Two-dimensional (2D) high-temperature ferromagnetic materials are important for spintronic application. Fortunately, a highly-air-stable PdSe2 monolayer semiconductor has been made through exfoliation from the layered bulk material. It is very highly desirable to realize robust ferromagnetism, even half-metallic ferromagnetism (100% spin polarization), in such excellent nonmagnetic monolayer semiconductors. Here, the first-principles investigation shows that the PdSe2 monolayer can be made to attain Stoner ferromagnetism with the maximal Curie temperature reaching to 800K, and the hole concentration threshold for ferromagnetism decreases with applied uniaxial stress. Furthermore, half-metallicity can be achieved in some hole concentration regions. For the strain of 10% (uniaxial tensile stress of 4.4 N/m), the monolayer can attain half-metallic ferromagnetism up to 150 K. The magnetic anisotropic energy is suitable to not only stabilizing the 2D ferromagnetism but also realizing fast magnetization reversal. The magnetization can be also controlled by applying a transverse uniaxial stress. The highly-air-stable PdSe2 monolayer, with these advantages, should be promising for spintronic applications.

We propose through first-principles investigation that the GaTeCl monolayer is an excellent two-dimensional (2D) multiferroic with giant mechanical anisotropy. The calculated phonon spectrum, molecular dynamic simulations, and elastic moduli confirm its dynamic and mechanical stability, and our cleavage energy analysis shows that exfoliating one GaTeCl monolayer from the existing GaTeCl bulk is feasible. The calculated in-plane ferroelectric polarization reaches 578 pC m-1. The energy barriers per formula unit of the ferroelastic 90° rotational and ferroelectric reversal transitions are 476 meV and 754 meV, respectively, being the greatest in the 2D multiferroics family so far. Importantly, on the other hand, a tensile stress of 4.7 N m-1 perpendicular to the polarization can drive the polarization to rotate by 90°. These can make the GaTeCl monolayer have not only robust ferroelasticity and ferroelectricity but also easy mechanical controllability. Furthermore, the GaTeCl monolayer has giant piezoelectricity and optical second harmonic generation, especially in the range of visible light, and a tensile stress of 0.3 N m-1 along the polarization can make the indirect gap transit to the direct gap. These interesting mechanical, electronic, and optical properties of the GaTeCl monolayer show its great potential in high-performance multi-functional applications.

In this work, we study the synergistic correlated states in two distinct types of interacting electronic systems coupled by interlayer Coulomb interactions. We propose that this scenario can be realized in a new type of Coulomb-coupled graphene-insulator heterostructures with gate tunable band alignment. We find that, by virtue of the interlayer Coulomb coupling between the interacting electrons in the two layers, intriguing correlated physics that is not seen in either individual layer emerges in a cooperative and synergistic manner. Specifically, as a result of the band alignment, charge carriers can be transferred between graphene and the substrate under the control of gate voltages, which can yield a long-wavelength electronic crystal at the surface of the substrate. This electronic crystal exerts a superlattice Coulomb potential on the Dirac electrons in graphene, which generates subbands with reduced non-interacting Fermi velocity. As a result, $e$-$e$ Coulomb interactions within graphene would play a more important role, giving rise to a gapped Dirac state at the charge neutrality point, accompanied by interaction-enhanced Fermi velocity. Moreover, the superlattice potential can give rise to topologically nontrivial subband structures which are tunable by superlattice's constant and anisotropy. Reciprocally, the electronic crystal formed in the substrate can be substantially stabilized in such coupled bilayer heterostructure by virtue of the cooperative interlayer Coulomb coupling. We further perform high-throughput first principles calculations to identify a number of promising insulating materials as candidate substrates for graphene to demonstrate these effects. Our findings provide new insights into the physics of correlated and topological electronic states in graphene-based heterostructures.

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