Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTheories for the correlated insulating states and quantum anomalous Hall phenomena in twisted bilayer graphene
85
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The experimentally observed correlated insulating states and quantum anomalous Hall (QAH) effect in twisted bilayer graphene (TBG) have drawn significant attention. However, up to date, the specific mechanisms of these intriguing phenomena are still open questions. Using a fully unrestricted Hartree-Fock variational method, we have explained the correlated insulating states and QAH effects at various integer fillings of the flat bands in TBG. Our results indicate that states breaking flavor (valley and spin) symmetries are energetically favored at all integer fillings. In particular, the correlated insulating states at $pm 1/2$ filling and at the charge neutrality point are all valley polarized sates which break $C_{2z}$ and time-reversal ($mathcal{T}$) symmetries, but preserves $C_{2z}mathcal{T}$ symmetry. Such valley polarized states exhibit moire orbital antiferromagnetic ordering on an emergent honeycomb lattice with compensating circulating current pattern in the moire supercell. Within the same theoretical framework, our calculations indicate that the $C!=!mp 1$ QAH states at $pm 3/4$ fillings of the magic-angle TBG are spin and orbital ferromagnetic states, which emerge when a staggered sublattice potential is present. We find that the nonlocalness of the exchange interactions tend to enhance the bandwidth of the low-energy bands due to the exchange-hole effect, which reduces the gaps of the correlated insulator phases. The nonlocal exchange interactions also dramatically enhance the spin polarization of the system, which significantly stabilize the orbital and spin ferromagnetic QAH state at $3/4$ filling of TBG aligned with hexagonal boron nitride (hBN). We also predict that, by virtue of the orbital ferromagnetic nature, the QAH effects at electron and hole fillings of hBN-aligned TBG would exhibit hysteresis loops with opposite chiralities.
rate research
Read More
We use a lowest Landau level model to study the recent observation of an anomalous Hall effect in twisted bilayer graphene. This effective model is rooted in the occurrence of Chern bands which arise due to the coupling between the graphene device and its encapsulating substrate. Our model exhibits a phase transition from a spin-valley polarized insulator to a partial or fully valley unpolarized metal as the bandwidth is increased relative to the interaction strength, consistent with experimental observations. In sharp contrast to standard quantum Hall ferromagnetism, the Chern number structure of the flat bands precludes an instability to an inter-valley coherent phase, but allows for an excitonic vortex lattice at large interaction anisotropy.
The recently observed superconductivity in twisted bilayer graphene emerges from insulating states believed to arise from electronic correlations. While there have been many proposals to explain the insulating behaviour, the commensurability at which these states appear suggests that they are Mott insulators. Here we focus on the insulating states with $pm 2$ electrons or holes with respect to the charge neutrality point. We show that the theoretical expectations for the Mott insulating states are not compatible with the experimentally observed dependence on temperature and magnetic field if, as frequently assumed, only the correlations between electrons on the same site are included. We argue that the inclusion of non-local (inter-site) correlations in the treatment of the Hubbard model can bring the predictions for the magnetic and temperature dependencies of the Mott transition to an agreement with experiments and have consequences for the critical interactions, the size of the gap, and possible pseudogap physics. The importance of the inter-site correlations to explain the experimental observations indicates that the observed insulating gap is not the one between the Hubbard bands and that antiferromagnetic-like correlations play a key role in the Mott transition.
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.
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 uncover topological features of neutral particle-hole pair excitations of correlated quantum anomalous Hall (QAH) insulators whose approximately flat conduction and valence bands have equal and opposite non-zero Chern number. Using an exactly solvable model we show that the underlying band topology affects both the center-of-mass and relative motion of particle-hole bound states. This leads to the formation of topological exciton bands whose features are robust to nonuniformity of both the dispersion and the Berry curvature. We apply these ideas to recently-reported broken-symmetry spontaneous QAH insulators in substrate aligned magic-angle twisted bilayer graphene.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
