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We study the collective dynamics of a two-dimensional honeycomb lattice of magnetic skyrmions. By performing large-scale micromagnetic simulations, we find multiple chiral and non-chiral edge modes of skyrmion oscillations in the lattice. The non-chiral edge states are due to the Tamm-Shockley mechanism, while the chiral ones are topologically protected against structure defects and hold different handednesses depending on the mode frequency. To interpret the emerging multiband nature of the chiral edge states, we generalize the massless Thieles equation by including a second-order inertial term of skyrmion mass as well as a third-order non-Newtonian gyroscopic term, which allows us to model the band structure of skrymion oscillations. Theoretical results compare well with numerical simulations. Our findings uncover the importance of high order effects in strongly coupled skyrmions and are helpful for designing novel topological devices.
Emerging new concepts, such as magnetic charge dynamics in two-dimensional magnetic material, can provide novel mechanism for spin based electrical transport at macroscopic length. In artificial spin ice of single domain elements, magnetic charges re
A stable skyrmion, representing the smallest realizable magnetic texture, could be an ideal element for ultra-dense magnetic memories. Here, we review recent progress in the field of skyrmionics, which is concerned with studies of tiny whirls of magn
Quantum materials that host a flat band, such as pseudospin-1 lattices and magic-angle twisted bilayer graphene, can exhibit drastically new physical phenomena including unconventional superconductivity, orbital ferromagnetism, and Chern insulating b
We theoretically study electronic properties of a graphene sheet on xy plane in a spatially nonuniform magnetic field, $B = B_0 hat{z}$ in one domain and $B = B_1 hat{z}$ in the other domain, in the quantum Hall regime and in the low-energy limit. We
The Luttinger liquid (LL) model of one-dimensional (1D) electronic systems provides a powerful tool for understanding strongly correlated physics including phenomena such as spin-charge separation. Substantial theoretical efforts have attempted to ex