Ab Initio Study On The Topological Electronic Properties Of Transition Metal Phosphides And Carbon Allotrope

Recent years have witnessed a booming research interest in the discovery of quantum materials.Topological semimetals are the novel states of quantum materials,which have extended the concept of non-trivial band topology from insulators to metals with exciting fundamental physics and promising device applications.Based on ab initio calculations,here we report a detailed study on the structural,electronic and topologi-cal properties of the transitions metals tetra-phosphide compounds,binary Skutterudite compounds and an all-sp²monoclinic carbon allotrope.Transition metal phosphides hold novel metallic,semimetallic,and semiconducting behaviors.Here we report by ab initio calculations a systematical study on the structural and electronic properties of MP₄（M=Cr,Mo,W）phosphides in monoclinic C2/c(C_2h⁶)symmetry with or without nodal line.Their dynamical stabilities have been confirmed by phonon modes calculations.Detailed analysis of the electronic band structures and density of states reveal that CrP₄is a semiconductor with an indirect band gap of 0.47eV in association with theorbital of P atoms,while MoP₄is a Dirac semimetal with an isolated nodal point at theΓpoint and WP₄is a topological nodal line semimetal with a closed nodal ring inside the first Brillouin zone relative to the d orbital of Moand W atoms,respectively.Here,we also make a comparison of the electronic properties of tetra-phosphides with group ⅤB,ⅦB and ⅧB transition metals,which shows a trend of change from metallic to semiconducting behavior from ⅤB-MP₄to ⅧB-MP₄compounds.These results provide a systematical understandings on the distinct electronic properties of these compounds.Searching for new topological phases of matter has long been a hot topic in con-densed matter physics and materials science based on its fundamental physics and promis-ing device applications.Here we report a systematical ab initio study on the topological electronic properties of CoAs₃,RhAs₃,and RhSb₃binary compounds.Without spin-orbit coupling,there is a six-fold band crossing node at the high-symmetricΓpoint with topological chargeC=0,which is denoted as‘‘six-fold excitation’’.This nodal point is formed by the highest occupied band and two of the lowest unoccupied bands,and protected by time-reversal symmetry,spatial-inversion symmetry and stabilized by the two-fold rotational symmetry.Detailed band structure and elementary band represen-tations analysis shows that the six-fold band degeneracy at theΓpoint near the Fermi level is formed by the bands of Ag@8c originating from thed-orbital of metal atoms.Meanwhile,with spin-orbit coupling,the six-fold nodal point becomes to a four-fold degenerate quadratic Dirac point with topological charge conserved asC=0.These results provide a systematical understanding for the electronic properties of the Skut-terudite compounds and enrich the families of topological fermions in condensed matter systems.Topological nodal line semimetal is an exotic class of quantum materials featuring the continuous line of nodes inside the first Brillouin zone.Here we identify by system-atical ab initio calculations a new all-²hybridized carbon allotrope with monoclinicC2/c(C_2h⁶)symmetry which is termed as bcm-C₁₆.Total energy calculations show that our proposed bcm-C₁₆carbon is energetically comparable to or stable than the previ-ously proposed bco-C₁₆,bct-C₁₆,and oP16 carbon.Its dynamical stability has been confirmed by phonon mode calculations.Detailed analysis of the electronic properties show that bcm-C₁₆carbon is a topological nodal line semimetal with a single closed nodal ring around theΓhigh symmetric point,protected by spatial inversion（P）and time-reversal（T）symmetry.When the nodal ring is projected onto the（001）surface,a topologically protected drumhead-like surface state can be seen inside or outside the nodal ring depending on the different surface terminations.Moreover,we also exam-ined the tensile-strain robustness of the electronic properties of bcm-C₁₆carbon.The nodal ring is robust under a tensile-strain along the crystalline x-and z-directions up to 20%.In addition,the simulated x-ray diffraction pattern（XRD）of bcm-C₁₆carbon matches with the experimental pattern found in the detonation and chimney soot experi-ment.The present proposal has enriched the family of carbon allotropes with topological nodal lines,and pave the way for further theoretical and experimental studies.