Emergent Andreev Reflection from a Lattice Duality Defect
Abstract
Andreev reflection converts an incoming fermion into an outgoing hole and is usually tied to a superconducting interface. We show that an analogous charge-conjugating boundary condition emerges from a purely lattice duality defect. Starting from a Majorana representation of the transverse-field Ising chain, we construct a folded lattice model in which a boundary Majorana impurity implements a one-site translation of a staggered Majorana chain. In the continuum, this translation becomes a chiral fermion-parity defect: it flips the sign of the only left-moving Majorana mode while leaving the right-moving mode unchanged. When the two Majorana modes are recombined into a complex fermion in the folded geometry, this sign flip becomes the Andreev-like boundary condition. Our lattice formulation gives a microscopic interpretation of the Emery--Kivelson boundary of the two-channel Kondo problem and of Maldacena--Ludwig monopole scattering, while identifying the boundary as the interface between a Kitaev-chain SPT phase and a gapless chain. The same Majorana translation defect also provides a lattice realization of an axial U(1)A-symmetric charge-flip boundary.
Versions
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BibTeX
@misc{ueda2026emergent,
title = {{Emergent Andreev Reflection from a Lattice Duality Defect}},
author = {Atsushi Ueda and Tokiro Numasawa and Boris De Vos and Masataka Watanabe},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.23684},
eprint = {2606.23684},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.23684},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Emergent Andreev Reflection from a Lattice Duality Defect
AU - Atsushi Ueda
AU - Tokiro Numasawa
AU - Boris De Vos
AU - Masataka Watanabe
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2606.23684
UR - https://arxiv.org/abs/2606.23684
AB - Andreev reflection converts an incoming fermion into an outgoing hole and is usually tied to a superconducting interface. We show that an analogous charge-conjugating boundary condition emerges from a purely lattice duality defect. Starting from a Majorana representation of the transverse-field Ising chain, we construct a folded lattice model in which a boundary Majorana impurity implements a one-site translation of a staggered Majorana chain. In the continuum, this translation becomes a chiral fermion-parity defect: it flips the sign of the only left-moving Majorana mode while leaving the right-moving mode unchanged. When the two Majorana modes are recombined into a complex fermion in the folded geometry, this sign flip becomes the Andreev-like boundary condition. Our lattice formulation gives a microscopic interpretation of the Emery--Kivelson boundary of the two-channel Kondo problem and of Maldacena--Ludwig monopole scattering, while identifying the boundary as the interface between a Kitaev-chain SPT phase and a gapless chain. The same Majorana translation defect also provides a lattice realization of an axial U(1)_A-symmetric charge-flip boundary.
ER -