Effective superlattice models for moiré electrons and excitons in twisted bilayers of anisotropic 2D semiconductors

Twisted bilayer heterostructures of 2D materials forming moiré patterns have recently emerged as a family of versatile tabletop quantum simulators. Among the most recent phases of matter realized in moiré systems are Luttinger liquids[1] in bilayers of anisotropic 2D semiconductors, where the moiré pattern dramatically amplifies the anisotropy of the constituting layers, leading to dimensional reduction from 2D to 1D[2]. Theoretically, these systems are typically described by atomistic simulations[3-6], limited by computational cost to large twist angles.

Here, we present effective low-energy models for electrons, holes, and excitons in twisted bilayers of anisotropic 2D semiconductors, taking phosphorene as a case study. Our models predict a dimensional reduction for the charge carriers into arrays of quasi-1D states at large twist angles, in good agreement with recent DFT results[3-5]. Moreover, we predict that moiré excitons in the system also undergo this dimensional reduction to 1D states at large twist angles, followed by a crossover to quantum-dot-like 0D states at small twist angles, realizing SU(2) Bose-Luttinger and Bose-Hubbard models, respectively. We show that the twist-dependent excitonic absorption spectrum bears clear signatures of these crossovers.

[1] Nature 605, 57-62 (2022)

[2] Phys. Rev. Lett. 86, 676-679 (2001)

[3] Phys. Rev. B 96, 195406 (2017)

[4] J. Phys.: Condens. Matter 32, 234001 (2020)

[5] Nat. Commun. 11, 1124 (2020)

[6] Nanoscale 14, 3758 (2022)