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Register a new userMoire minibands in graphene heterostructures with almost commensurate sqrt3 x sqrt3 hexagonal crystals
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We present a phenomenological theory of the low energy moire minibands of Dirac electrons in graphene placed on an almost commensurate hexagonal underlay with a unit cell pproximately three times larger than that of graphene.A slight incommensurability results in a periodically modulated intervalley scattering for electrons in graphene. In contrast to the perfectly commensurate Kekule distortion of graphene, such supperlattice perturbation leaves the zero energy Dirac cones intact, but is able to open a band gap at the edge of the first moire subbband, asymmetrically in the conduction and valence bands.
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We find a systematic reappearance of massive Dirac features at the edges of consecutive minibands formed at magnetic fields B_{p/q}= pphi_0/(qS) providing rational magnetic flux through a unit cell of the moire superlattice created by a hexagonal substrate for electrons in graphene. The Dirac-type features in the minibands at B=B_{p/q} determine a hierarchy of gaps in the surrounding fractal spectrum, and show that these minibands have topological insulator properties. Using the additional $q$-fold degeneracy of magnetic minibands at B_{p/q}, we trace the hierarchy of the gaps to their manifestation in the form of incompressible states upon variation of the carrier density and magnetic field.
Interference of double moire patterns of graphene (G) encapsulated by hexagonal boron nitride (BN) can alter the electronic structure features near the primary/secondary Dirac points and the electron-hole symmetry introduced by a single G/BN moire pattern depending on the relative stacking arrangements of the top/bottom BN layers. We show that strong interference effects are found in nearly aligned BN/G/BN and BN/G/NB and obtain the evolution of the associated density of states as a function of moire superlattice twist angles. For equal moire periods and commensurate patterns with $Delta phi = 0^{circ}$ modulo $60^{circ}$ angle differences the patterns can add up constructively leading to large pseudogaps of about $sim 0.5$ eV on the hole side or cancel out destructively depending on their relative sliding, e.g. partially recovering electron-hole symmetry. The electronic structure of moire quasicrystals for $Delta phi =30^{circ}$ differences reveal double moire features in the density of states with almost isolated van Hove singularities where we can expect strong correlations.
Growing attention has been drawn in the past years to the alpha-phase (1/3 monolayer) of Sn on Ge(111), which undergoes a transition from the low temperature (3x3) phase to the room temperature (sqrt3 x sqrt3)R30° one. On the basis of scanning tunnelling microscopy experiments, this transition was claimed to be the manifestation of a surface charge density wave (SCDW), i.e. a periodic redistribution of charge, possibly accompanied by a periodic lattice distortion, which determines a change of the surface symmetry. Recent He diffraction studies of the (3x3) long range order have shown the transition to be of the order-disorder type with a critical temperature Tc=220 K and belonging to the 3-state Potts universality class. These findings clearly exclude an SCDW driven mechanism at 220 K, but they cannot exclude the occurence of a displacive transition at higher temperature. Here we present photoelectron diffraction data taken at 300 K and photoemission data taken up to 500 K (which is the maximum temperature where the (sqrt3 x sqrt3)R30° is stable) . From our analysis it is shown that the atomic structure of the Sn overlayer does not change throughout the transition up to 500 K. As a consequence the displacive hypothesis must be discarded in favour of a genuine order-disorder model.
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.
Spontaneous orbital magnetism observed in twisted bilayer graphene (tBG) on nearly aligned hexagonal boron nitride (BN) substrate builds on top of the electronic structure resulting from combined G/G and G/BN double moire interfaces. Here we show that tBG/BN commensurate double moire patterns can be classified into two types, each favoring the narrowing of either the conduction or valence bands on average, and obtain the evolution of the bands as a function of the interlayer sliding vectors and electric fields. Finite valley Chern numbers $pm 1$ are found in a wide range of parameter space when the moire bands are isolated through gaps, while the local density of states associated to the flat bands are weakly affected by the BN substrate invariably concentrating around the AA-stacked regions of tBG. We illustrate the impact of the BN substrate for a particularly pronounced electron-hole asymmetric band structure by calculating the optical conductivities of twisted bilayer graphene near the magic angle as a function of carrier density. The band structures corresponding to other $N$-multiple commensurate moire period ratios indicate it is possible to achieve narrow width $W lesssim 30$ meV isolated folded band bundles for tBG angles $theta lesssim 1^{circ}$.
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