Magnetic-Field Effects on the Electronic States of the K 4 Lattice

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. 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. 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]. 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.