Majorana interface states in anisotropic and tilted Dirac and Weyl systems
Abstract
Anisotropy and cone tilt change how Majorana states propagate along an interface and decay away from it. We derive a two-dimensional Majorana surface Hamiltonian from a fully gapped three-dimensional superconductor, with the surface mass generated by the relative phase between triplet and singlet pairing. For a mass domain wall on this surface, we obtain the wave function, propagation velocity, and localization length of the resulting one-dimensional channel for a general invertible velocity tensor and an arbitrary wall orientation. The product of propagation speed and localization length is independent of wall orientation in the anisotropic model. For a smooth closed channel without a vortex, the propagation time around the wall determines the lowest excitation energy. For a tilted surface cone, the normal and parallel components of tilt affect confinement and propagation differently. We also solve a separate three-dimensional Weyl model with uniform singlet pairing and a reversing exchange field. In the regime supporting interface states, its bulk remains gapless. At zero chemical potential, two states confined perpendicular to the wall and propagating within its plane have the same dispersion over a finite momentum interval. Numerical diagonalization confirms the analytical energies and wave functions.
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BibTeX
@misc{paez2026majorana,
title = {{Majorana interface states in anisotropic and tilted Dirac and Weyl systems}},
author = {Abraham Kaleb Plascencia Pérez Páez and Alireza Qaiumzadeh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.19707},
eprint = {2607.19707},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.19707},
}
RIS
TY - UNPB
TI - Majorana interface states in anisotropic and tilted Dirac and Weyl systems
AU - Abraham Kaleb Plascencia Pérez Páez
AU - Alireza Qaiumzadeh
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2607.19707
UR - https://arxiv.org/abs/2607.19707
AB - Anisotropy and cone tilt change how Majorana states propagate along an interface and decay away from it. We derive a two-dimensional Majorana surface Hamiltonian from a fully gapped three-dimensional superconductor, with the surface mass generated by the relative phase between triplet and singlet pairing. For a mass domain wall on this surface, we obtain the wave function, propagation velocity, and localization length of the resulting one-dimensional channel for a general invertible velocity tensor and an arbitrary wall orientation. The product of propagation speed and localization length is independent of wall orientation in the anisotropic model. For a smooth closed channel without a vortex, the propagation time around the wall determines the lowest excitation energy. For a tilted surface cone, the normal and parallel components of tilt affect confinement and propagation differently. We also solve a separate three-dimensional Weyl model with uniform singlet pairing and a reversing exchange field. In the regime supporting interface states, its bulk remains gapless. At zero chemical potential, two states confined perpendicular to the wall and propagating within its plane have the same dispersion over a finite momentum interval. Numerical diagonalization confirms the analytical energies and wave functions.
ER -