相关论文: Landau Levels of the Euler Class 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,…
The last years have witnessed rapid progress in the topological characterization of out-of-equilibrium systems. We report on robust signatures of a new type of topology -- the Euler class -- in such a dynamical setting. The enigmatic…
We study the Hofstadter butterfly and Landau levels of the twisted bilayer graphene (TBG). We show that the nontrivial fragile topology of the lowest two bands near the charge neutral point makes their Hofstadter butterfly generically…
The Euler class characterizes the topology of two real bands isolated from other bands in two-dimensions. Despite various intriguing topological properties predicted up to now, the candidate real materials hosting electronic Euler bands are…
Symmetries play a crucial role in the classification of topological phases of matter. Although recent studies have established a powerful framework to search for and classify topological phases based on symmetry indicators, there exists a…
We show that the Wannier obstruction and the fragile topology of the nearly flat bands in twisted bilayer graphene at magic angle are manifestations of the nontrivial topology of two-dimensional real wave functions characterized by the…
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…
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…
In two-dimensional systems with space-time inversion symmetry, such as $C_{2z}T$, the reality condition on wave functions gives rise to real band topology characterized by the Euler class, a $\mathbb{Z}$-valued topological invariant for a…
Flat bands underlie a diverse range of quantum phenomena, from strongly correlated phases to superconductivity. We theoretically establish that a two-dimensional electron gas under a linear magnetic-field gradient and a transverse electric…
Real band topology often appears in systems with space-time inversion symmetry and is characterized by invariants such as the Euler and second Stiefel-Whitney classes. Here, we examine the generic band topology of Bogoliubov de-Gennes (BdG)…
A single Landau level (LL) dressed with periodic electrostatic potentials can realize a plethora of interacting topological phases where the Hall conductivity generally does not equal to the LL filling factor. Their physics can be captured…
We study the effects of the Coulomb interactions between electrons on the Hofstadter butterfly, which characterizes the subband structure of the Landau levels of a two-dimensional electron gas in a perpendicular homogeneous magnetic field…
Monolayer graphene placed with a twist on top of AB-stacked bilayer graphene hosts topological flat bands in a wide range of twist angles. The dispersion of these bands and gaps between them can be efficiently controlled by a perpendicular…
We calculate the energy bands for graphene monolayers when electrons move through a periodic electrostatic potential in the presence of a uniform perpendicular magnetic field. We clearly demonstrate the quantum fractal nature of the energy…
We analyze quantum-geometric bounds on optical weights in topological phases with pairs of bands hosting nontrivial Euler class, a multigap invariant characterizing non-Abelian band topology. We show how the bounds constrain the combined…
We develop a theoretical framework for Landau levels in quasi-periodic twisted bilayer graphene at a $30^\circ$ twist angle, a system without translational symmetry but possessing 12-fold rotational symmetry. Using a quasi-band formalism,…
Moir\'e systems featuring flat electronic bands exhibit a vast landscape of emergent exotic quantum states, making them one of the resourceful platforms in condensed matter physics in recent times. Tuning these systems via twist angle and…
We investigate topological insulating states in both two and three dimensions with the harmonic potential and strong spin-orbit couplings breaking the inversion symmetry. Landau-level like quantizations appear with the full 2D and 3D…
According to the Onsager's semiclassical quantization rule, the Landau levels of a band are bounded by its upper and lower band edges at zero magnetic field. However, there are two notable systems where the Landau level spectra violate this…