We study the adiabatic topological charge pumping driven by interlayer sliding in the moiré superlattices. We show that, when we slide a single layer of the twisted bilayer system relatively to the other, a moiré pattern flow and a quantized transport of electrons occurs. When the Fermi energy is in a spectral gap, the number of pumped charges in the interlayer sliding process is quantized to a sliding Chern number, which obeys a Diophantine equation analogous to the quantum Hall effect. We apply the argument to the twisted bilayer graphene, and find that energy gaps above and below the nearly-flat bands has non-zero sliding Chern numbers. When the Fermi energy is in either of those gaps, the slide-driven topological pumping occurs perpendicularly to the sliding direction.
Using synchrotron radiation x-ray diffraction techniques, the equation of state of monoclinic ZrO2 has been investigated under a hydrostatic pressure condition at 298 K. Monoclinic ZrO2 transformed to the orthorhombic I phase at between 5.7 and 7.0 GPa. Lattice constants of monoclinic ZrO2 refined from the Reitveld analysis showed extreme anisotropic pressure dependence. From the pressure–volume data, using least-squares fit of the Birch–Murnaghan formula, the bulk modulus, K0 and its pressure derivative: K0′, were estimated to be 159(3) GPa and −3.6(6), respectively. A negative K0′ suggests the abnormal softening of the elastic modulus in monoclinic ZrO2 with compression. First-principles calculations supported present experimental results.
Monoclinic ZrO 2 baddeleyite exhibits anomalous softenings of the bulk modulus and atom vibrations with compression. The pressure evolution of the structure is investigated using neutron powder diffraction combined with ab initio calculations. The results show that the anomalous pressure response of the bulk modulus is related not to the change in the bonding characters but to the deformation of an oxygen sublattice, especially one of the layers made of oxygen atoms in the crystallographic a* plane. The layer consists of two parallelograms; one is rotated with little distortion and the other is distorted with increasing pressure. The deformation of this layer lengthens one of the Zr-O distances, resulting in the softening of some atom vibrational modes.
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