Orbital magnetic susceptibility involves rich physics such as interband effects despite of its conceptual simplicity. In order to appreciate the rich physics related to the orbital magnetic susceptibility, it is essential to derive a formula to decom
pose the susceptibility into the contributions from each band. Here, we propose a scheme to perform this decomposition using the modified Wannier functions. The derived formula nicely decomposes the susceptibility into intraband and interband contributions, and from the other aspect, into itinerant and local contributions. The validity of the formula is tested in a couple of simple models. Interestingly, it is revealed that the quality of the decomposition depends on the degree of localization of the used Wannier functions. The formula here complements another formula using Bloch functions, or the formula derived in the semiclassical theory, which deepens our understanding of the orbital magnetic susceptibility and may serve as a foundation of a better computational method. The relationship to the Berry curvature in the present scheme is also clarified.
The electric structure of twisted bilayer GeSe, which shows a rectangular moir{e} pattern, is analyzed using a $bm{k}cdotbm{p}$ type effective continuum model. The effective model is constructed on the basis of the the local approximation method, whe
re the local lattice structure of a twisted bilayer system is approximated by its untwisted bilayer with parallel displacement, and the required parameters are fixed with the help of the first-principles method. By inspecting the twist angle dependence of the physical properties, we reveal a relation between the effective potential under moir{e} pattern and the alignment of the Ge atoms, and also the resultant one-dimensional flat band, where the band is flattened stronger in a specific direction than the perpendicular direction. Due to the relatively large effective mass of the original monolayers, the flat band with its band width as small as a few meV appear in a relatively large angle. This gives us an opportunity to explore the dimensional crossover in the twisted bilayer platform.
A salient feature of topological phases are surface states and many of the widely studied physical properties are directly tied to their existence. Although less explored, a variety of topological phases can however similarly be distinguished by thei
r response to localized flux defects, resulting in the binding of modes whose stability can be traced back to that of convectional edge states. The reduced dimensionality of these objects renders the possibility of arranging them in distinct geometries, such as arrays that branch or terminate in the bulk. We show that the prospect of hybridizing the modes in such new kinds of channels poses profound opportunities in a dynamical context. In particular, we find that creating junctions of $pi$-flux chains or extending them as function of time can induce transistor and stop-and-go effects. Pending controllable initial conditions certain branches of the extended defect array can be actively biased. Discussing these physical effects within a generally applicable framework that relates to a variety of established artificial topological materials, such as mass-spring setups and LC circuits, our results offer an avenue to explore and manipulate new transport effects that are rooted in the topological characterization of the underlying system.
The entanglement Chern number, the Chern number for the entanglement Hamiltonian, is used to charac- terize the Kane-Mele model, which is a typical model of the quantum spin Hall phase with the time reversal symmetry. We first obtain the global phase
diagram of the Kane-Mele model in terms of the entanglement spin Chern number, which is defined by using a spin subspace as a subspace to be traced out in preparing the entanglement Hamiltonian. We further demonstrate the effectiveness of the entanglement Chern number without the time reversal symmetry and spin conservation by extending the Kane-Mele model to include the Zeeman term. The numerical results confirm that the sum of the entanglement spin Chern number equals to the Chern number.
