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We design a multiferroic metal that combines seemingly incompatible ferromagnetism, ferroelectricity, and metallicity by hole doping a two-dimensional (2D) ferroelectric with high density of states near the Fermi level. The strong magnetoelectric effect is demonstrated in hole-doped and arsenic-doped monolayer {\alpha}-In2Se3 using first-principles calculations. Taking advantage of the oppositely charged surfaces created by an out-of-plane polarization, the 2D magnetization and metallicity can be electrically switched on and off in an asymmetrically doped monolayer. The substitutional arsenic defect pair exhibits an intriguing electric field-tunable charge disproportionation process accompanied with an on-off switch of local magnetic moments. The charge ordering process can be controlled by tuning the relative strength of on-site Coulomb repulsion and defect dipole-polarization coupling via strain engineering. Our design principle relying on no transition metal broadens the materials design space for 2D multiferroic metals., Comment: 23 pages,5 figures

The coexistence of ferroelectric and topological orders in two-dimensional (2D) atomic crystals allows non-volatile and switchable quantum spin Hall states. Here we offer a general design principle for 2D bilayer heterostructures that can host ferroelectricity and nontrivial band topology simultaneously using only topologically trivial building blocks. The built-in electric field arising from the out-of-plane polarization across the heterostrucuture enables a robust control of the band gap size and band inversion strength, which can be utilized to manipulate topological phase transitions. Using first-principles calculations, we demonstrate a series of bilayer heterostructures are 2D ferroelectric topological insulators (2DFETIs) characterized with a direct coupling between band topology and polarization state. We propose a few 2DFETI-based quantum electronics including domain-wall quantum circuits and topological memristor.

Xenes, graphene-like two-dimensional (2D) monoelemental crystals with a honeycomb symmetry, have been the focus of numerous experimental and theoretical studies. In comparison, single-element 2D materials with a triangular lattice symmetry have not received due attention. Here, taking Pb as an example, we investigate the triangular-lattice monolayer made of group-IV atoms employing first-principles density functional theory calculations. The flat Pb monolayer supports a mirror-symmetry-protected spinless nodal line in the absence spin-orbit coupling (SOC). The introduction of an out-of-plane buckling creates a glide mirror, protecting an anisotropic Dirac nodal loop. Both flat and buckled Pb monolayers become topologically trivial after including SOC. A large buckling will make the Pb sheet a 2D semiconductor with symmetry-protected Dirac points below the Fermi level. The electronic structures of other group-IV triangular lattices such as Ge and Sn demonstrate strong similarity to Pb. We further design a quasi-3D crystal PbHfO$_2$ by alternately stacking Pb and 1T-HfO$_2$ monolayers. The new compound PbHfO$_2$ is dynamically stable and retains the properties of Pb monolayer. By applying epitaxial strains to PbHfO$_2$, it is possible to drive an insulator-to-metal transition coupled with an anti-ferroelectric-to-paraelectric phase transition. Our results suggest the potential of the 2D triangular lattice as a complimentary platform to design new type of broadly-defined Xenes.

Superconductivity in crystals without inversion symmetry has received extensive attention due to its unconventional pairing and possible nontrivial topological properties. Using first-principles calculations, we systemically study the electronic structure of noncentrosymmetric superconductors $A_2$Cr$_3$As$_3$ ($A$=Na, K, Rb and Cs). Topologically protected triply degenerate points connected by one-dimensional arcs appear along the $C_{3}$ axis, coexisting with strong ferromagnetic (FM) fluctuations in the non-superconducting state. Within random phase approximation, our calculations show that strong enhancements of spin fluctuations are present in K$_2$Cr$_3$As$_3$ and Rb$_2$Cr$_3$As$_3$, and are substantially reduced in Na$_2$Cr$_3$As$_3$ and Cs$_2$Cr$_3$As$_3$. Symmetry analysis of spin-orbit coupling $g_{k}$ suggests that the arc surface states might remain stable in the superconducting state, giving rise to possible nontrivial topological properties., Comment: We have some typos corrected and add discussion about the effect of ferromagnetic fluctuations on the band topology. We also add discussion on the topological property in the superconducting state with the symmetry indicators method recently proposed

We have performed systematic first principles study of the electronic structure and band topology properties of $LnPn$ compounds ($Ln$=Ce, Pr, Gd, Sm, Yb; $Pn$=Sb, Bi). Assuming the $f$-electrons are well localized in these materials, both hybrid functional and modified Becke-Johnson calculations yield electronic structure in good agreement with experimental observations, while generalized gradient approximation calculations severely overestimate the band inversions. From Ce to Yb, a systematic reduction of band inversion with respect to the increasing $Ln$ atomic number is observed, and $\mathcal{Z}_2$ for Ce$Pn$ and Yb$Pn$ are [1;000] and [0;000], respectively. In both hybrid functional and modified Becke-Johns calculations, a topologically nontrivial to trivial transition is expected around SmSb for the antimonides and around DyBi for the bismuthides. Such variation is related with lanthanide contraction, but is different from simple pressure effect., Comment: Updated version