Spontaneous Valley Spirals in Magnetically Encapsulated Twisted Bilayer Graphene

Abstract

Van der Waals heterostructures provide a rich platform for emergent physics due to their tunable hybridization of layers, orbitals, and spin. Here, we find that twisted bilayer graphene stacked between antialigned ferromagnetic insulators can feature flat electronic bands due to the interplay between twist, exchange proximity, and spin-orbit coupling. These flat bands are nearly degenerate in valley only and are effectively described by a triangular superlattice model. At half filling, we find that interactions induce spontaneous valley correlations that favor spiral order and derive a low-energy valley-Heisenberg model with symmetric and antisymmetric exchange couplings. We also show how electric interlayer bias broadens the bands and tunes these couplings. Our results put forward magnetic van der Waals heterostructures as a platform to explore valley-correlated states.

Emulating Heavy Fermions in Twisted Trilayer Graphene

“…In particular, it is observed that for interlayer biases of V ≈ 0.5t ⊥ the bandwidth becomes drastically reduced. Moreover, in the presence of interlayer bias, the electronic states can still be associated with a well-defined valley quantum number V z (computed in the real-space basis using the valley operator [39][40][41][42][43]). In summary, we have the coexistence of valley polarized and spin degenerate ultraflat states and dispersive modes, as shown schematically in Fig.…”

“…In the SU(4) scenario, the exchange coupling between local modes takes the form H Exc ¼ J P hiji S i • S j . Interestingly, exchange couplings in twisted van der Waals materials have been shown to be tunable all the way from ferromagnetic to antiferromagnetic [16,43,81]. We now compute the exchange J between two neighboring localized modes by means of the magnetic force theorem [56][57][58][59].…”

Spin-orbit correlations and exchange-bias control in twisted Janus dichalcogenide multilayers

“…While usually boron-nitride encapsulation is used, other different insulators can be considered. In particular, the use of van der Waals ferromagnetic insulators [58][59][60] such as CrCl 3 61 , CrBr 3 62 , and CrI 3 63 as encapsulation [64][65][66][67][68] pro- vide an interesting possibility with regards to controlling a correlated state in the twisted Janus bilayer. We now will show how a magnetic encapsulation allows controlling the underlying electronic structure of the Janus system, and in particular, tuning the non-collinear magnetic order of the correlated state.…”

Tunable moire spinons in magnetically encapsulated twisted van der Waals quantum spin-liquids

“…A paradigmatic example of these phenomena is twisted bilayer graphene, where the emergence of flat bands has lead to a variety of unconventional many-body states [43][44][45][46][47]. Interestingly, twist engineering generically provides a platform for correlated phases with electrical tunability [48][49][50] and topologically nontrivial electronic structures [51][52][53][54][55][56]. The versatility offered by stacked van der Waals heterostructures motivates the search for analogous phenomena in the realm of van der Waals magnets [57,58] that can ultimately lead to novel spinon phenomena in moire quantum spin-liquids.…”

“…, where d is the inter-layer distance, r ij is the distance between sites i and j, λ is the parameter that controls the decay of the interlayer coupling, and t ⊥,0 is the largest possible inter-layer coupling realized at r ij = d. In the following we take t ⊥,0 = 0.36t, λ = 10/a, and d = a, where a is the lattice constant of the triangular lattice. From the computational point of view, we will use the twist scaling relation for computational convenience [65,66], and we compute the valley expectation V z = ±1 by means of the valley operator [49,[67][68][69][70].…”