Related papers: Moire Butterflies
We address the energy spectrum of honeycomb lattice with various defects or impurities under a perpendicular magnetic field. We use a tight-binding Hamiltonian including interactions with the nearest neighbors and investigate its energy…
We study thermodynamic properties of the two-dimensional (2D) Falicov-Kimball model in the presence of external magnetic field perpendicular to the lattice. The field is taken into account by the Peierls substitution in the hopping term. In…
I revisit the problem of a charged particle on a two-dimensional lattice immersed in a constant (electro)magnetic field, and discuss the energy spectrum - Hofstadter's butterfly - from a new, quantum field theoretical perspective. In…
Integral Apollonian packing, the packing of circles with integer curvatures, where every circle is tangent to three other mutually tangent circles, is shown to encode the fractal structure of the energy spectrum of two-dimensional Bloch…
We revisit the problem of self-similar properties of the Hofstadter butterfly spectrum, focusing on spectral as well as topological characteristics. In our studies involving any value of magnetic flux and arbitrary flux interval, we single…
The $\alpha$-$T_3$ model extrapolates between the pseudospin $S=1/2$ honeycomb lattice of graphene and the pseudospin $S=1$ dice lattice via parameter $\alpha$. We present calculations of the magnetic properties of this hybrid pseudospin…
We study the relation between the global topology of the Hofstadter butterfly of a multiband insulator and the topological invariants of the underlying Hamiltonian. The global topology of the butterfly, i.e., the displacement of the energy…
Staking layered materials revealed to be a very powerful method to tailor their electronic properties. It has indeed been theoretically and experimentally shown that twisted bilayers of graphene (tBLG) with a rotation angle $\theta$,…
Moir\'e superlattices engineer band properties and enable observation of fractal energy spectra of Hofstadter butterfly. Recently, correlated-electron physics hosted by flat bands in small-angle moir\'e systems has been at the foreground.…
We explore the moir\'e magnon bands in twisted bilayer magnets with next-nearest neighboring Dzyaloshinskii-Moriya interactions, assuming that the out-of-plane collinear magnetic order is preserved under weak interlayer coupling. By…
The electronic bands of twisted bilayer graphene (TBLG) with a large-period moir\'e superlattice fracture to form narrow Bloch minibands that are spectrally isolated by forbidden energy gaps from remote dispersive bands. When these gaps are…
Periodic systems feature the Hofstadter butterfly spectrum produced by Brown--Zak minibands of electrons formed when magnetic field flux through the lattice unit cell is commensurate with flux quantum and manifested by magneto-transport…
In magic angle twisted bilayer graphene (MATBG), the moir\'e superlattice potential gives rise to narrow electronic bands1 which support a multitude of many-body quantum phases. Further richness arises in the presence of a perpendicular…
Twisted bilayer graphene (tBLG) has emerged as a promising platform to explore exotic electronic phases. However, the formation of moir\'e patterns in tBLG has thus far been confined to the introduction of twist angles between the layers.…
We develop a theory of photoluminescence using a time-dependent Hartree-Fock approximation that is appropriate for the two-dimensional Wigner crystal in a strong magnetic field. The cases of localized and itinerant holes are both studied.…
It has been shown that Bernal stacked bilayer graphene (BLG) in a uniform magnetic field demonstrates integer quantum Hall effect with a zero Landau-level anomaly \cite{Geimbilayer}. In this article we consider such system in a two…
We revisit the Hofstadter butterfly for a subset of topologically trivial Bloch bands arising from a continuum free electron Hamiltonian in a periodic lattice potential. We employ the recently developed procedure -- which was previously…
Landau's quantization for incompletely nested Fermi surfaces is known to give rise to magnetic-field-induced spin-density waves(FISDW) in two-dimensional organic metals. Here we show that three-dimensional(3D) systems can have 3D-specific…
We present a new simple and easy-to-implement one-dimensional phononic system whose spectrum exactly corresponds to the Hofstadter butterfly when a parameter is modulated. The system consists of masses that are coupled by linear springs and…
Magnetic field effects on single-particle energy bands (Hofstadter butterfly), Hall conductance, flat-band ferromagnetism, and magnetoresistance of two-dimensional Kagome lattices are studied. The flat-band ferromagnetism is shown to be…