model. The mirror Chern number is also discussed. In order to reveal the gapless hinge states in the presence of mirror Chern surface states, several ways of opening the surface gap are proposed and confirmed by calculation, including cleaving the crystal to reveal a low-symmetry surface, building a heterostructure, and applying strain. Upon opening the surface gap, we are able to study the hinge states by computing the momentum space band structure and real space distribution of mid-gap states.
## I Introduction
The recent classification \[ [1](https://ar5iv.labs.arxiv.org/html/2002.02969#bib.bib1 ""), [2](https://ar5iv.labs.arxiv.org/html/2002.02969#bib.bib2 ""), [3](https://ar5iv.labs.arxiv.org/html/2002.02969#bib.bib3 ""), [4](https://ar5iv.labs.arxiv.org/html/2002.02969#bib.bib4 ""), [5](https://ar5iv.labs.arxiv.org/html/2002.02969#bib.bib5 ""), [6](https://ar5iv.labs.arxiv.org/html/2002.02969#bib.bib6 ""), [7](https://ar5iv.labs.arxiv.org/html/2002.02969#bib.bib7 ""), [8](https://ar5iv.labs.arxiv.org/html/2002.02969#bib.bib8 "")\] of topological insulators with crystal symmetry has led to the discovery of a new type of topological phase, the higher order topological insulator (HOTI) \[ [9](https://ar5iv.labs.arxiv.org/html/2002.02969#bib.bib9 ""), [10](https://ar5iv.labs.arxiv.org/html/2002.02969#bib.bib10 ""), [11](https://ar5iv.labs.arxiv.org/html/2002.02969#bib.bib11 ""), [12](https://ar5iv.labs.arxiv.org/html/2002.02969#bib.bib12 ""), [13](https://ar5iv.labs.arxiv.org/html/2002.02969#bib.bib13 ""), [14](https://ar5iv.labs.arxiv.org/html/2002.02969#bib.bib14 ""), [15](https://ar5iv.labs.arxiv.org/html/2002.02969#bib.bib15 ""), [16](https://ar5iv.labs.arxiv.org/html/2002.02969#bib.bib16 ""), [17](https://ar5iv.labs.arxiv.org/html/2002.02969#bib.bib17 ""), [18](https://ar5iv.labs.arxiv.org/html/2002.02969#bib.bib18 ""), [19](https://ar5iv.labs.arxiv.org/html/2002.02969#bib.bib19 ""), [20](https://ar5iv.labs.arxiv.org/html/2002.02969#bib.bib20 ""), [21](https://ar5iv.labs.arxiv.org/html/2002.02969#bib.bib21 ""), [22](https://ar5iv.labs.arxiv.org/html/2002.02969#bib.bib22 "")\].
HOTIs in three dimensions (3D) are gapped in the bulk and on all s
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