Magnetic-Field Effects on the Electronic States of the K4 Lattice
Abstract
We investigate the electronic states of the K4 lattice in a uniform magnetic field within a nearest-neighbor tight-binding model. The K4 lattice is a \rev{noncentrosymmetric three-dimensional network with triple-Dirac cones at the Γ and H points}. By fixing the Bloch momentum component parallel to the field, the Peierls-substituted tight-binding problem reduces to an effective two-dimensional problem and yields a Hofstadter spectrum \rev{whose self-similar subpatterns reflect the geometry of the lattice projected onto the plane perpendicular to the field}. A square-like substructure emerges on the flux scale ϕ= 1/8 for B∥[100], and honeycomb- and triangular-like substructures emerge on the finer scale ϕ= 1/32 for B∥[111]\rev{. Here ϕ is the flux through the elementary plaquette of the projected lattice, and these scales correspond to one flux quantum per projected unit cell. Owing to the screw axes of the chiral K4 network, the field-parallel momentum acts as an additional flux, which, for commensurate values of this momentum, shifts the spectrum along the flux axis and brings the second triple-Dirac cone at the H point into the magnetic spectrum}. In the weak-field limit, we derive the Landau-level structure from a low-energy effective Hamiltonian around the Γ point. The three-component nature of the triple-Dirac cone gives rise to a cubic secular equation, whose solutions describe how a pseudospin-flat branch coexists with two relativistic Landau ladders \rev{and a single chiral n=0 level dispersing linearly along the field, in agreement with the lattice calculation}.
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BibTeX
@misc{takahashi2026magneticfield,
title = {{Magnetic-Field Effects on the Electronic States of the K$_4$ Lattice}},
author = {Katsuhiro Takahashi and Shouya Yoshida and Katsunori Wakabayashi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27539},
eprint = {2610.27539},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27539},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Magnetic-Field Effects on the Electronic States of the K_4 Lattice
AU - Katsuhiro Takahashi
AU - Shouya Yoshida
AU - Katsunori Wakabayashi
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27539
UR - https://arxiv.org/abs/2610.27539
AB - We investigate the electronic states of the K_4 lattice in a uniform magnetic field within a nearest-neighbor tight-binding model. The K_4 lattice is a \rev{noncentrosymmetric three-dimensional network with triple-Dirac cones at the Γ and H points}. By fixing the Bloch momentum component parallel to the field, the Peierls-substituted tight-binding problem reduces to an effective two-dimensional problem and yields a Hofstadter spectrum \rev{whose self-similar subpatterns reflect the geometry of the lattice projected onto the plane perpendicular to the field}. A square-like substructure emerges on the flux scale ϕ= 1/8 for B∥[100], and honeycomb- and triangular-like substructures emerge on the finer scale ϕ= 1/32 for B∥[111]\rev{. Here ϕ is the flux through the elementary plaquette of the projected lattice, and these scales correspond to one flux quantum per projected unit cell. Owing to the screw axes of the chiral K_4 network, the field-parallel momentum acts as an additional flux, which, for commensurate values of this momentum, shifts the spectrum along the flux axis and brings the second triple-Dirac cone at the H point into the magnetic spectrum}. In the weak-field limit, we derive the Landau-level structure from a low-energy effective Hamiltonian around the Γ point. The three-component nature of the triple-Dirac cone gives rise to a cubic secular equation, whose solutions describe how a pseudospin-flat branch coexists with two relativistic Landau ladders \rev{and a single chiral n=0 level dispersing linearly along the field, in agreement with the lattice calculation}.
ER -