Topological properties after light ion irradiation on Weyl semimetal niobium phosphide from first principles

Materials Today Communications 24 (2020) 100939

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Topological properties after light ion irradiation on Weyl semimetal niobium phosphide from first principles

T

Yan-Long Fua, Hai-Bo Sanga, Wei Chenga,d,*, Feng-Shou Zhanga,b,c,* a Key Laboratory of Beam Technology and Materials Modification of the Ministry of Education, College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, People's Republic of China b Beijing Radiation Center, Beijing 100875, People's Republic of China c Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator of Lanzhou, Lanzhou 730000, People's Republic of China d Ningbo Institute of Industrial Technology, Chinese Academy of Sciences, Ningbo 315201, People's Republic of China

A R T I C LE I N FO

A B S T R A C T

Keywords: Weyl semimetal Point defects Band structures First-principles calculations

A member of the nonmagnetic Weyl semimetal family, niobium phosphide (NbP), is a new low-energy dissipative material due to the properties of its nontrivial energy band structure and topologically protected nodes. This paper mainly focus on the changes of the topological properties of the crystal NbP after H and He ions irradiation, a novel research view. In order to demonstrate the formation process of doping defects, we use TDDFT to simulate the whole path of H ion passing the bulk NbP, while both the total energy change for system and the radial drag force as a function of the projectile position are investigated. The energy band structures and density of states for the equilibrium point defect have been analyzed by means of the DFT method based on the CASTEP package. A strikingly phenomenon discovered is that diverse kinds of defects are able to modify the symmetrically protected Weyl points to some extent. Specifically, when H or He as an interstitial particle in the crystal NbP, the degenerate bands are uncoupled; meanwhile, the Fermi levels are shifted upward 0.12 eV and 0.18 eV, respectively. In contrast to the defect structures formed by P, the defects caused by Nb present the greater destructive power to the Weyl points. By contrast, the calculations of formation energy have demonstrated that H substitute for Nb is the most easily formed defect structure, and the defect with interstitial H atom is most stable structure within the scope of this research.

1. Introduction The Weyl semimetal as a material possessing unique electronic band structure [1–5] has become the focus of attention in condensed matter physics [6–8]. At the Fermi level, it is worth noting that the Weyl nodes as the massless chiral fermions [9,8,10–12] exhibit the bulk electronic band degeneracy. One can say, the conductance and valence bands cross into the isolated point at EF = 0. In momentum space, the chiraldependent Weyl nodes called topological charges, bringing about monopoles and anti-monopoles of Berry flux being determined by whether the chirality of crossing node is 1 or −1 [13,14,16], which (the splitting) acts as the topological invariant. The Weyl nodes in Weyl semimetals compare with the Dirac nodes in topological insulators, the former presents most robust electrons and only strongly dependent on the crystal symmetry. Since it is not affected by other symmetries, the Weyl points in the bulk have more freedom of movement, and the surface states possessing

the Fermi arc [17,18,5] show the nontrivial topological property. Therefore, a hallmark of the Weyl semimetal can only emerge in the case of an absence of the time-reversal symmetry or the inversion symmetry. In 2011, Wan et al. predicted for the first time that the solid material Y 2 Ir 2 O 7 with Weyl fermions has magnetic properties [19]. Soon afterwards, Xu et al. reported that HgCr 2 Se 4 with the pair of the Weyl nodes might be another ferromagnetic semimetal [20], namely, so-called the double Weyl semimetal. However, in the bulk Weyl semimetals, it is not easy to detect the existence of Weyl fermions by the angle resolved photoemission spectroscopy (ARPES) because of the influence of magnetic properties on the observation of Weyl points in experiments. As far as the symmetry of this kind of magnetic Weyl semimetal is concerned, the inversion symmetry is maintained, while the time-reversal symmetry is destroyed. On the contrary, for the nonmagnetic Weyl semimetals, they are protected by the time-reversal symmetry, but the inversion symmetry is absent. Recently, a novel family of the Weyl semimetals consisting of TX

⁎ Corresponding author at: Key Laboratory of Beam Technology and Materials Modification of the Ministry of Education, College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, People's Republic of China. E-mail addresses: [email protected] (W. Cheng), [email protected] (F.-S. Zhang).

https://doi.org/10.1016/j.mtcomm.2020.100939 Received 5 November 2019; Received in revised form 16 January 2020; Accepted 17 January 2020 Available online 28 January 2020 2352-4928/ © 2020 Elsevier Ltd. All rights reserved.

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Fig. 1. Based on perfect super-lattice Nb 32 P 32 , crystal structures of different defects are established. Inserting the H (He) atom to the super-cell center to produce I H (I He ). Removing the Nb (P) atom marked by the element symbol to form V Nb (V P ). Replacing the Nb (P) atom with H and He to build H Nb (H P ) and He Nb (He P ), respectively. The green box is first Brillouin zone of Nb 32 P 32 . Γ (G) is the BZ center, dispersion curves are along G-Z-T-Y-S-X-U-R.

(T = Ta, Nb; X = As, P) [21–23,2,24,3,6,25–27] is predicated in the calculation of electronic properties. These four isostructural family materials are nonmagnetic and noncentral symmetric Weyl semimetal materials, which provide an observable platform for the experimental research of Weyl semimetal. NbP as an ideal Weyl semimetal candidate material among them can be obtained by crystal growth method [28,29], in the experiment, the Fermi arcs on the surface and the Weyl nodes in the bulk are directly observed by using ARPES [30,9,26]. More significant feature is that, even if there is no Weyl fermion quasiparticles in the bulk NbP, the topological Fermi arc state can be maintained on the surface [14]. Thus, the NbP material is more suitable for the potential applications and experimental researches in the future. In this work, we employ the density functional theory to perform geometry optimization calculations, and the role of point defects in the topological material is investigated by analyzing electronic properties. Due to the gradual improvement of the requirements for the performance of electronic technology products, the overheat behavior of existing electronic components has become the main bottleneck of the progress of scientific and technological products. The Weyl semimetal is considered to be the optimal low-energy dissipative material to replace the semiconductor in the future [15]. To study the changes of the topological properties caused by the defects formed by particles deposition [31,23,32] in Weyl semimetal is crucial. Firstly, in this work, the total energy of system and the radial drag force acted on H and He ion during the forming process of defects are calculated based on real time-dependent density functional theory. In addition, to compare the difficult degree and stability of defect formation, the formation energy of defects has been analyzed. More importantly, the variations of band structures [33] and the density of states (DOS) of several defects (i.e., electronic properties) are evaluated and discussed by applying the first principles. Through analysing the band crossing nodes (i.e., the Weyl points), we reveal the influence of the point defects on the topological properties of crystal NbP. The extra content of this paper is constructed by following several sections. In Section 2, we mainly introduce simulation methods used in the calculation and clearly present crystal structures built. The results of electron dispersion curves and DOS are analyzed and discussed detailed in Section 3. Finally, in Section 4, we briefly summarize the main results and conclusions.

GGA EXC [n↑, n↓] =

∫ d3r n εXunif (n) FXC (rs, ζ , t ).

(1)

εXunif

(n) is the exchange energy of each particle in the uniform Here electron gas case. The independent variable rs and ζ as well as t represent the local Seitz radius, the relative spin polarization and a dimensionless density gradient, respectively. The FXC is an enhancement factor related to exchange correlation. To achieve accurate calculation results, we have chosen the normconserving pseudopotential. Pseudo atomic calculations performed for Nb 4d45s1 and P 3s 23p3 (the valence electron configures) are adopted, respectively. Monkhorst–Pack k -point grid chosen is 15 × 15 × 4 for the sampling of Brillouin zone (BZ). With regard to the self-consistent field (SCF), the cut-off energy for the plane wave basis is set to be 600 eV, and the convergence SCF tolerance energy is chosen as 5.0 × 10−6 eV per atom, which are helpful to ensure high convergence and get the minimum energy structures. The Gaussian smearing width of 0.1 eV is applied for the electron orbital occupancy. The maximum force exerted on each atom is 0.01 eV/Å (i.e. geometry optimization can achieve the convergence only if the force acting on all atoms is reduced to less than this value.); furthermore, the maximum stress acted on the crystal lattice is 0.02 GPa, which is considered for the fully relaxation of the crystal material. NbP belongs to the stable body-centered-tetragonal crystal structure with the I41md (No. 109) symmetric space group, the symmetry of the atoms in unit cell is the C4v point group. We built the primitive lattice with the experimental values of parameters a = b = 3.334 Å, and c = 11.376 Å [22]. The corresponding Wyckoff positions for Nb and P atoms are (0, 0, 0) and (0, 0, 0.417), respectively. Optimizing the unit cell and the atoms positions obtains the lattice parameters of a = b = 3.373284 Å and c = 11.475470 Å, as well as the corresponding Wyckoff positions of relaxed Nb (0, 0, −0.000441) and P (0, 0, 0.417441). These results are remarkably in conformity with the experimental values. The various 2 × 2 × 2 defect structures based on the perfect super-cell (including 32 Nb and 32 P atoms) and the corresponding first BZ are presented in Fig. 1. In order to simulate the forming process of defects, we take H ion passing through crystalline material NbP as a case for the irradiation evolving with the real time. The time-dependent density functional theory (TD-DFT) contained in the OCTOPUS code [39–41] is carried out for the moving particles. The framework of the time-evolving Molecular Dynamics employed is presented as follows:

2. Simulation methods and crystal structures

iφ˙ (x , t ) = Hˆ e (R (t )) φ (x , t ),

In this work, the density functional theory (DFT) based on the CASTEP code [34,35] is employed to obtain the formation energy of defects, the energy band structures and DOS in the equilibrium configuration. Since NbP is the inhomogeneous crystal, we use the generalized gradient approximation of the PBE type (GGA-PBE) [36–38] as the exchange correlation potential for the geometry optimization of crystal structures, and the corresponding expression is given as follows:

(2)

··

→ MI RI (t )= −

∫ drφ* (x, t ) ∇I Hˆ e (R (t )) φ (x, t )

− ∇I

∑ J ≠I

ZI ZJ ⇀

⇀

|RI − RJ |

. (3)

Here Hˆ e and φ are the Hamiltonian and the wave functions of many2

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electron system, respectively; MI and ZI represent the mass and charge of atom I , respectively. R is the time-dependent position of nucleus. It is obvious that the Eq. (3) is the force acting on the projectile, so we need to obtain the electronic wave function φ . Since it is time-consuming and complex to solve the electronic wave function from the Eq. (2), the time-dependent Kohn–Sham (TD-KS) is employed to solving φ , in which the equation is written as follows: ⇀ ⎛ 1 iφ˙ i (x , t )= ⎜− ∇2 + Vne (R (t ), r ) + 2 ⎝

⇀,

∫ d3r′ n⇀(r ′

t)

⇀

|r − r ′|

⇀

+ VXC [n](r , t )) φi (x , t ) (i = 1, …, N),

(4)

where the four items in parentheses are the electronic kinetic energy, the electron-nucleus potentials and the Hatree potential as well as the exchange-correction (XC) potentials, respectively. For the model based on the TD-DFT calculation, in many systems, this method was demonstrated to be able to reasonably describe the penetration process of the projectile. For example, in the cases of the insulator LiF and SiO 2 [42,43], the metal Cu and Al [44,45], the semiconductor Si [46] and the semimetal HgTe [47], the results from the TD-DFT calculation are in good agreement with the experimental data and the semi-empirical values from SRIM. Therefore, this calculated method was demonstrated to be a reasonable way to reproduce the dynamic process. As an example, Fig. 2 depicts that H ion with the 0.5 atomic units (a.u.) velocity travels through NbP along − y direction, three typical snapshots of the electron density distribution at different times are presented. The H in Fig. 2(b) acts as an interstitial particle lie in the center of super-lattice, forming the transient crystal defect, which becomes the basic platform for us to study the interstitial defect. The same is true for the He passing NbP case, and here we no longer repeat it. Fig. 3. Total energy of the systems H + NbP (upper) and He + NbP (lower) as a function of projectile position y. The red lines are the fitting lines of the corresponding energy curves. The insets show the positions of H and He ions in the crystal NbP at y = 0 from the − x axis view.

3. Results and discussions Fig. 3 presents the total energy of the system when H and He ions with a velocity of 0.5 a.u. passes through the crystal NbP. Because the projectiles pass through the crystal along the center-channel at low speed, the deceleration of projectiles is not obvious. For this reason, the projectiles are limited to moving at a constant velocity, so the total energy of the system is non-conservative. It is obvious the fact that the total energy fluctuates with the increase of incident depth, which indicates the periodicity of lattice. In the meantime, the valley-like total

energy caused by the periodicity of lattice at y = 0 is found. This phenomenon suggests that the projectile is in a relatively stable state at the y = 0 position; the insets (snapshots) of Fig. 3 show, at the moment, the positions of H (upper panel) and He (lower panel) ions in the crystal NbP from the − x axis view.

Fig. 2. Snapshots of the 0.5 a.u. H ion (Being unlabelled with element symbol) moving through the crystalline NbP along − y center channel direction. (a) t = 0.01 fs, H ion captures a small amount of electron when it begins to enter the crystal. (b) t = 0.64 fs, H ion locates in the middle of the crystal along y direction, and it acquires a large number of electrons from Nb and P atoms. (c) t = 1.18 fs, H ion is separated from the dielectric crystal and packages a portion of the electrons. 3

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equation of formation energy [48–50] used is as follows:

ΔE = Edef − Ebulk ±

∑ Δni ui, i

(5)

where Edef and Ebulk denote the energies of super-lattices with and without defect, respectively. ui is the chemical potential of the i th doped or removed atom. Δni is the number of the changed atom. The positive sign represents the removing atom while the negative sign represents the doping atom. In Table 1, by comparing the calculated results, we find that the substitute site defects involving the H atom are much easier to be formed; however, the substitute site defects involving the He atom are more difficult to form because the formation energies of He Nb and He P are more larger than the other defects. In addition, it is worth noting that the formation energy of the defect I H is −2.340860 eV as the negative value, where the negative sign denotes that H atom stay in the cell, hence this structure is a most stable species in these defects. Fig. 4. Radial drag force acted on the 0.5 a.u. velocity H and He ion vs. corresponding position y when they go through NbP along − y center channel direction under the different exchange-correction potentials.

3.2. Electronic band structures and density of states For the electronic dispersion curves of various crystals reported below, the perfect super-lattice structure is the symmetric space group with I41md (No. 109), while the remaining defect super-lattice structures are the symmetric space group with Pmm2 (No. 25). It is well known that the spin degeneracy of the Weyl points is generally protected by either the inversion symmetry or the time-reversal symmetry. The nodal points (also called as crossing points or nodes) of electronic band structure close to the Fermi energy level is a typical band feature of semimetal. For the NbP as a nonmagnetic Weyl semimetal, because of the lack of the inversion symmetry [51,9], its crossing points are maintained in four-fold degenerate near the Fermi level. The effects of the single H and He atoms related interstitial defects, vacancy site defects and substitute site defects on the electronic band structure of NbP are investigated and evaluated.

Moreover, when the projectile passes through the crystal along the channel, the projectile is subjected to radial drag force from the Coulomb interaction with the surrounding atoms. For the case of H and He ions, the results are shown in Fig. 4, the variation of the forces presents the periodic fluctuation; thus, as with the fluctuation of the total energy, this also implies the periodicity of the crystal. It is worth noting that, near y = 0 , the local (relative) minimum of the force acting on the doped ion is observed; this value reflects that the projectile is relatively stable here. We have simulated the dynamic process of the projectile in crystal NbP by employing the different XC potentials (including PBE generalized gradient approximation (GGA-PBE) and Perdew–Wang local density approximation (LDA-PW)). As shown in Fig. 4, the different XC potentials present minor differences; however, for the interstitial He particle, by comparing GGA-PBE with LDA-PW, we find that the valley-like of GGA-PBE at y = 0 is deeper than that of LDA-PW, hence the structure obtained from the GGA-PBE method is more stable. Therefore, we have selected the GGA-PBE as the XC potential to perform the calculations in this work. Furthermore, based on the above estimation, the stable defect structures formed by the interstitial H and He particles at the y = 0 site are selected, which are served as the platform for the following electronic properties on the interstitial defects.

3.2.1. Super-lattice NbP In the absence of spin-orbit coupling (SOC), we calculate the electronic band structure of perfect structure Nb 32 P 32 based on GGA-PBE and plot it in Fig. 5(a). We clearly find the band crossing nodes (red dashed circles) along ZT, TY and XU lines near the Fermi level, i.e., socalled Weyl points. Around the EF = 0 (the Fermi level), the bottom of conduction band is mostly from P-3p states and the top of valence band is mostly determined by the Nb-4d states. The energy bands in the vicinity of the Fermi level are primarily composed of Nb-4d and P-3p electron orbits with the extremely strong SOC, so the SOC can lead to significant changes in the band structure features around the Fermi energy. Including SOC, the corresponding band structure is shown in Fig. 5(b), and the four-fold band texture features are split into the twofold bands. Meanwhile, we observe the fact that the band crossing nodes with line dispersion are apparently opened a small band gap ∼0.03 eV by SOC.

3.1. Defect formation energy To calculate the formation energies of various defects, the optimized lattice parameters are obtained by the optimizing super-lattice structures from first principles calculations; the corresponding lattice parameters and the formation energies are summarized in Table 1. The Table 1 The optimized lattice parameters and the defect formation energies for various structures. Super-lattice structures

a (Å)

b (Å)

c (Å)

Formation energy ΔE (eV)

Nb 32 P 32 I H (HNb 32 P 32 ) I He (HeNb 32 P 32 ) V Nb (Nb 31P 32 ) V P (Nb 32 P 31) H Nb (HNb 31P 32 ) H P (HNb 32 P 31) He Nb (HeNb 31P 32 ) He P (HeNb 32 P 31)

6.747633 6.754796 6.767322 6.738940 6.738809 6.730927 6.737874 6.746949 6.746962

6.747503 6.745169 6.734242 6.733797 6.732257 6.739784 6.728650 6.738127 6.754023

22.943014 22.975287 23.060037 23.018432 22.928328 23.052438 22.942997 23.061466 22.904538

– −2.340860

3.2.2. Interstitial doping defects I H and I He are the defect structures that a H or He atom is implanted into the NbP, where H and He serve as the interstitial particle; the structure consists of 32 Nb, 32 P and one H or He atom. Since an atom is inserted into the crystal, the spatial symmetry of the structure is changed from I41md to Pmm 2; the doping defect concentration is 1/65. Through optimizing atom positions of the crystal I H , in the absence of SOC, the electronic band structure are obtained and shown in Fig. 6(a). There is clear the separated dispersion curve and the band crossing points along ZT, TY and XU paths near the Fermi level. Compared with Fig. 5(a), the opened two-fold degenerate band is the result of the destruction of the spatial symmetry by the interstitial H; meanwhile, we find that the electronic band crossing node along ZT path

3.607364 3.980212 5.195910 1.290524 2.480458 5.119667 7.154187

4

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Fig. 5. (a) The electronic band structure (left panel) and partial DOS (right panel) of perfect structure Nb 32 P 32 without SOC. (b) The electronic band structure of this one with SOC considered.

particle. Similar to H atom as an interstitial particle in the above discussion, the four-fold degenerate bands are also separated into the twofold bands. However, the Fermi level is lifted up about 0.18 eV, and then the nodal points deviate from the Fermi level; the Fermi level of I He is raised higher than that of I H . This is because the 1s orbital of He atom contributes one more electron than that of H atom to the valence bands of I He . In the vicinity of the Fermi level, the range of energy bands at G point are expanded from 0.38 eV of the perfect NbP (Fig. 5(a)) to 0.56 eV. The degenerate bands are separated up and down under He perturbation, which implies that the destroyed symmetry strength of He is 0.09 eV. This value is lager than the corresponding value of interstitial H, indirectly indicating that the interstitial He has a stronger ability to dissociate the bands than the interstitial H. Considering SOC,

near the Fermi level is sensitive to the perturbation of H atom. Extraordinarily, the Fermi level is lifted up about 0.12 eV, which is attributed to the fact that 1s orbital electron of H atom increases occupation of the valence bands of I H . In the vicinity of the Fermi level, the range of energy bands at G point are expanded from 0.38 eV of the perfect NbP (Fig. 5(a)) to 0.48 eV. Since the degenerate bands are separated up and down under H perturbation, which implies that the destroyed symmetry strength of H is 0.05 eV. When SOC is included, as shown in Fig. 6(b), the two-fold band texture is split into the non-degenerate bands; moreover, the band crossing points along TY and XU paths near the Fermi level are opened with the tiny band gaps about 0.01 eV. Fig. 7(a) presents the electronic band structure and partial DOS of I He without including SOC for the case of He atom as an interstitial

Fig. 6. (a) The electronic band structure (left panel) and partial DOS (right panel) of HNb 32 P 32 without SOC. (b) The electronic band structure of this one with SOC included. 5

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Fig. 7. (a) The electronic band structure (left panel) and partial DOS (right panel) of HeNb 32 P 32 without SOC. (b) The electronic band structure of this one with SOC included.

as plotted in Fig. 7(b), it is obvious that the amplitude of variation from the two-fold degeneracy to non-degeneracy is greater than that in Fig. 6(b); however, compared with Fig. 6(b), the band crossing point along TY path near the Fermi level is not opened, which may be due to that the dramatic change in the non-degenerate band texture annihilates the band gap. 3.2.3. Vacancy site defects Removing a Nb or P atom (the labeled atoms in Fig. 1) from the super-cell NbP, the vacancy defect V Nb and V P with the space group Pmm 2 are obtained. The vacancy defect concentration is 1/64. Using the first principles to optimize the lattice, the electronic band structure together with its DOS for V Nb and V P are plotted in Fig. 8(a) and (b), respectively. If SOC is included in the optimization, it is difficult to find the Weyl nodes because some extraneous non-degenerate bands can contaminate and disrupt the crossing points. Therefore, SOC is neglected in the optimizing calculations of the vacancy defects; the results of two defects are shown in Fig. 8, including the electronic band structures and partial DOSs of V Nb and V P . For the lattice V Nb including 31 Nb and 32 P atoms, compared with the perfect NbP in Fig. 5(a), we find that the crossing points along ZT and TY paths near the Fermi level is lifted and widely opened, which is caused by removing vacancy Nb with the partial valence electrons and reducing occupancy in the electronic bands of the bulk V Nb . However, for the lattice V P including 32 Nb and 31 P atoms, as shown in Fig. 8(b), the crossing points (red dashed circles) along ZT, TY and XU paths keep intersecting without being opened. The result implies that the Weyl nodes are insensitive to the lost P atom and V P still maintains excellent semimetallic properties. Therefore, through the above discussion, we can know that the vacancy Nb is more destructive to the topological property of the crystal NbP surface than the vacancy P. For the cases of vacancy defects V Nb and V P , around the Fermi level, the range of energy bands at G point are expanded from 0.38 eV of the perfect NbP (Fig. 5(a)) to 0.44 eV. Since the degenerate bands are separated up and down under vacancy perturbations, this implies that the destroyed symmetry strength of vacancy Nb and P is 0.03 eV.

Fig. 8. The electronic band structures (left panel) and partial DOS (right panel) of vacancy defects (a) Nb 31P 32 and (b) Nb 32 P 31 without including SOC.

by H and He atoms in perfect NbP, respectively. The symmetry group of substitute site defects transforms from the space group of perfect lattice I41md to Pmm 2. The defect concentration of substitute Nb is 1/64. Fig. 9 (a) shows the electronic band structure and partial DOS of H Nb . It is worth noting that H Nb is similar to the electronic band texture of V Nb ; the same result is that the crossing points along ZT and TY lines near the Fermi level are opened, while the node along XU line keeps crossing. For the electronic band structure of He Nb in Fig. 9 (b), the situation at the crossing point is consistent with H Nb , only the crossing point along XU lines near the Fermi level remains closed. The results suggest that H and He atoms do not have the ability to repair the vacancy Nb in NbP;

3.2.4. Substitute site defects H Nb and He Nb denote the defects in which a Nb atom is substituted 6

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Fig. 9. The electronic band structures (left panel) and partial DOS (right panel) of substitute site defects (a) HNb 31P 32 and (b) HeNb 31P 32 without including SOC.

Fig. 10. The electronic band structures (left panel) and partial DOS (right panel) of substitute site defects (a) HNb 32 P 31 and (b) HeNb 32 P 31 without including SOC.

this is markedly different from the role of H in TaAs, which we studied earlier [52]. In addition, for the cases of substitute defects H Nb and He Nb , the range of energy bands around the Fermi level at G point are expanded from 0.38 eV of the perfect NbP (Fig. 5 (a)) to 0.44 eV. Since the degenerate bands are separated up and down under H and He perturbations, this implies that the destroyed symmetry strength of replaced H and He is 0.03 eV; this result is consistent with the vacancy cases discussed above. For the case of the replaced P atom, H P and He P represent the lattice in which a P atom in perfect NbP is substituted by H and He atoms, respectively. The symmetric space group of two defect structures is Pmm 2. The defect concentration of substitute P is 1/64. As shown in Fig. 10 (a), the electronic band structure of H P near the Fermi level is similar to the vacancy defect V P , i.e., there is clear band crossing points along ZT, TY and XU lines near the Fermi level. Therefore, the result suggests that the topological property of vacancy P is unaffected by the doping H atom. However, for the substitute defect He P , compared with the vacancy defect V P , we have only found that the band crossing points along ZT and TY lines near the Fermi level are completely closed, while the band crossing points along XU line near the Fermi level is lifted and a band gap ∼0.02 eV is opened. It nevertheless indicates that the replaced He atom breaks part of topological property of the vacancy defect V P and the He atom plays an important role in the substitute defect He P . Moreover, for the substitute defects H P and He P , we find that the range of energy bands around the Fermi level at G point are expanded from 0.38 eV of the perfect NbP (Fig. 5 (a)) to 0.60 eV. Since the degenerate bands are separated up and down under H and He perturbations, implying that the destroyed symmetry strength of replaced H and He is 0.11 eV. This value is lager than the corresponding value of replaced Nb, which indirectly indicates that the replaced P site has a stronger ability to dissociate the bands than the replaced Nb site.

4. Conclusions Based on the TD-DFT calculation, when H and He ions traveling through the crystal NbP, we have found the equilibrium position of the interstitial H and He ions in the super-lattice NbP by analyzing the total energy of the system and the radial drag force acting on the projectiles. Using DFT to optimize the positions of atom to reduce energy in the system, we have established that the defect formation energy of I H provides a more stable defect structure and the substitute site defects involving the H atom are much easier to be formed than those containing the He atom. The electronic band structure of the perfect NbP without considering SOC shows the crossing points along ZT, TY and XU lines around the Fermi level; in the presence of SOC, three nodes are opened to a band gap ∼0.03 eV and the four-fold degenerate band texture is split into the two-fold bands. For the interstitial doping defects I H and I He , the electronic band textures are broken by the interstitial atoms if SOC is neglected, and they are changed from four-fold bands to twofold bands; the Fermi level of I H and I He are lift up ∼0.12 and ∼0.18 eV, respectively. If SOC is included, the two-fold degenerate band textures are split into the non-degenerate bands; and partial crossing points are opened a tiny band gap. In addition, we find that the vacancy Nb can break partial crossing points (the Weyl nodes), which indicate that the partial topological property of the crystal NbP are missed. However, the vacancy P has no substantial effect on the Weyl nodes and V p still maintains excellent semimetallic properties. For a H or He atom filling the vacancy Nb (i.e., H Nb and He Nb ), H and He atom do not have the ability to repair the vacancy Nb in NbP. For a H or He atom filling the vacancy P (i.e., H P and He P ), the band structures between H P and V p are similar; however, the band structure of He P is markedly different from V p . As well, a crossing point is opened, which indicates that He atom breaks the partial topological property of V p and the He atom play an essential role in the defect He P . In conclusion, various point defects have different effects on the topological properties of the crystal NbP. The modification of electronic 7

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properties are responsible for the disintegration of the Weyl points caused by doping.

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