TY - JOUR

T1 - Topologically nontrivial Andreev bound states

AU - Marra, Pasquale

AU - Nitta, Muneto

N1 - Funding Information:
We thank D. Inotani for useful discussions and suggestions, and the anonymous reviewers whose comments have greatly improved this manuscript. This work is supported by the Ministry of Education, Culture, Sports, Science, and Technology (MEXT)-Supported Program for the Strategic Research Foundation at Private Universities “Topological Science” (Grant No. S1511006). The work of M.N. is also supported in part by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (KAKENHI) Grants No. 16H03984 and No. 18H01217 and by a Grant-in-Aid for Scientific Research on Innovative Areas “Topological Materials Science” (KAKENHI Grant No. 15H05855) from MEXT of Japan.
Publisher Copyright:
© 2019 American Physical Society.

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.

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U2 - 10.1103/PhysRevB.100.220502

DO - 10.1103/PhysRevB.100.220502

M3 - Article

AN - SCOPUS:85076582031

SN - 2469-9950

VL - 100

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

IS - 22

M1 - 220502

ER -