Related papers: Emulating moir\'e materials with quasiperiodic cir…
Moir\'e materials have enabled the realization of flat electron bands and quantum phases that are driven by strong correlations associated with flat bands. Superconductivity has been observed, but solely, in graphene moir\'e materials. The…
Majorana Fermions, strange particles that are their own antiparticles, were predicted in 1937 and have been sought after ever since. In condensed matter they are predicted to exist as vortex core or edge excitations in certain exotic…
In flat bands, superconductivity can lead to surprising transport effects. The superfluid "mobility", in the form of the superfluid weight $D_s$, does not draw from the curvature of the band but has a purely band-geometric origin. In a…
We review the theoretical modelling of moir\'e materials, focusing on various aspects of magic-angle twisted bilayer graphene (MA-TBG) viewed through the lens of Hartree-Fock mean-field theory. We first provide an elementary introduction to…
We show that one-dimensional quasi-periodic optical lattice systems can exhibit edge states and topological phases which are generally believed to appear in two-dimensional systems. When the Fermi energy lies in gaps, the Fermi system on…
Despite the multi-band spectrum of the widely-known Hofstadter butterfly, it turns out that the pairing correlations of the time-reversal-symmetric Hofstadter-Hubbard model are well-described by a single order parameter that is uniform in…
We investigate the effect of the trapping potential on the quantum phases of strongly correlated ultracold bosons in one-dimensional periodic and quasiperiodic optical lattices. By means of a decoupling meanfield approach, we characterize…
The Hofstadter butterfly is one of the first and most fascinating examples of the fractal and self-similar quantum nature of free electrons in a lattice pierced by a perpendicular magnetic field. However, the direct experimental…
We report on the theoretical electronic spectra of twisted phosphorene bilayers exhibiting moir\'e patterns, as computed by means of a continuous approximation to the moir\'e superlattice Hamiltonian. Our model is constructed by…
Quantized electric quadrupole insulators have recently been proposed as novel quantum states of matter in two spatial dimensions. Gapped otherwise, they can feature zero-dimensional topological corner mid-gap states protected by the bulk…
Electron correlation and topology are two central threads of modern condensed matter physics. Semiconductor moir\'e materials provide a highly tunable platform for studies of electron correlation. Correlation-driven phenomena, including the…
Stacking two atomic crystals with a twist between their crystal axes produces moir\'e potentials that modify the electronic properties. Here we show that double moir\'e potentials generated by superposing three atomic crystals create a new…
Twistronics, the study of moir\'e superlattices of twisted bilayer 2D materials creating nontrivial physical effects, has recently revolutionized diverse subjects from materials to optoelectronics, nanophotonics, and beyond. Here, breaking…
Moir\'e materials host a wealth of intertwined correlated and topological states of matter, all arising from flat electronic bands with nontrivial quantum geometry. A prominent example is the family of alternating-twist magic-angle graphene…
The Aubry-Andr\'e model describes a system with quasiperiodic lattice modulation. In one dimension the AAH model is known to exhibit a sharp metal to insulator transition at a self-dual critical point at which all the states in the spectrum…
Experimental demonstrations of tunable correlation effects in magic-angle twisted bilayer graphene have put two-dimensional moir\'e quantum materials at the forefront of condensed-matter research. Other twisted few-layer graphitic…
We propose that Hofstadter's butterfly accompanied by quantum Hall effect that is similar to those predicted to occur in 3D tight-binding systems by Koshino {\it et al.} [Phys. Rev. Lett. {\bf 86}, 1062 (2001)] can be realized in an…
Topological edge states are known to emerge in certain quasicrystals. We investigate a topological quasicrystal in the presence of nonlinearity by generalizing the Toda lattice to include modulated periodic hoppings, where the period is…
Topological description of hierarchical sets of spectral gaps of Hofstadter butterfly is found to be encoded in a quasicrystal where magnetic flux plays the role of a phase factor that shifts the origin of the quasiperiodic order. Revealing…
Although evidence of inter-valley attraction-mediated by phonon or topological fluctuations is accumulating, the origin of superconductivity in the flat-band quantum moir\'e materials remains an open question. Here, instead of attempting to…