### Abstract

Andreev bound states are low-energy excitations appearing below the particle-hole gap of superconductors, and are expected to be topologically trivial. Here, we report the theoretical prediction of topologically nontrivial Andreev bound states in one-dimensional superconductors. These states correspond to another topological invariant defined in a synthetic two-dimensional space, the particle-hole Chern number, which we construct in analogy to the spin Chern number in quantum spin Hall systems. Nontrivial Andreev bound states have distinct features and are topologically nonequivalent to Majorana bound states. Yet, they can coexist in the same system, have similar spectral signatures, and materialize with the concomitant opening of the particle-hole gap. The coexistence of Majorana and nontrivial Andreev bound state is the direct consequence of "double dimensionality", i.e., the dimensional embedding of the one-dimensional system in a synthetic two-dimensional space, which allows the definition of two distinct topological invariants (Z2 and Z) in different dimensionalities.

Original language | English |
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Article number | 220502 |

Journal | Physical Review B |

Volume | 100 |

Issue number | 22 |

DOIs | |

Publication status | Published - 2019 Dec 5 |

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### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

*Physical Review B*,

*100*(22), [220502]. https://doi.org/10.1103/PhysRevB.100.220502

**Topologically nontrivial Andreev bound states.** / Marra, Pasquale; Nitta, Muneto.

Research output: Contribution to journal › Article

*Physical Review B*, vol. 100, no. 22, 220502. https://doi.org/10.1103/PhysRevB.100.220502

}

TY - JOUR

T1 - Topologically nontrivial Andreev bound states

AU - Marra, Pasquale

AU - Nitta, Muneto

PY - 2019/12/5

Y1 - 2019/12/5

N2 - Andreev bound states are low-energy excitations appearing below the particle-hole gap of superconductors, and are expected to be topologically trivial. Here, we report the theoretical prediction of topologically nontrivial Andreev bound states in one-dimensional superconductors. These states correspond to another topological invariant defined in a synthetic two-dimensional space, the particle-hole Chern number, which we construct in analogy to the spin Chern number in quantum spin Hall systems. Nontrivial Andreev bound states have distinct features and are topologically nonequivalent to Majorana bound states. Yet, they can coexist in the same system, have similar spectral signatures, and materialize with the concomitant opening of the particle-hole gap. The coexistence of Majorana and nontrivial Andreev bound state is the direct consequence of "double dimensionality", i.e., the dimensional embedding of the one-dimensional system in a synthetic two-dimensional space, which allows the definition of two distinct topological invariants (Z2 and Z) in different dimensionalities.

AB - Andreev bound states are low-energy excitations appearing below the particle-hole gap of superconductors, and are expected to be topologically trivial. Here, we report the theoretical prediction of topologically nontrivial Andreev bound states in one-dimensional superconductors. These states correspond to another topological invariant defined in a synthetic two-dimensional space, the particle-hole Chern number, which we construct in analogy to the spin Chern number in quantum spin Hall systems. Nontrivial Andreev bound states have distinct features and are topologically nonequivalent to Majorana bound states. Yet, they can coexist in the same system, have similar spectral signatures, and materialize with the concomitant opening of the particle-hole gap. The coexistence of Majorana and nontrivial Andreev bound state is the direct consequence of "double dimensionality", i.e., the dimensional embedding of the one-dimensional system in a synthetic two-dimensional space, which allows the definition of two distinct topological invariants (Z2 and Z) in different dimensionalities.

UR - http://www.scopus.com/inward/record.url?scp=85076582031&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevB.100.220502

DO - 10.1103/PhysRevB.100.220502

M3 - Article

AN - SCOPUS:85076582031

VL - 100

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 2469-9950

IS - 22

M1 - 220502

ER -