Bilayer twisting as a mean to isolate connected flat bands in a kagome lattice through Wigner crystallization

The physics of flat band is novel and rich but difficult to access. In this regard, recently twisting of bilayer van der Waals(vd W)-bounded two-dimensional(2 D) materials has attracted much attention, because the reduction of Brillouin zone will eventually lead to a diminishing kinetic energy. Alternatively, one may start with a 2 D kagome lattice, which already possesses flat bands at the Fermi level, but unfortunately these bands connect quadratically to other(dispersive)bands, leading to undesirable effects. Here, we propose, by first-principles calculation and tight-binding modeling, that the same bilayer twisting approach can be used to isolate the kagome flat bands. As the starting kinetic energy is already vanishingly small, the interlayer vd W potential is always sufficiently large irrespective of the twisting angle. As such the electronic states in the(connected) flat bands become unstable against a spontaneous Wigner crystallization, which is expected to have interesting interplays with other flat-band phenomena such as novel superconductivity and anomalous quantum Hall effect.