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We theoretically investigate the flow of information in an interacting two-skyrmion system confined in a box at finite temperature. Using numerical simulations based on the Thiele-Langevin equation, we demonstrate that the skyrmion motion cannot be fully described by the master equation, highlighting the system's simplicity with its nontrivial dynamics. Particularly, due to the chiral motion of skyrmion, we find asymmetric flow of information even in equilibrium, which is demonstrated by the violation of the detailed balance condition. We analyze this novel system using information-theoretical quantities including Shannon entropy, mutual information, and transfer entropy. By the analyses, the physical significance of transfer entropy as a measure of flow of information, which has been overlooked in previous studies, is elucidated. Notably, the peak position of the transfer entropy, as a function of time delay, is found to be independent of the interaction range between the two skyrmions yet dependent on the box size. This peak corresponds to the characteristic time required for changing the skyrmion state: the box size divided by the average velocity of skyrmions. We can understand that the information transmission time consists of the time to obtain mutual information and the time to write the information. Since the unusual asymmetric circulation of information is revealed in this two-skyrmion system, it can be a unique platform for future applications to natural computing using flow of information, including more efficient machine learning algorithm., Comment: 13 pages, 8 figures

We calculate the perpendicular electrical conductivity in twisted three-dimensional graphite (rotationally stacked graphite pieces) by using the effective continuum model and the recursive Green's function method. In the low twist angle regime $(\theta \lesssim 2^\circ)$, the conductivity shows a nonmonotonic dependence with a peak and dip structure as a function of the twist angle. By analyzing the momentum-resolved conductance and the local density of states, this behavior is attributed to the Fano resonance between continuum states of bulk graphite and interface-localized states, which is a remnant of the flat band in the magic-angle twisted bilayer graphene. We also apply the formulation to the high-angle regime near the commensurate angle $\theta \approx 21.8^\circ$, and reproduce the conductance peak observed in the experiment., Comment: 15 pages, 13 figures

We theoretically study emergent edge and corner states in monolayer blue phosphorus (blue phosphorene) using the first-principles calculation and tight-binding model. We show that the existence of the Wannier orbitals at every bond center yields edge states both in zigzag and armchair nanoribbons. The properties of the edge states can be well described by a simple effective Hamiltonian for uncoupled edge orbitals, where the structural relaxation near the boundary significantly affects the edge band structure. For corner states, we examine two types of corner structures consisting of zigzag and armchair edges, where we find that multiple corner states emerge in the bulk gap as a consequence of hybridization of edge and corner uncoupled orbitals. In the armchair corner, in particular, we demonstrate that corner states appear right at the Fermi energy, which leads to the emergence of fractional corner charge due to filling anomaly. Finally, we discuss the relationship between blue phosphorene and black phosphorene, and show that two systems share the equivalent Wannier orbital positions and similar edge/corner state properties even though their atomic structures are totally different., Comment: 15 pages, 10 figures