Dirac states from p_(x,y) orbitals in the buckled honeycomb structures:A tight-binding model and first-principles combined study

Dirac states composed of p_(x,y) orbitals have been reported in many two-dimensional(2 D) systems with honeycomb lattices recently. Their potential importance has aroused strong interest in a comprehensive understanding of such states.Here, we construct a four-band tight-binding model for the p_(x,y)-orbital Dirac states considering both the nearest neighbor hopping interactions and the lattice-buckling effect. We find that p_(x,y)-orbital Dirac states are accompanied with two additional narrow bands that are flat in the limit of vanishing π bonding, which is in agreement with previous studies. Most importantly, we analytically obtain the linear dispersion relationship between energy and momentum vector near the Dirac cone. We find that the Fermi velocity is determined not only by the hopping through π bonding but also by the hopping through σ bonding of p_(x,y) orbitals, which is in contrast to the case of p_z-orbital Dirac states. Consequently, p_(x,y)-orbital Dirac states offer more flexible engineering, with the Fermi velocity being more sensitive to the changes of lattice constants and buckling angles, if strain is exerted. We further validate our tight-binding scheme by direct first-principles calculations of model-materials including hydrogenated monolayer Bi and Sb honeycomb lattices. Our work provides a more in-depth understanding of p_(x,y)-orbital Dirac states in honeycomb lattices, which is useful for the applications of this family of materials in nanoelectronics.     

Rational Design of Two-Dimensional Magnetic Chromium Borides Based on First-Principles Calculation

Two-dimensional(2D) magnetic materials have been experimentally recognized recently,however,the Curie temperatures(TC) of known 2D systems are quite low.Generally,magnetic systems can be seen as constituent magnetic elements providing spins and the non-magnetic elements providing frameworks to host the magnetic elements.Short bond lengths between the magnetic and non-magnetic elements would be beneficial for strong magnetic interactions and thus high TC.Based on this,we propose to combine the magnetic element Cr and the non-magnetic element boron to design novel 2D magnetic systems.Using our self-developed software package IM2 ODE,we design a series of chromium-boride based 2D magnetic materials.Nine stable magnetic systems are identified.Among them,we find that CrB4-Ⅰ,CrB4-Ⅱ and CrBs-Ⅰ with common structural units [CrB8] are ferromagnetic metals with estimated TC of 270 K,120 K and 110 K,respectively.On the other hand,five CrB3 phases with structural units [Cr2B12] are antiferromagnetic metals.Additionally,we also find one antiferromagnetic semiconductor CrB2-Ⅰ.Our work may open new directions for identifying 2D magnetic systems with high TC.