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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.
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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 perform the inverse frequency expansion by focusing on the high frequency region. Using the obtained effective Floquet Hamiltonian, we study nonequilibrium magnon dynamics away from the adiabatic limit and its effect on topological phenomena. We show that a linearly polarized laser can generate helical edge magnon states and induce the magnonic spin Nernst effect, whereas a circularly polarized laser can generate chiral edge magnon states and induce the magnonic thermal Hall effect. In particular, in the latter, we find that the direction of the magnon chiral edge modes and the resulting thermal Hall effect can be controlled by the chirality of the circularly polarized laser through the change from the left-circular to the right-circular polarization. Our results thus provide a handle to control and design magnon topological properties in the insulating AF.
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) heterostructures, the lattice mismatch between the two atomic crystals generates a unique kind of periodic structure known as a moire superlattice. Of particular interests is the emergent phenomena related to the reconstructed band-structure of graphene, such as the Hofstadter butterfly, topological currents, gate dependent pseudospin mixing, and ballistic miniband conduction. However, most studies so far have been limited to the lower-order minibands, e.g. the 1st and 2nd minibands counted from charge neutrality, and consequently the fundamental nature of the reconstructed higher-order miniband spectra still remains largely unknown. Here we report on probing the higher-order minibands of precisely aligned graphene moire superlattices by transport spectroscopy. Using dual electrostatic gating, the edges of these high-order minibands, i.e. the 3rd and 4th minibands, can be reached. Interestingly, we have observed interband Landau level (LL) crossinginducing gap closures in a multiband magneto-transport regime, which originates from band overlap between the 2nd and 3rd minibands. As observed high-order minibands and LL reconstruction qualitatively match our simulated results. Our findings highlight the synergistic effect of minibands in transport, thus presenting a new opportunity for graphene electronic devices.
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, we show that this mechanism can stabilize topological magnon excitations in honeycomb ferromagnets and in optical lattices. We find that the irradiated quantum magnet is described by a Haldane model for magnons that hosts topologically-protected edge modes. We study the evolution of the magnon spectrum in the Floquet regime and via time propagation of the magnon Hamiltonian for a slowly varying pulse envelope. Compared to similar but conceptually distinct driving schemes based on the Aharanov-Casher effect, the dimensionless light-matter coupling parameter $lambda = eEa/hbaromega$ at fixed electric field strength is enhanced by a factor $sim 10^5$. This increase of the coupling parameter allows to induce a topological gap of the order of $Delta approx 2$ meV with realistic laser pulses, bringing an experimental realization of light-induced topological magnon edge states within reach.
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-gap, continues to be the foundation of valleytronics. It is often assumed that achieving valley selective excitation in pristine graphene with all-optical means is not possible due to the inversion symmetry of the system. Here we demonstrate that both valley-selective excitation and valley-selective high-harmonic generation can be achieved in pristine graphene by using the combination of two counter-rotating circularly polarized fields, the fundamental and its second harmonic. Controlling the relative phase between the two colours allows us to select the valleys where the electron-hole pairs and higher-order harmonics are generated. We also describe an all-optical method for measuring valley polarization in graphene with a weak probe pulse. This work offers a robust recipe to write and read valley-selective electron excitations in materials with zero bandgap and zero Berry curvature.
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 has opened new vistas in the topological materials landscape. Here we report on evidence, obtained by combining thermodynamic measurements, local and non-local transport measurements, and theoretical calculations, that robust topologically non-trivial, valley Chern insulators occur at charge neutrality in twisted double-bilayer graphene (TDBG). These time reversal-conserving valley Chern insulators are enabled by valley-number conservation, a symmetry that emerges from the moire pattern. The thermodynamic gap extracted from chemical potential measurements proves that TDBG is a bulk insulator under transverse electric field, while transport measurements confirm the existence of conducting edge states. A Landauer-Buttiker analysis of measurements on multi-terminal samples allows us to quantitatively assess edge state scattering and demonstrate that it does not destroy the edge states, leaving the bulk-boundary correspondence largely intact.
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