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The honeycomb lattice sets the basic arena for numerous ideas to implement electronic, photonic, or phononic topological bands in (meta-)materials. Novel opportunities to manipulate Dirac electrons in graphene through band engineering arise from superlattice potentials as induced by a substrate such as hexagonal boron-nitride. Making use of the general form of a weak substrate potential as dictated by symmetry, we analytically derive the low-energy minibands of the superstructure, including a characteristic 1.5 Dirac cone deriving from a three-band crossing at the Brillouin zone edge. Assuming a large supercell, we focus on a single Dirac cone (or valley) and find all possible arrangements of the low-energy electron and hole bands in a complete six-dimensional parameter space. We identify the various symmetry planes in parameter space inducing gap closures and find the sectors hosting topological minibands, including also complex band crossings that generate a valley Chern number atypically larger than one. Our map provides a starting point for the systematic design of topological bands by substrate engineering.
We study the laser control of magnon topological phases induced by the Aharonov-Casher effect in insulating antiferromagnets (AFs). Since the laser electric field can be considered as a time-periodic perturbation, we apply the Floquet theory and perf
The propagation of Dirac fermions in graphene through a long-period periodic potential would result in a band folding together with the emergence of a series of cloned Dirac points (DPs). In highly aligned graphene/hexagonal boron nitride (G/hBN) het
Driving a two-dimensional Mott insulator with circularly polarized light breaks time-reversal and inversion symmetry, which induces an optically-tunable synthetic scalar spin chirality interaction in the effective low-energy spin Hamiltonian. Here, w
Electrons in two-dimensional hexagonal materials have valley degree of freedom, which can be used to encode and process quantum information. The valley-selective excitations, governed by the circularly polarised light resonant with the materials band
Topological insulators realized in materials with strong spin-orbit interactions challenged the long-held view that electronic materials are classified as either conductors or insulators. The emergence of controlled, two-dimensional moire patterns ha