Novel electronic properties of monoclinic MP4 (M = Cr, Mo, W) compounds with or without topological nodal line

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {MP}_4$$\end{document}MP4 (M = Cr, Mo, W) phosphides in monoclinic C2/c (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{2h}^6$$\end{document}C2h6) symmetry. Their dynamical stabilities have been confirmed by phonon modes calculations. Detailed analysis of the electronic band structures and density of states reveal that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {CrP}_4$$\end{document}CrP4 is a semiconductor with an indirect band gap of 0.47 eV in association with the p orbital of P atoms, while \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {MoP}_4$$\end{document}MoP4 is a Dirac semimetal with an isolated nodal point at the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma$$\end{document}Γ point and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {WP}_4$$\end{document}WP4 is a topological nodal line semimetal with a closed nodal ring inside the first Brillouin zone relative to the d orbital of Mo and W atoms, respectively. Comparison of the phosphides with group VB, VIB and VIIB transition metals shows a trend of change from metallic to semiconducting behavior from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {VB-MP}_4$$\end{document}VB-MP4 to VIIB-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {MP}_4$$\end{document}MP4 compounds. These results provide a systematical understandings on the distinct electronic properties of these compounds.

Transition metal phosphides (TMPs) have been attracted considerable research interest due to their structural and compositional diversity that results in a broad range of novel electronic, magnetic and catalytic properties [1][2][3][4] . This family consists of large number of materials, having distinct crystallographic structures and morphologies because of choices of different TMs and phosphorus atoms 5 . These compounds have been studied extensively due to their outstanding physical and chemical properties such as high catalytic activity 6 , good electrical conductivity 7 , and magnetocaloric behaviors 8,9 . TMPs have been appeared as an efficient catalyst for hydrogen evolution reduction (HER) 4,10-13 . For example, nanowires of FeP and FeP 2 have been used widely for hydrogen evolution in both strong alkaline and acidic aqueous solutions 10 . CoP 11 , CoP 3 12 , and MoP 2 13 are also reported as an excellent materials for HER and oxygen evolution reduction (OER) due to their good stability. Moreover, phosphorus rich phases have been found more effective for HER and OER, and have better stability because of the presence of a large number of negatively charge P-atom centers 14,15 . In addition to electrocatalysis process, TMPs have various potential device applications, such as usage in electrotonic components, luminescent and semiconductor devices and as an anode material in lithium-ion batteries [16][17][18][19] . Moreover, some TMPs such as TaP 20 hold topological Weyl semimetal feature, and WP has been recently reported to have Dirac like points near the Fermi level 21 . Similarly, transition metal diphosphide compounds, like MoP 2 and WP 2 , were predicated as type-II Weyl topological semimetals 22 .
In this paper, based on ab initio calculations, we systematically investigate the transition metal phosphides MP 4 ( M = Cr , Mo, W) for the structural stability and electronic properties. These three compounds are all in monoclinic phase with C2/c ( C 6 2h ) symmetry, while CrP 4 and MoP 4 have been experimentally synthesized 55 and WP 4 is not yet reported. Their mechanical stabilities are confirmed with phonon mode analysis. Electronic band calculations show that CrP 4 is a semiconductor with an indirect band gap of 0.47 eV, MoP 4 is a topological Dirac semimetal with isolated band crossing at the Ŵ point, and WP 4 is a topological nodal line semimetal with a closed nodal ring inside the first BZ. We also make a comparison of the phosphides with group VB and VIIB transition metals and a trend of change from metallic to semiconducting is observed from VB-MP 4 to VIIB-MP 4 compounds.

Results and discussion
We first present the structural characterization. Figure 1a shows the structure of monoclinic compounds of MP 4 ( M = Cr , Mo, W) in C2/c ( C 6 2h , No. 15) symmetry. The M atoms are depicted in black occupying the 4e Wyckoff positions, while there are two kinds of P atoms ( P 1 and P 2 ) depicted in orange occupying two distinct 8f Wyckoff positions, respectively, as listed in Table 1. The metals environments in MP 4 compounds can be described as the octahedral coordination environment, in which metal atoms are always octahedrally surrounded by P atoms, while P atoms have tetrahedrally coordinated environment. Basically, the crystalline structure of monoclinic MP 4 compounds can be seen as a layered structure of black phosphorus in which metal atoms are inserted 56 between two buckled phosphorus layers (Fig. 1b). Metal atoms intercalate and reorder the atomic stacks similar to Na atom insertion in black phosphorus 57 . A sandwiched structure is formed where wave like metal atom layers are in between the two buckled phosphorus layers.
There are three unique types of bonds in monoclinic compounds MP 4 , namely M-P 1 , M-P 2 , and P 1 -P 2 chemical bonds. In CrP 4 , the bond lengths are 2.277-2.373 Å for Cr-P 1 , 2.316 Å for Cr-P 2 , and 2.215-2.240 Å for P 1 -P 2 ; in MoP 4 , the bond lengths are 2.396-2.456 Å for Mo-P 1 , 2.456 Å for Mo-P 2 , and 2.208-2.243 Å for P 1 -P 2 ; while in WP 4 , the bond lengths are 2.398-2.477 Å for W-P 1 , 2.453 Å for W-P 2 , and 2.215-2.245 Å for P 1 -P 2 . Meanwhile,  It can be seen that the bond lengths between P-P atoms are almost same in the three MP 4 compounds, while the bond lengths between Mo-P and W-P atoms are clearly larger than that between Cr-P atoms. Meanwhile, ∠P 1 -M-P 2 are found larger than the other angles in all MP 4 compounds. The calculated equilibrium lattice parameters, bond lengths, and bond angles for MP 4 compounds are listed in Table 2. It is seen that our calculated structural parameters matches well with the reported experimental and calculated data 55,58,59 .
To examine the dynamical stability of MP 4 compounds, we have calculated the phonon band structures and partial phonon density of states (PDOS) with equilibrium lattice parameters in a 2 × 2 × 2 supercell, as shown in Fig. 2. For CrP 4 , MoP 4 and WP 4 , no imaginary frequencies occur in the whole BZ and PDOS, thus confirming the structural stability of the three compounds. There are some similarities in the phonon band structures and PDOS for CrP 4 , MoP 4 and WP 4 due to the same space symmetry groups and elementary components for the three compounds. The highest vibrational frequencies all happen near the Ŵ point and the values are 519.8 cm −1 for CrP 4 , 521.8 cm −1 for MoP 4 and 526.8 cm −1 for WP 4 , respectively. It is seen from the PDOS that the lower frequency modes are mainly contributed by the metal atoms because of their heavier masses while the higher frequency modes are mainly contributed by the P atoms with lighter masses.
Next we discuss the electronic properties of MP 4 ( M = Cr , Mo, W) compounds. Figure 3 represents the calculated electronic band structures along the high symmetry directions of the BZ using HSE06 functional 60 and the fermi energy ( E F ) is set to zero. For CrP 4 as shown in Fig. 3a, the conduction band minimum (CBM) is located along H-Z direction and valence band maximum (VBM) is located along F-H direction, showing a semiconducting behavior with an indirect band gap of 0.47 eV, which is smaller than the reported direct band gap of 0.63 eV 58 . For MoP 4 as shown in Fig. 3b, the lowest conduction band and highest valence band are degenerate at Ŵ point near the E F , indicating that MoP 4 is a Dirac semimetal with a four-fold degenerate Dirac point at the Ŵ point 61 . Moreover, our calculations show that the valence and conduction bands of WP 4 exhibit linear dispersion near the E F and cross along the Ŵ -X high symmetry direction (Fig. 3c) due to the band inversion mechanism 39,40 . To further explore the topological electronic properties, we establish a tight binding (TB) model using the maximally localized Wannier functions (MLWFs) 62,63 to search the nodal points in the 3D BZ. We find that the nodal points (or band crossing points) of valence and conduction bands in WP 4 form a continuous nodal ring in the full BZ (see Fig. 3d), thus, WP 4 can be termed as a topological nodal line semimetal with a closed nodal ring protected by PT symmetry 34,35,41 .
It is interesting to notice that although Cr, Mo and W are all in the VIB group of the Periodic Table of Elements, CrP 4 is an indirect band gap semiconductor, MoP 4 is a Dirac semimetal with a single nodal point, and WP 4 is a nodal line semimetal with a closed nodal ring. The metallicity of CrP 4 , MoP 4 , and WP 4 grows with the increase of the elementary ordinal from 3d to 5d transition metals. To further understand the electronic properties, we have plotted the total and partial density of states (DOS) of MP 4 compounds as shown in Fig. 4. For CrP 4 (Fig. 4a), there is a band gap of 0.47 eV as depicted in Fig. 3a. The states around the Fermi level are mainly contributed by the p states of P atoms (Fig. 4b), relative to the covalent bonds between P-P atoms. For MoP 4 (Fig. 4c), there is a little peak on the Fermi level, the states at the Fermi level are mainly composed of d orbital of Mo atoms (see Fig. 4d). Moreover, for WP 4 (Fig. 4e), there is a little peak on the Fermi level, but larger than that in MoP 4 , the states at the Fermi level are predominantly composed of P-p orbital and W-d orbital (Fig. 4f). It can be inferred that the electronic behaviors in CrP 4 are mainly dominated by the P-P covalent bonds in CrP 4 , so that CrP 4 tend to be a semiconductor due to covalent bonding properties between P-P atoms. While in MoP 4 and WP 4 , the electronic properties are largely determined by the metal atoms which have metallic bonds with P atoms, so that they show semimetallic properties. The small peaks on the Fermi level in MoP 4 and WP 4 semimetals are related to the band touching point between the top of valance and the bottom of conduction bands. Similar DOSs around the Fermi level are also found in CaP 3 family of nodal line semimetals 41 .
We have further examined the band structures of MoP 4 and WP 4 with spin-orbital coupling (SOC) as shown in Fig. S1 in Supplementary Information. For MoP 4 , the SOC induced band gap is about 0.1 meV at the Ŵ point, while for WP 4 , the SOC induced band gap is about 29 meV along the high-symmetric X-Ŵ direction. We can  parameters (a, b, c and β ), bond lengths ( d M−P1 , d M−P2 , and d P−P ), and electronic band gap E g for MP 4 ( M = Cr , Mo, W) compounds, comparing with experimental and previously calculated data 55,58,59 . www.nature.com/scientificreports/ see that when SOC is included, MoP 4 and WP 4 become strong topological insulators with the symmetry-based indicators 64-66 ( z 2 , z 2 , z 2 , z 4 ) as (0,0,0,1), like as the finding in CaP 3 family of materials 41 . In order to better understand the electronic properties of VIB-MP 4 ( M = Cr , Mo, W) compounds, we have also examined the electronic properties of the VP 4 , NbP 4 , TaP 4 , MnP 4 , TcP 4 and ReP 4 , while V, Nb and Ta are in the VB group, and Mn, Tc and Re are in the VIIB group, which are all next to Cr, Mo and W in the Periodic Table  of Elements. The TcP 4 and ReP 4 are experimentally synthesized by the reaction of their constituent elements [67][68][69] . The calculated equilibrium lattice parameters and electronic band structures are given in Table S1 and Fig. S2 in Supplementary Information, respectively. The structural parameters and electronic behavior that is, VP 4 is metallic and MnP 4 is a semiconductor reported by Gong et al. 58 . We find that VB-MP 4 ( M = V , Nb, Ta) have metallic behavior, while VIIB-MP 4 ( M = Mn , Tc, Re) are semiconductors. It is clearly seen that from VB-MP 4 to VIIB-MP 4 , the metallicity of these phosphides grow weaker with a change from metallic to semiconducting, while from top (3d) to bottom (5d) in each group, the metallicity of these phosphides grow stronger. So it is reasonable that CrP 4 should be a semiconductor, MoP 4 is a semimetal with isolated nodal points and WP 4 is a topological nodal line semimetal with a line of nodes.

Methods
Our calculations were carried out using the density functional theory as implemented in the Vienna ab initio simulation package (VASP) 70 . The projector augmented wave (PAW) 71 method was adopted with valence electrons of 3s 2 3p 3 for P, 3p 6 3d 5 4s 1 for Cr, 4p 6 4d 5 5s 1 for Mo, and 5p 6 5d 4 6s 1 for W. Generalized gradient approximation (GGA) developed by Perdew, Burke and Ernzerhof (PBE) 72 is used as the exchange-correlation potential. A 5 × 8 × 6 Monkhorst-Pack grid of BZ sampling is used and an energy cutoff of 500 eV is set for the plane-wave basis. The structures are fully optimized until the total energy difference is less then 10 −6 eV and convergence criteria for atomic forces is set to be 10 −3 eV/Å. The electronic properties are calculated with the Heyd-Scuseria-Ernzerhof hybrid functional (HSE06) 60 and the phonon properties are calculated with phononpy package 73 .
To further explore the topological electronic properties, we establish a tight binding (TB) model using the maximally localized Wannier functions (MLWFs) 62,63 implemented in Wannier90 package 74 and searched the band crossing points in the entire BZ with WannierTools pacakge 75 .