Unconventional states of matter in a domain-wall network of moiré bilayer systems

Moiré bilayer systems have attracted significant attention for their potential to host unconventional states of matter [1]. When subjected to an interlayer bias, these systems reveal gapless domain-wall modes between AB- and BA-stacking domains, forming a triangular network of one-dimensional channels [2]. Here, we investigate correlated phenomena in the domain-wall network by incorporating electron-electron interactions through bosonization [3]. We introduce a general operator that accounts for various scatterings based on conservation laws, which have potential to destabilize the network, paving the way for unconventional states of matter. Within the renormalization-group framework, we classify the scattering operators and the emergent correlated states. Our analysis uncovers generalized umklapp scatterings facilitated by the moiré patterns in twisted bilayer structures, leading to correlated states at fractional fillings. We identify a set of scatterings leading to a gapped bulk while preserving gapless edge modes, reminiscent of the observed (quantum) anomalous Hall states [4]. We show that our description can offer insights in predicting observable features in spectroscopic probes and edge transport measurements.

References:

[1] Cao et al., Nature 556, 43 (2018); Cao et al., Nature 556, 80 (2018).

[2] Efimkin & MacDonald, PRB 98, 035404 (2018).

[3] Hsu, Loss & Klinovaja, PRB 108, L121409 (2023).

[4] Sharpe et al., Science 365, 605 (2019); Serlin et al., Science 367, 900 (2020).