Related papers: The Landau Level of Fragile Topology
We propose Landau levels as a probe for the topological character of electronic bands in two-dimensional moir\'e superlattices. We consider two configurations of twisted double bilayer graphene (TDBG) that have very similar band structures,…
Moir\'e superlattices in two-dimensional (2D) van der Waals (vdW) heterostructures provide 20 an efficient way to engineer electron band properties. The recent discovery of exotic quantum phases and their interplay in twisted bilayer…
Two-dimensional systems with $C_{2}\mathcal{T}$ ($P\mathcal{T}$) symmetry exhibit the Euler class topology $E\in\mathbb{Z}$ in each two-band subspace realizing a fragile topology beyond the symmetry indicators. By systematically studying…
Twisted bilayer graphene has been argued theoretically to host exceptionally flat bands when the angle between the two layers falls within a magic range near 1.1$^\circ$. This is now strongly supported by experiment, which furthermore…
We theoretically study the Hofstadter butterfly of a triangular network model in minimally twisted bilayer graphene (mTBLG). The band structure manifests periodicity in energy, mimicking that of Floquet systems. The butterfly diagrams…
Twisted graphene moire superlattice has been demonstrated as an exotic platform for investigating correlated states and nontrivial topology. Among the moire family, twisted double bilayer graphene (TDBG) is a tunable flat band system…
We calculate the electronic spectrum of bilayer graphene in perpendicular magnetic fields nonperturbatively. To accommodate arbitrary displacements between the two layers, we apply a periodic gauge based on singular flux vortices of phase…
Twisted bilayer graphene (TBG) is remarkable for its topological flat bands, which drive strongly-interacting physics at integer fillings, and its simple theoretical description facilitated by the Bistritzer-MacDonald Hamiltonian, a…
We develop a new, efficient, and general method to determine the Hofstadter spectrum of isolated narrow bands. The method works for topological as well as for trivial narrow bands by projecting the zero $\mathbf{B}$-field hybrid Wannier…
We present transport measurements of bilayer graphene with 1.38{\deg} interlayer twist and apparent additional alignment to its hexagonal boron nitride cladding. As with other devices with twist angles substantially larger than the magic…
We propose that the electronic structure of twisted bilayer graphene (TBG) can be understood as Dirac fermions coupled with opposite pseudo magnetic fields generated by the moir\'e pattern. The two low-energy flat bands from each monolayer…
The recently introduced topological heavy fermion model (THFM) provides a means for interpreting the low-energy electronic degrees of freedom of the magic angle twisted bilayer graphene as hybridization amidst highly dispersing topological…
We study graphene antidot lattices (GALs) in magnetic fields. Using a tight-binding model and a recursive Green's function technique that we extend to deal with periodic structures, we calculate Hofstadter butterflies of GALs. We compare…
In Bernal-stacked bilayer graphene (BBG), the Landau levels give rise to an intimate connection between valley and layer degrees of freedom. Adding a moir\'e superlattice potential enriches the BBG physics with the formation of topological…
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 investigate the electronic spectra and quantum Hall effect in twisted bilayer graphenes with various rotation angles under magnetic fields, using a model rigorously including the interlayer interaction. We describe the spectral evolution…
The large lattice constant of Moire superlattice formed in twisted bilayer graphene for small twist enables observing the Landau levels splitting into Hofstadter butterflies in energy spectra for moderate magnetic field. This is expected…
The magnetic field generated Hofstadter butterfly in single-twist trilayer graphene (TLG) is investigated using circularly polarized light (CPL) and longitudinal light emanating from a waveguide. We show that single-twist TLG has two…
We study the topological bands in twisted bilayer transition metal dichalcogenides in an external magnetic field. We first focus on a paradigmatic model of WSe$_2$, which can be described in an adiabatic approximation as particles moving in…
We investigate the effect of a magnetic field on the band structure of bilayer graphene with a magic twist angle of 1.08{\deg}. The coupling of a tight-binding model and the Peierls phase allows the calculation of the energy bands of…