Theoretical study of HgCr2Se3.5Te0.5: a doping-site-dependent semimetal

Weyl semimetals have recently attracted enormous attention due to their unusual features. So far, this novel state has been predicted theoretically and confirmed experimentally in several materials, such as HgTe, LaPtBi, Y2Ir2O7, TaAs, TaP, NbAs, NbP and HgCr2Se4. Doping plays an important role in the research of condensed-matter materials. However, its influence on the Weyl semimetal has been little investigated. Here, we present detailed first-principles and theoretical studies on HgCr2Se4 with doping of Te atoms at the Se sites. A special case where only one pair of crossing points locates at the Fermi level is realized in HgCr2Se3.5Te0.5 where one of the Se atoms in the primitive unit cell is replaced by a Te atom. A further study of k·p theory shows that the two points constitute a pair of Weyl nodes with opposite chiralities in the momentum space, and only one edge state and one single Fermi arc are obtained at each boundary of a film. Moreover, through investigations and analyses of different doping cases of HgCr2Se3.5Te0.5, we find that when the type of doping induces inversion symmetry or positional disorder, the Weyl nodes transform into Dirac points resulting in a change from a Weyl semimetal to a Dirac semimetal.


1
In the absence of lattice parameters of HgCr 2 Se 3.5 Te 0.5 where one of the Se atoms is replaced by a Te atom in the primitive unit cell of HgCr 2 Se 4 , we relaxed the unit cell with consideration of spin polarization. After optimization of the atomic coordinates, two steps are performed for further structural optimization. First, maintaining the value of c : a which is the same to that of HgCr 2 Se 4 [1], we calculated the total energy of HgCr 2 Se 3.5 Te 0.5 by changing the volume until the minimum-energy volume is obtained (Fig. S 1). The optimized lattice parameters are given in the figure and the corresponding volume of primitive cell is 332.59Å 3 (2244.43 bohr 3 ). Second, based on the minimum-energy volume, the value of c : a is optimized, as plotted in the inset of Fig. S1. We find that the difference between the initial value and the optimal value is less than 1%, which is small and can be ignored. Fig. S 2 shows the band structures of k · p and first-preinciples methods along Γ − M/3 and Γ − Z.
By comparing them near the Fermi level, we can see that they agree well with each other around the Γ point.
The doping configuration that Te atoms are doped into special Se sites has been studied detailedly in the main text. In order to clarify whether the configuration is the lowestenergy one and investigate the influence on Weyl semimetal state with different doping positions, we have considered 25 kinds of doping cases by using supercell with the fixed doping concentration (HgCr 2 Se 3.5 Te 0.5 ). All the considered structures are fully optimized by using the Vienna ab initio simulation package (VASP) [2]. The exchange-correlation functional within a generalized gradient approximation parametrized by Perdew, Burke, and Ernzerhof (PBE-GGA) has been used[3]. The energy cut-off is set to be 500 eV and the force on each ion is converged to an accuracy 0.02 eV/Å. The schematic configurations and their corresponding total energies are shown in Fig. S 3. Eight Se atoms in the primitive unit cell of HgCr 2 Se 4 are labeled with Z1(2), A1(2), B1(2) and C1(2). The configurations X-n(n = 1 ∼ 11), Y-1 and Z-1(2) belong to the uniform doping case that each primitive unit cell of HgCr 2 Se 4 is doped with only one Te atom. The others belong to the nonuniform doping case that some primitive unit cells are doped with more than one Te atom or undoped.
The Weyl-semimetal ground state of the configuration X-1 has been confirmed and studied in the main text. However, by comparing the total energies, we can see that the lowestenergy configuration is not X-1 but X-10 among the configurations under consideration. The latter lattice structure is shown in Fig. S 3 (d). Despite this, the configuration X-1 is still of basic importance. Basing on its results, we can further analyze the properties of other configurations, such as the number and topology of the crossing points near the Fermi level.
We further calculate the electronic structures of X-10 with space group P 2 1 /m. Although we have considered 25 kinds of configurations with different doping cases and compared their total energies after the full structural relaxation, it is not enough to determine the lowest-energy configuration. Moreover, the atomic properties of Te and Se are very similar and the energy difference between different configurations is small (Fig. S 3 (c)). Therefore, it is highly possible that the compound HgCr 2 Se 3.5 Te 0.5 is synthesized via uniformly random doping in reality. If this doping case is present, the Weyl nodes will also disappear. Instead, there will be eight Dirac points in Fig. 5 (b) of the main text.
In addition, the electronic structures of the doping configurations X-7 and X-9 ( can be determined that the two crossing points are Dirac points. For the configuration X-9, four Te atoms are respectively doped into Z1, A2, B2 and C2 sites and there are four pairs of crossing points in the Brillouin zone as illustrated in the band structure (Fig. S 6). Because of the lack of inversion symmetry (space group Cm), one can speculate that these crossing points are Weyl nodes. The number of crossing points above has been checked carefully in the entire Brillouin zone. Although these two configurations are not the lowest-energy ones, Total energies as a function of c : a with fixed minimum-energy volume marked by red arrow. 0% corresponds to c : a value of HgCr 2 Se 4 . The optimized value is less than 1%, which is so small that it can be ignored (For the deviation 1%, a decreases by 0.3% and c increases by 0.7%.). The red crosses correspond to our calculated data and the green and blue curves are the fitting results.
During the lattice relaxation process, for each lattice structure the energy convergence precision is 0.0001Ry (1.36 meV).
their results of calculations are in agreement with our previous discussion and support our conclusion.