Topological Hopf-Chern insulators and the Hopf superconductor

Ricardo Kennedy

doi:10.1103/PhysRevB.94.035137

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Topological Hopf-Chern insulators and the Hopf superconductor

Ricardo Kennedy

DOI 10.1103/PhysRevB.94.035137 · Physical Review B

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Abstract

We introduce new three-dimensional (3D) topological phases of two-band models using the Pontryagin-Thom construction. In symmetry class A these are the infinitely many Hopf-Chern topological insulators, which are hybrids of layered Chern insulators and Hopf insulators. Being constructed by a modification of the experimentally observed Chern insulators, these provide promising candidates for the observation of a genuinely 3D topological phase in class A. In symmetry class C, there is a Z2 classification with the nontrivial topological phase, the Hopf superconductor, being realized by a construction that doubles a Hopf insulator in momentum space. For these new topological phases we introduce concrete tight-binding Hamiltonians and investigate their energy spectra in the presence of a boundary, revealing gapless surface modes in accordance with the bulk-boundary correspondence.