Topological superconductors and Majorana fermions based on X-wave magnets with $X=p,d,f,g,i $
Abstract
We study superconductors coupled with X-wave magnets with X=p,d,f,g,i. They are essentially different between altermagnets with X=d,g,i and odd-parity magnets X=p,f due to the compatibility of the spin-singlet formation of the s-wave superconductor. The altermagnets and odd-parity magnets show rich superconducting phase diagrams depending on the strength of the magnetic order, the chemical potential and the ratio of the on-site and nearest-neighbor interactions. Especially, we find that the altermagnetic order stabilizes the chiral (px+ipy)-wave superconductor, which is a class D topological superconductor hosting Majorana chiral edge states. It is characterized by the Chern number. Especially, there emerge two chiral edge modes in the i-wave altermagnet, which are characterized by the Chern number 2. On the other hand, the p (f)-wave odd-parity magnetic order stabilizes the p (f)-wave topological superconductor, which is a class DIII topological superconductor hosting Majorana flat bands. It is characterized by the winding number. Majorana flat bands are robust in the presence of the mixing with the s-wave superconductivity, which is inevitable for odd-parity magnets although the magnitude of the mixing is tiny.
Related
- Topological Quantum Spin Liquids in a Ladder with Majorana fermions and p-wave Superconductivity
- Majorana zero modes in half-quantum vortices of pair density wave superconductors
- A Clifford-index approach connecting boundary Dirac fermions to sigma-model topological terms in the periodic table of topological insulators and superconductors
- Hierarchy of topological superconductivity generated via heterostructures of unconventional p-wave magnets
- Free Majorana fermions with superconducting quantum wires and a magnetic impurity
BibTeX
@misc{ezawa2026topological,
title = {{Topological superconductors and Majorana fermions based on $X$-wave magnets with $X=p,d,f,g,i $}},
author = {Motohiko Ezawa},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16084},
eprint = {2609.16084},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16084},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Topological superconductors and Majorana fermions based on X-wave magnets with $X=p,d,f,g,i $
AU - Motohiko Ezawa
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.16084
UR - https://arxiv.org/abs/2609.16084
AB - We study superconductors coupled with X-wave magnets with X=p,d,f,g,i. They are essentially different between altermagnets with X=d,g,i and odd-parity magnets X=p,f due to the compatibility of the spin-singlet formation of the s-wave superconductor. The altermagnets and odd-parity magnets show rich superconducting phase diagrams depending on the strength of the magnetic order, the chemical potential and the ratio of the on-site and nearest-neighbor interactions. Especially, we find that the altermagnetic order stabilizes the chiral (p_x+ip_y)-wave superconductor, which is a class D topological superconductor hosting Majorana chiral edge states. It is characterized by the Chern number. Especially, there emerge two chiral edge modes in the i-wave altermagnet, which are characterized by the Chern number 2. On the other hand, the p (f)-wave odd-parity magnetic order stabilizes the p (f)-wave topological superconductor, which is a class DIII topological superconductor hosting Majorana flat bands. It is characterized by the winding number. Majorana flat bands are robust in the presence of the mixing with the s-wave superconductivity, which is inevitable for odd-parity magnets although the magnitude of the mixing is tiny.
ER -