(10) Moiré excitons with Wannier functions: Twisted bilayers of two-dimensional (2D) materials have emerged as a highly tunable platform to study and engineer properties of excitons. However, the atomistic description of these properties has remained a significant challenge as a consequence of the large unit cells of the emergent moiré superlattices. To address this problem, we introduce an efficient approach to solve the Bethe-Salpeter equation that exploits the localization of atomic Wannier functions. Using this newly developed method, we study the twist angle-dependent intralayer and interlayer excitons in WS₂/WSe₂. 

This work is freely available on the arXiv. Also, find the peer-reviewed version at NPJ 2DMaterials&App. 

Funding: Marie Sklodowska-Curie Grant agreement No. 101028468.

(9) Excitonic Mott insulator: When two distinct 2D materials are layered one on top of the other, the optical excitations can lead to the creation of an interlayer exciton, in which the electron and hole exist in separate layers. We collaborated with Prof. Sufei Shi's group (now at Carnegie Melon University) to illustrate a pronounced electric repulsion between these interlayer excitons and the formation of an excitonic Mott insulating state with finite doping. 

This work is freely available on the arXiv. Also, find the peer-reviewed version at Nature Physics. 

Funding: Marie Sklodowska-Curie Grant agreement No. 101028468.

(5) Moiré created with strain: Moiré patterns formed by twisting the layers host interesting correlated electronic phases through the realizations of Hubbard models and have been extensively studied. We have demonstrated that the strained moiré patterns provide an interesting platform to realize Hubbard and ionic-Hubbard models. While the properties of the strained moiré pattern have some similarities to those of the moiré pattern formed by twist, there are many important differences. 

Figure (b) shows that the topological point defects are aster defects and domain walls are tensile solitons for strained moiré patterns. On the other hand,  figure (c) shows that the topological point defects are vortex defects and domain walls are shear solitons for twisted moiré patterns. This work is freely available on the arXiv. Also, find the peer-reviewed version at Phys. Rev. B. 

(4) Moiré lattice reconstruction: An important step in understanding and designing the exotic properties of moiré materials is to carefully take into account the effects of atomic relaxations. Conventionally it is presumed that the lattice constant of the unrelaxed moiré pattern remains intact even after relaxation. We have theoretically demonstrated that the presumption is not always valid in moiré materials. 

The figure shows evidence of lattice reconstructions (from left to right) found using simulated annealing in the twisted bilayer of MoS2. This work is freely available on the arXiv. Also, find the peer-reviewed version at Phys. Rev. B. Letter.

(3) Twistnonics and phasons: The twist angle dependent interlayer coupling in moiré materials provides a unique way to manipulate the phonons and related properties. We refer to this engineering of phononic properties as twistnonics. We have also demonstrated the appearance of ultra-low frequency incipient phason modes (very similar to acoustic modes) in moiré materials. 

The figure shows the twist angle dependence of the low-frequency shear (stars) and breathing modes (circles) in bilayer MoS2. This work is freely available on the arXiv. Also, find the peer-reviewed version at Phys. Rev. Research. 

(2) Twistnonics and High-frequency phonons: Raman spectroscopy is a great way to establish the twist angle-dependent phonon mode renormalizations in moiré materials (and thus, twistnonics). We collaborated with experimentalists at the Indian Institute of Science to demonstrate the evolution of doping-dependent high-frequency Raman active modes with twist angles.

The figure compares the theoretical and experimental twist angle dependence of the A1g mode in bilayer MoS2. This work is freely available on the arXiv. Also, find the peer-reviewed version at Nanoscale. 

(1) Breathing modes in a non-perturbative way: Relative out-of-plane displacements of the constituent layers of 2D materials give rise to unique low-frequency breathing modes. We have developed an accurate method to compute the breathing modes at any temperature including all the third and higher-order anharmonic effects. 

The figure compares our results (SW+LJ) with those computed using ab-initio simulations (DFPT) and measured in experiments for MoS2. This work is freely available on the arXiv. Also, find the peer-reviewed version at Phys. Rev. B Rapid Communication.