1/4 is the new 1/2 when topology is intertwined with Mottness

Abstract

In non-interacting systems, bands from non-trivial topology emerge strictly at half-filling and exhibit either the quantum anomalous Hall or spin Hall effects. Here we show using determinantal quantum Monte Carlo and an exactly solvable strongly interacting model that these topological states now shift to quarter filling. A topological Mott insulator is the underlying cause. The peak in the spin susceptibility is consistent with a possible ferromagnetic state at T = 0. The onset of such magnetism would convert the quantum spin Hall to a quantum anomalous Hall effect. While such a symmetry-broken phase typically is accompanied by a gap, we find that the interaction strength must exceed a critical value for this to occur. Hence, we predict that topology can obtain in a gapless phase but only in the presence of interactions in dispersive bands. These results explain the recent quarter-filled quantum anomalous Hall effects seen in moiré systems.

Mapping twist-tuned multiband topology in bilayer WSe 2

“…This highlights the importance of moiré wavelength as a tuning parameter, which is only accessible in low-twist, lattice-matched systems. Our work motivates further studies to confirm the specific spin/valley symmetry breaking of the odd-integer gaps, as well as transport studies to confirm whether quantum spin Hall insulating states are realized at even integers, including a potential double quantum spin Hall insulator at ν=−4 ( 29 ). More generally, this work opens a platform for studying tunable topological bands in the limit of larger moiré wavelengths where interacting phases such as fractional Chern insulators may be more readily stabilized ( 46 , 47 ).…”

“…Our experiment is most consistent with the pair of lowest-energy moiré bands having identical Chern numbers in a single spin/valley sector (supplementary text S2 and S3). This is beyond any two-band tight binding model (which must have a zero total Chern number), highlighting that the topological structure in tWSe 2 extends beyond the Kane-Mele model ( 26 , 29 , 43 ).…”

“…Theoretical calculations have predicted that certain TMD moiré homobilayers realize a generalized version of the Kane-Mele model—in which the lowest-energy pair of bands have nonzero Chern numbers—and that these bands could support QAH states at odd filling thanks to interactions ( 26 ). However, there has been disagreement in the literature about the exact parameters for which topological bands are expected ( 27 – 29 ). Although there has been no experimental evidence of topology in TMD homobilayers, recent experiments in AB-stacked MoTe 2 /WSe 2 heterobilayers were able to mimic similar physics, using a large out-of-plane electric field to hybridize the electronic states on the two layers, and realized QAH and quantum spin Hall insulating states at moiré filling factors ν=−1 and ν=−2, respectively ( 15 , 30 , 31 ).…”

“…Although there has been no experimental evidence of topology in TMD homobilayers, recent experiments in AB-stacked MoTe 2 /WSe 2 heterobilayers were able to mimic similar physics, using a large out-of-plane electric field to hybridize the electronic states on the two layers, and realized QAH and quantum spin Hall insulating states at moiré filling factors ν=−1 and ν=−2, respectively ( 15 , 30 , 31 ). The precise symmetry breaking that underlies these insulating phases is a subject of ongoing experimental and theoretical studies ( 29 , 32 – 39 ).…”

Another Twist in the Understanding of Moiré Materials

“…They also highlight the difference between TMD bilayers and graphene multilayers. Already, in the time between this study's preprint and publication, experimentalists have revealed an additional topological phase in the same material [5], and theorists have proposed new models to explain the unusual topological phenomena found in moiré TMDs [6,7]. The new information about valley coherence in twisted MoTe 2 /WSe 2 bilayers will inevitably result in experiments to further elucidate the origin of the zero-field spin pattern and of the QAH effect.…”