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Register a new userTopological Flat Bands and Correlated States in Twisted Monolayer-Bilayer Graphene
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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 electric field, which induces topological transitions accompanied by changes of the Chern numbers. In the regime where the applied electric field induces gaps between the flat bands, we find a relatively uniform distribution of the Berry curvature. Consequently, interaction-induced valley- and/or spin-polarized states at integer filling factors are energetically favorable. In particular, we predict a quantum anomalous Hall state at filling factor $ u=1$ for a range of twist angles $1^circ<theta <1.4^circ$. Furthermore, to characterize the response of the system to magnetic field, we computed the Hofstadter butterfly and the Wannier plot, which can be used to probe the dispersion and topology of the flat bands in this material.
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Flat band moire superlattices have recently emerged as unique platforms for investigating the interplay between strong electronic correlations, nontrivial band topology, and multiple isospin flavor symmetries. Twisted monolayer-bilayer graphene (tMBG) is an especially rich system owing to its low crystal symmetry and the tunability of its bandwidth and topology with an external electric field. Here, we find that orbital magnetism is abundant within the correlated phase diagram of tMBG, giving rise to the anomalous Hall effect (AHE) in correlated metallic states nearby most odd integer fillings of the flat conduction band, as well as correlated Chern insulator states stabilized in an external magnetic field. The behavior of the states at zero field appears to be inconsistent with simple spin and valley polarization for the specific range of twist angles we investigate, and instead may plausibly result from an intervalley coherent (IVC) state with an order parameter that breaks time reversal symmetry. The application of a magnetic field further tunes the competition between correlated states, in some cases driving first-order topological phase transitions. Our results underscore the rich interplay between closely competing correlated ground states in tMBG, with possible implications for probing exotic IVC ordering.
We investigate the band structure of twisted monolayer-bilayer graphene (tMBG), or twisted graphene on bilayer graphene (tGBG), as a function of twist angles and perpendicular electric fields in search of optimum conditions for achieving isolated nearly flat bands. Narrow bandwidths comparable or smaller than the effective Coulomb energies satisfying $U_{textrm{eff}} /W gtrsim 1$ are expected for twist angles in the range of $0.3^{circ} sim 1.5^{circ}$, more specifically in islands around $theta sim 0.5^{circ}, , 0.85^{circ}, ,1.3^{circ}$ for appropriate perpendicular electric field magnitudes and directions. The valley Chern numbers of the electron-hole asymmetric bands depend intrinsically on the details of the hopping terms in the bilayer graphene, and extrinsically on factors like electric fields or average staggered potentials in the graphene layer aligned with the contacting hexagonal boron nitride substrate. This tunability of the band isolation, bandwidth, and valley Chern numbers makes of tMBG a more versatile system than twisted bilayer graphene for finding nearly flat bands prone to strong correlations.
The crystal structure of a material creates a periodic potential that electrons move through giving rise to the electronic band structure of the material. When two-dimensional materials are stacked, the twist angle between the layers becomes an additional degree freedom for the resulting heterostructure. As this angle changes, the electronic band structure is modified leading to the possibility of flat bands with localized states and enhanced electronic correlations. In transition metal dichalcogenides, flat bands have been theoretically predicted to occur for long moire wavelengths over a range of twist angles around 0 and 60 degrees giving much wider versatility than magic angle twisted bilayer graphene. Here we show the existence of a flat band in the electronic structure of 3{deg} and 57.5{deg} twisted bilayer WSe2 samples using scanning tunneling spectroscopy. Direct spatial mapping of wavefunctions at the flat band energy have shown that the flat bands are localized differently for 3{deg} and 57.5{deg}, in excellent agreement with first-principle density functional theory calculations.
The discovery of interaction-driven insulating and superconducting phases in moire van der Waals heterostructures has sparked considerable interest in understanding the novel correlated physics of these systems. While a significant number of studies have focused on twisted bilayer graphene, correlated insulating states and a superconductivity-like transition up to 12 K have been reported in recent transport measurements of twisted double bilayer graphene. Here we present a scanning tunneling microscopy and spectroscopy study of gate-tunable twisted double bilayer graphene devices. We observe splitting of the van Hove singularity peak by ~20 meV at half-filling of the conduction flat band, with a corresponding reduction of the local density of states at the Fermi level. By mapping the tunneling differential conductance we show that this correlated system exhibits energetically split states that are spatially delocalized throughout the different regions in the moire unit cell, inconsistent with order originating solely from onsite Coulomb repulsion within strongly-localized orbitals. We have performed self-consistent Hartree-Fock calculations that suggest exchange-driven spontaneous symmetry breaking in the degenerate conduction flat band is the origin of the observed correlated state. Our results provide new insight into the nature of electron-electron interactions in twisted double bilayer graphene and related moire systems.
We discuss twisted bilayer graphene (TBG) based on a theorem of flat band ferromagnetism put forward by Mielke and Tasaki. According to this theorem, ferromagnetism occurs if the single particle density matrix of the flat band states is irreducible and we argue that this result can be applied to the quasi-flat bands of TBG that emerge around the charge-neutrality point for twist angles around the magic angle $thetasim1.05^circ$. We show that the density matrix is irreducible in this case, thus predicting a ferromagnetic ground state for neutral TBG ($n=0$). We then show that the theorem can also be applied only to the flat conduction or valence bands, if the substrate induces a single-particle gap at charge neutrality. Also in this case, the corresponding density matrix turns out to be irreducible, leading to ferromagnetism at half filling ($n=pm2$).
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