Transferred graphene provides a promising III-nitride semiconductor epitaxial platform for fabricating multifunctional devices beyond the limitation of conventional substrates. Despite its tremendous fundamental and technological importance, it remains an open question on which kind of epitaxy is preferred for single-crystal III-nitrides. Popular answers to this include the remote epitaxy where the III-nitride/graphene interface is coupled by nonchemical bonds, and the quasi-van der Waals epitaxy (quasi-vdWe) where the interface is mainly coupled by covalent bonds. Here, we show the preferred one on wet-transferred graphene is quasi-vdWe. Using aluminum nitride (AlN), a strong polar III-nitride, as an example, we demonstrate that the remote interaction from the graphene/AlN template can inhibit out-of-plane lattice inversion other than in-plane lattice twist of the nuclei, resulting in a polycrystalline AlN film. In contrast, quasi-vdWe always leads to single-crystal film. By answering this long-standing controversy, this work could facilitate the development of III-nitride semiconductor devices on two-dimensional materials such as graphene.

Quantum spin-Hall insulators (QSHIs) possess nontrivial band topology. Using first-principles many-body perturbation theory ($GW+\text{Bathe-Salpeter}$ equation), we show that excitonic insulators (EIs) can exist in QSHIs AsO and ${\mathrm{Mo}}_2{\mathrm{TiC}}_2{\mathrm{O}}_2$ with nonvanishing band gaps. Their single-particle topological properties can be described by the same low-energy model, and we show that the EI phase in this model is of spin-triplet type due to the nontrivial band geometry. The rotational symmetry is broken by the $s$-wave EI order parameter, and the anisotropic absorption together with possible lattice reconstruction can be used as signatures for this spin-triplet topological EI phase. Large amounts of spin-triplet excitons emerge spontaneously when an EI is achieved and exciton spin-Hall effect may be observed.

While excitonic insulators (EIs) have been intensively studied, proper platforms of them with stable lattice and non-cryogenic T _C are rare. By analysing their Bardeen–Cooper–Schieffer-like gap equation, we propose that high T _C EIs can exist in small indirect band gap 2D materials. After screening 2D transition-metal dichalcogenides from existing computational works, we select 2H-TiTe₂ and 1T-PdTe₂, and show that their T _C can be as high as 150 to 200 K under strains. A transition of their condensate EI state from that composed by Wannier excitons to that composed by plasmonic ones exists, even if negligible changes are reflected by the EI band structures, demonstrating the rich quantum feature of these systems. The high T _C also implies that they are ideal platforms for the demonstration and applications of EIs and their related quantum states in non-cryogenic environments.

We study the exciton condensation in the heterostructures where the electron layer and the hole layer formed by gapped chiral fermion (GCF) systems are separately gated. High angular momentum such as $p$- and $d$-wave-like excitonic pairing may emerge when the gap of the GCF systems is small compared to the Fermi energy, and the chiral winding numbers of the electrons and holes are the same. This is a result of the nontrivial band geometry and can be linked to the Berry curvature when projected onto the Fermi surface. In realistic systems, we propose that staggered graphene and surface states of magnetically doped topological insulators or intrinsic axion insulators are promising candidates for realizing $p$-wave exciton superfluid, and anomalous Hall conductivity can be used as a signature in experiments.