Next Article in Journal
Scalable Wettability Modification of Aluminum Surface through Single-Shot Nanosecond Laser Processing
Previous Article in Journal
A Comparison of Shell Theories for Vibration Analysis of Single-Walled Carbon Nanotubes Based on an Anisotropic Elastic Shell Model
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Nanomaterials
Volume 13
Issue 8
10.3390/nano13081389
nanomaterials-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles thumb_up
...
Endorse textsms
...
Comment
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Nontrivial Topological Properties and Synthesis of Sn2CoS with L21 Structure

by
Guifeng Chen
1,2,*,
Bolin Long
1,2,
Lei Jin
1,2,
Hui Zhang
1,2,
Zishuang Cheng
1,2,
Xiaoming Zhang
1,2,* and
Guodong Liu
1,2,*
1
Hebei Engineering Laboratory of Photoelectronic Functional Crystals, Hebei University of Technology, Tianjin 300130, China
2
School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300130, China
*
Authors to whom correspondence should be addressed.
Nanomaterials 2023, 13(8), 1389; https://0-doi-org.brum.beds.ac.uk/10.3390/nano13081389
Submission received: 22 February 2023 / Revised: 3 April 2023 / Accepted: 10 April 2023 / Published: 17 April 2023
Browse Figures
Review Reports Versions Notes

Abstract

:
We synthesize Sn2CoS in experiment and study its topological properties in theory. By first-principles calculations, we study the band structure and surface state of Sn2CoS with L21 structure. It is found that the material has type-II nodal line in the Brillouin zone and clear drumhead-like surface state when the spin–orbit coupling is not considered. In the case of spin–orbit coupling, the nodal line will open gap, leaving the Dirac points. To check the stability of the material in nature, we synthesize Sn2CoS nanowires with L21 structure in an anodic aluminum oxide (AAO) template directly by the electrochemical deposition (ECD) method with direct current (DC). Additionally, the diameter of the typical Sn2CoS nanowires is about 70 nm, with a length of about 70 μm. The Sn2CoS nanowires are single crystals with an axis direction of [100], and the lattice constant determined by XRD and TEM is 6.0 Å. Overall, our work provides realistic material to study the nodal line and Dirac fermions.

1. Introduction

In recent years, topological semimetals have received extensive research interest [1,2,3]. According to the dimension of the band crossing, topological semimetals can be divided into zero-dimensional nodal-point semimetal [4,5,6,7,8,9], one-dimensional nodal-line semimetal [10,11,12,13,14,15,16,17,18,19], and two-dimensional nodal-surface semimetal [20,21,22,23]. According to the energy band dispersion, the nodal point can actually be divided into type I and type II. The type-I nodal point has a positive cone dispersion, which completely separates electrons and holes. The type-II nodal point has a sloping cone dispersion, which can realize the coexistence of electrons and holes. Nodal lines are similar to the classification of nodal points and can also be further divided into type I, type II [24,25,26], and hybrid type [27,28]. If all band crossings on a nodal line belong to type I (type II), then the nodal line is type I (type II). If it contains both type-I and type-II band crossings, the nodal line belongs to the hybrid type. Type-II nodal lines are currently found in two-dimensional and three-dimensional materials, including K4P3 [24], Mg3Bi2 [24], pure Ti metal [26], and YCd [9]. The type-II nodal line is different from the traditional type-I nodal line. It has many interesting properties, including high anisotropic magnetoresistance, a direction-reliant chiral anomaly, and novel Klein tunneling in the momentum space [29,30,31,32,33]. In addition, nodal points can also be classified by degeneracy, including Dirac [34,35,36,37,38], Weyl [39], and triple degeneracy points [40,41]. The Dirac point is a fourfold degenerate point, which can be seen as a combination of a pair of Weyl points with opposite chirality. According to the energy band dispersion, Dirac points can also be divided into two types: type I and type II.
Condensed matter physics is different from high-energy physics and does not require Lorentz invariance, so type-II Dirac fermions are also Lorentz-violating fermions. Although the research on Dirac semimetals is very extensive, there are few studies on the type-II Dirac fermion. One major reason is that the excellent candidate materials for type-II Dirac semimetals are still limited. Another major challenge is that among the candidate materials, there are fewer materials that can be synthesized experimentally and stably exist in an ambient environment. Actually, type-II Dirac semimetals were found in XMg2Ag (X = Pr, Nd, Sm), XInPd2 (X = Ti, Zr, Hf), VAl3, PtSe2, PtTe2, NiTe2, YPd2Sn, and RbMgBi [42,43,44,45,46]. Among the reported materials, only the materials including VAl3, PtSe2, PtTe2, and NiTe2 have been confirmed in experiments. Even though the materials can be synthesized, not every material has a good measurable topological signal. The type-II Dirac points in PtSe2 and PtTe2 locate quite far away from the Fermi level (at −1 eV to −2.54 eV), which leads to the fact that the topological signal of a type-II Dirac point cannot be detected in practical application. NiTe2 is prepared by a two-step solvothermal technique [47], and the NiTe2 synthesized by this method is a polycrystalline powder with a small grain size. In this polycrystalline powder, the topological signal generated by the surface state cannot play a role in practical devices. As for VAl3, so far, only bulk single crystals are grown by the flux method above 1000 °C, and the synthesis time exceeds 24 h [43]. Nanowire and thin film form materials with type-II Dirac points suitable for practical applications still do not appear. Therefore, the search for new type-II Dirac metals, especially those that can be synthesized experimentally and exist in an ambient environment, is the primary task.
Motivated by the present situation on the type-II Dirac metals, in this work, we investigate the topological properties and the synthesis method of Sn2CoS with an L21 crystal structure. We will show that Sn2CoS has a type-II Dirac point at 0.15 eV, which is quite close to the Fermi level and available to detect the topological signal in an experiment. The nanowires of Sn2CoS are successfully grown by the ECD method. The nanowires are single crystals with an axis direction of [100]. The surface state can play a role in practical devices that are based on the topological electrical transport properties of nanowires.

2. Computational Details and Experimental Methods

The band structure calculations are performed based on the density functional theory (DFT), as implemented in the Vienna ab initio simulation package (VASP). The generalized gradient approximation with the realization of the Perdew–Burke–Ernzerhof functional is adopted for the exchange-correlation potential. The cutoff energy is set to 500 eV, and the Brillouin zone is sampled with 11 × 11 × 11 Γ-centered k mesh. The energy convergence criterion is chosen to be 10−6 eV. The surface states are calculated by using the Wannier tools package.
The Sn2CoS nanowires were synthesized in an AAO template by direct current electrochemical deposition. The AAO template was used as the working electrode, and Pt as the counter electrode. In the electrochemical deposition synthesis process of compounds, the chemical composition ratio of compounds is determined by the reduction and precipitation rate of metal ion co-deposition, the reduction potential, and the ion mobility of the ion source [48]. The cathode overpotential is the main factor affecting the reduction and precipitation rate. Compared with the standard hydrogen electrode, the reduction potentials of Sn, Co, and S are −0.136 V, −0.277 V, and −0.476 V, respectively. Among them, S has the highest reduction potential, the lowest reduction potential, and the larger ion radius. It quickly migrates to the cathode and reduces the ion mobility of Co ions, resulting in excessive S deposition and Co deficiency. In order to obtain a standard composition ratio of 2:1:1 (Sn:Co:S) with an L21 structure, we adjust the amount of Co source and S source to deviate from the standard ratio during the electrochemical deposition process. The optimized electrolyte contains 0.2 M CoSO4·7H2O, 0.1 M SnSO4, and 0.05 M C2H5NS for electrochemical deposition. In addition, 0.1 M boric acid (H3BO3) is added as a buffer to make electrochemical deposition easier, as well as 0.006 M ascorbic acid (C6H8O6) and 0.005 M NaCl, which are added to enhance the conductivity of the solution, respectively. A small amount of sodium dodecyl sulfate (C12H25NaO4S) can act as an active agent. Here, 0.002 M C12H25NaO4S is used as an anionic surfactant to reduce the surface energy and allow better access of the solution to enter the pores of the template. As a complexing agent in the electrolyte solution, sodium gluconate is added to help the electrode potential of ions to gather together.
After preparing the solution required for electrochemical deposition, we performed electrochemical deposition for 1 h by DC constant voltage of −1 V at room temperature. Then, the AAO template with nanowires was taken from the solution to immerse in 2 M NaOH for 6 h. After the dissolution of the AAO template, the achieved nanowires were cleaned in deionized water by ultrasonic cleaning equipment.
We analyzed the structure of the nanowires using X-ray diffraction (XRD) (Cu Kα) and transmission electron microscope (TEM). A scanning electron microscope (SEM) with energy dispersion spectroscopy (EDS) was used to observe the morphology and detect the chemical composition ratio of nanowires. The high-resolution images (HRTEM) and electron diffraction patterns were achieved by the TEM examinations. The nanowire samples used for SEM and TEM were made by dropping the alcohol suspension of nanowires onto the silicon wafer or copper mesh.

3. Results and Discussion

The L21 structure model of Sn2CoS is shown in Figure 1a. The positions of the Sn atoms are (1/4, 1/4, 1/4), while the Co and S atoms are located at (0, 0, 0) and (1/2, 1/2, 1/2) in Wyckoff coordinates, respectively. The L21 structure belongs to space group Fm 3 ¯ m (No. 225).
Figure 2a shows the band structure of Sn2CoS with an L21 structure calculated without spin–orbit coupling (SOC). It obviously shows a metallic band structure with several bands traversing the Fermi level. Very interestingly, as shown in Figure 2a, there are two bands that cross along the Γ-X-K path, forming two band-crossing points near the Fermi level (at 0.15 eV), named P1 and P2. The crossing points so close to the Fermi level are conducive to the detection of topological signals by angle-resolved photoemission spectroscopy (ARPES) in the future. Noticing that the structure of Sn2CoS reserves both the time-reversal (T) and spatial inversion (P) symmetries, thus P1 and P2 are not isolated nodal points but may belong to a nodal line. In order to confirm the characteristics of the nodal line, careful investigation of the band structure near the crossing points P1 and P2 was performed by calculating the band structure along the selected four k paths, namely X-a, X-b, X-c, and X-d (see Figure 2c). Figure 2b,d show the band structures along the k-paths as indicated in Figure 2c and the profile of the nodal loop in Sn2CoS. It is clearly illustrated that the crossing points P1 and P2 belong to a type-II nodal loop centering the X point. For nodal lines, one typical signature is that they can show drumhead-like surface states. To obtain the surface states of Sn2CoS, we constructed a first-principles tight-binding model by projecting onto the Wannier orbitals. We calculated the (1 1 0) surface state of Sn2CoS, and the results are shown in Figure 2e. We can observe clear drumhead-like surface state originating from the bulk band crossings, as pointed out by the arrows.
Now we turn to the band structure of Sn2CoS with SOC considered in the calculation as shown in Figure 3a. With the action of the spin orbit, P1 and P2 points are usually into Dirac points. So, in Figure 3a, we rename them as D1 and D2 points to distinguish them in discussions. Compared with Figure 2a, it can be observed that the D1 point still exists, but D2 is gapped with a small band gap (38.3 meV). Due to the coexistence of P and T symmetries in the system, the bands are both doubly degenerate. Thus, the band-crossing D1 forms a Dirac point, as shown in Figure 3a. Figure 3b shows the three-dimensional (3D) band structure about Dirac point (D1). We can clearly observe a type-II dispersion. Dirac metals usually manifest Fermi-arc surface states. In Figure 3c, we show the surface state band structure on the (1 1 0) of Sn2CoS with SOC. The exact positions of the Dirac point (D1) are indicated and two Fermi arcs (pointed out by the arrows) originating from the Dirac point are observed in the projected spectrum shown in Figure 3c. Through detailed research, we also find that there are seven Dirac points near the Fermi energy level, as shown in Figure S1. Further, we also give a list of more detailed information on all the Dirac points in Figures S1 and S2 and Table S1, including the positions in the k-space and the energy levels. Based on the above observation and discussion of the theoretical calculation results, it can be predicted that Sn2CoS with an L21 structure is a type-II Dirac metal.
Next, we provide more details of the orbital-projected band structure and the density of states (DOS) of Sn2CoS in Figure 4. By analyzing the orbital components, we find that two bands forming nodal line mainly originate from the Co-d orbital and S-p orbital (see Figure 4b). Since PBE computations may underestimate the band gap, we also check the band structure using the modified Becke–Johnson (MBJ) potential. As shown in Figure 5, the results are consistent with those calculated by PBE. In addition, we consider Coulomb interaction (using GGA + U method) and calculate the band structures with U values of 2, 4, 6, 8, and 10, respectively, as shown in Figure S3. In accordance with the actual experimental value, we choose the band structure of Sn2CoS without the U value finally, as shown in Table S2.
Encouraged by the theoretical results, we try to synthesize the Sn2CoS with an L21 structure in experiments. Firstly, we use the solution with the standard ratio of 2:1:1 (Sn:Co:S) to prepare the nanowires. It was found that no matter what deposition voltage is used, the Sn2CoS with an L21 structure cannot be grown. As described in Section 2, it is impossible to obtain Sn2CoS with an L21 structure and the standard composition ratio of 2:1:1 (Sn:Co:S) if the deposition voltage just meets the deposition potential of the three elements but the proportion of various elements in the solution does not match the deposition voltage. Therefore, we adjust the amount of Co source and S source to the chemical composition ratio of 2:4:1 (Sn:Co:S) for the electrochemical deposition process as described in Section 2 of this work.
Proper voltage is necessary for the solution with the corresponding element ratio. Using the solution with the chemical composition ratio of 2:4:1 (Sn:Co:S), the nanowires are grown at different deposition voltages to investigate the relationship between voltage and the composition of nanowires. As typical examples, Figure 6a,c show the XRD patterns of the samples prepared at the deposition voltages of −0.5 V and −1 V, respectively. It can be found that whether at −0.5 V or −1 V, ions can enter holes in the AAO template to form nanowires. However, the difference is that the nanowires deposited at −0.5 V not only deviate from the standard composition ratio of 2:1:1 (see EDX spectroscopy in Figure 6d) but also do not crystallize in L21 structure (see XRD pattern Figure 6c). This is because the precipitation potential of Sn ions has relatively high potential energy when the deposition voltage is −0.5 V, and their deposition rate on the cathode is very rapid, which can easily inhibit the migration rate of Co. So, Sn, and some intermediate compounds (such as SnS) are introduced, which makes the three elements unable to deposit uniformly. As shown in Figure 6c, the diffraction peaks of Sn are observed as the main ones of nanowires on the XRD patterns. When we increase the deposition voltage to −1 V, the principal peaks of the L21 structure, namely, (200), (220), and (400) peaks, can be clearly observed on the XRD pattern of nanowires in Figure 6a. Except for the diffraction peaks of the AAO template substrate (Al2O3), no secondary phase diffraction peak appears on the XRD patterns. Figure 6b shows the EDX spectroscopy and the chemical composition ratio of nanowires prepared at −1 V. The chemical composition ratio of nanowires is quite close to the standard composition ratio of 2:1:1 (Sn:Co:S). All these results show that the nanowires of Sn2CoS with an L21 structure have been successfully grown in the solution with the chemical composition ratio of 2:4:1 (Sn:Co:S) by electrochemical deposition process at −1 V. The lattice constant of nanowires of Sn2CoS with an L21 structure obtained from XRD analysis is 6.0 Å, which is consistent with the results achieved by TEM given later. In addition, it should be noted that the nanowires of Sn2CoS with an L21 structure show the excellent preferred orientation of [100] along the axis direction, which implies that nanowires are likely to be single crystals.
Figure 6e shows the nanowire array image on the template obtained after etching the surface of the AAO template. It can be clearly seen that these nanowires lean against each other to form bundles. In order to observe a single nanowire, we dispersed the nanowires in an alcohol solution by the ultrasonic method after the template was etched completely. The alcohol solution with the released nanowires was dropped on the silicon wafer, dried, and observed by SEM. Figure 6f shows an image of the nanowires released after dissolving the AAO template. These nanowires are uniform in length and thickness. Their length is about 70 μm. The nanowires were also picked up by copper mesh for TEM observation. With the help of the images of the single nanowire detected by TEM as shown in Figure 7a,b, it can be obtained that the diameter of the single nanowire is 70 nm ± 10 nm, which fits the size of the hole in the AAO template. This indicates that the nanowires are filled with holes in thickness. In addition, it is worth mentioning that the deposition time has an important influence on the length of nanowires in the AAO template. When the deposition time is less than 1 h in our AAO template, nanowires are hidden in holes and cannot be exposed. Additionally, when the deposition time exceeds 1 h, the nanowires will overflow from the holes of the AAO template to gradually form a film-like covering on the surface of the template. The top of the nanowires will be connected together, just like turf, which is hard to separate. All these results indicate that the nanowires grow from bottom to top, not from the hole wall to the hole center. This growth mode is an important guarantee for the growth of nanowires into single crystals. The Sn2CoS nanowires are single crystals, which will be confirmed in the following detection of TEM. When the deposition rate of Sn2CoS is about 70 μm/h, a deposition time of 1 h is the best nanowire growth time for the AAO template in this work. In addition, it is possible to grow nanowires with different lengths or radii by using AAO templates with different pore sizes or thicknesses within an appropriate deposition time.
Figure 7c shows a high-resolution transmission electron microscopy (HRTEM) observation. The structure of Sn2CoS nanowires is captured clearly, and the well-defined lattice fringes with a space of 0.128 nm can be indexed along the [111] crystal direction. According to the space of 0.128 nm, we can figure out the lattice parameter is 6.0 Å, which is consistent with the result from the XRD pattern. The exposed surface is (110) (inset in Figure 7c). We also performed a series of selective area electron diffraction (SAED) patterns along the growth direction of nanowires to confirm that the Sn2CoS nanowires are single crystals as shown in Figure 7d,e. These results show that the Sn2CoS nanowires are single crystals along the axial direction of [100].

4. Conclusions

We synthesized Sn2CoS in experiment and theoretically study the topological properties of this material. By first-principles calculation, we find that Sn2CoS has type-II nodal-line and drumhead-like surface states near the Fermi level without SOC. When SOC is considered, the nodal line opens the band gap, leaving type-II Dirac point and Fermi-arc surface states. Most importantly, we also synthesized Sn2CoS in experiment. In this work, Sn2CoS nanowires with the L21 structure are synthesized successfully by the ECD method. The single-crystal nanowires of Sn2CoS with a length of about 70 μm, a diameter of about 70 nm, and an axis direction of [100] were achieved. The nanowires grow from bottom to top in the holes of AAO templates. Nanowires with different lengths or radii can be obtained by using AAO with different pore sizes or thicknesses within an appropriate deposition time. Our experimental synthesis and theoretical study of Sn2CoS will provide candidate materials for further measurements by angle-resolved photoemission spectroscopy (ARPES) in the future.

Supplementary Materials

The following supporting information can be downloaded at: https://0-www-mdpi-com.brum.beds.ac.uk/article/10.3390/nano13081389/s1, Figure S1. Electronic band structure of Sn2CoS with SOC. The point and gapped nodal point are indicated by D1, D2, D3, D4, D5, D6 and D7, and the detail electronic band structure near the above points. Figure S2. The bulk Brillouin zone of the Sn2CoS with D1, D3, D4, D5, D6 and D7. Figure S3. The band structure of Sn2CoS with different U values. Table S1. The energy level of D1, D3, D4, D5, D6 and D7. Table S2. The magnetic of Sn2CoS with different DFT + U value.

Author Contributions

G.C.: Conceptualization, Supervision, Writing—Review and Editing, Funding acquisition; B.L.: Investigation, Formal analysis, Visualization, Writing—Original draft preparation; L.J.: Software, Investigation; H.Z.: Formal analysis, Project administration; Z.C.: Investigation, Visualization; X.Z.: Methodology, Resources, Writing—Review and Editing, Funding acquisition; G.L.: Conceptualization, Supervision, Writing—Review and Editing, Funding acquisition. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the National Natural Science Foundation of China (Grant No. 51871089), the project for Science and Technology Correspondent of Tianjin City (Grant No. 20YDTPJC01710), and the Research Foundation of Education Bureau of Hebei (Grant No. QN2021044).

Data Availability Statement

Data are contained within the article.

Conflicts of Interest

The authors declare no conflict of interest.

References

  1. Qi, X.L.; Zhang, S.C. Topological insulators and superconductors. Rev. Mod. Phys. 2011, 83, 1057–1110. [Google Scholar] [CrossRef]
  2. Hasan, M.Z.; Kane, C.L. Colloquium: Topological insulators. Rev. Mod. Phys. 2010, 82, 3045–3067. [Google Scholar] [CrossRef]
  3. Armitage, N.P.; Mele, E.J.; Vishwanath, A. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 2018, 90, 015001. [Google Scholar] [CrossRef]
  4. Burkov, A.A.; Balents, L. Weyl semimetal in a topological insulator multilayer. Phys. Rev. Lett. 2011, 107, 127205. [Google Scholar] [CrossRef]
  5. Weng, H.M.; Fang, C.; Fang, Z.; Bernevig, B.A.; Dai, X. Weyl semimetal phase in noncentrosymmetric transition-metal monophosphides. Phys. Rev. X 2015, 5, 011029. [Google Scholar] [CrossRef]
  6. Young, S.M.; Zaheer, S.; Teo, J.C.; Kane, C.L.; Mele, E.J.; Rappe, A.M. Dirac semimetal in three dimensions. Phys. Rev. Lett. 2012, 108, 140405. [Google Scholar] [CrossRef] [PubMed]
  7. Wang, Z.J.; Sun, Y.; Chen, X.Q.; Franchini, C.; Xu, G.; Weng, H.M.; Dai, X.; Fang, Z. Dirac semimetal and topological phase transitions in A3Bi (A = Na, K, Rb). Phys. Rev. B 2012, 85, 195320. [Google Scholar] [CrossRef]
  8. Jin, L.; Zhang, X.M.; Dai, X.F.; Liu, H.Y.; Chen, G.F.; Liu, G.D. Centrosymmetric Li2NaN: A superior topological electronic material with critical-type triply degenerate nodal points. J. Mater. Chem. C 2019, 7, 1316–1320. [Google Scholar] [CrossRef]
  9. Jin, L.; Zhang, X.M.; Dai, X.F.; Wang, L.Y.; Liu, H.Y.; Liu, G.D. Screening topological materials with a CsCl-type structure in crystallographic databases. IUCrJ 2019, 6, 688–694. [Google Scholar] [CrossRef]
  10. Weng, H.M.; Liang, Y.Y.; Xu, Q.N.; Yu, R.; Fang, Z.; Dai, X.; Kawazoe, Y. Topological node-line semimetal in three-dimensional graphene networks. Phys. Rev. B 2015, 92, 045108. [Google Scholar] [CrossRef]
  11. Yang, S.A.; Pan, H.; Zhang, F. Dirac and Weyl superconductors in three dimensions. Phys. Rev. Lett. 2014, 113, 046401. [Google Scholar] [CrossRef] [PubMed]
  12. Zhang, X.M.; Yu, Z.M.; Sheng, X.L.; Yang, H.Y.; Yang, S.A. Coexistence of four-band nodal rings and triply degenerate nodal points in centrosymmetric metal diborides. Phys. Rev. B 2017, 95, 235116. [Google Scholar] [CrossRef]
  13. Xie, L.S.; Schoop, L.M.; Seibel, E.M.; Gibson, Q.D.; Xie, W.W.; Cava, R.J. Line of Dirac Nodes in Hyperhoneycomb Lattices. APL Mater. 2015, 3, 083602. [Google Scholar] [CrossRef]
  14. Chan, Y.H.; Chiu, C.K.; Chou, M.Y.; Schnyder, A.P. Ca3P2 and other topological semimetals with line nodes and drumhead surface states. Phys. Rev. B 2016, 93, 205132. [Google Scholar] [CrossRef]
  15. Jin, L.; Zhang, X.M.; He, T.L.; Meng, W.Z.; Dai, X.F.; Liu, G.D. Ferromagnetic two-dimensional metal-chlorides MCl (M = Sc, Y, and La): Candidates for Weyl nodal line semimetals with small spin-orbit coupling gaps. Appl. Surf. Sci. 2020, 520, 146376. [Google Scholar] [CrossRef]
  16. Li, R.; Ma, H.; Cheng, X.; Wang, S.; Li, D.; Zhang, Z.; Li, Y.; Chen, X.Q. Dirac node lines in pure alkali earth metals. Phys. Rev. Lett. 2016, 117, 096401. [Google Scholar] [CrossRef]
  17. Meng, W.Z.; Zhang, X.M.; He, T.L.; Jin, L.; Dai, X.F.; Liu, G.D. Crystal Structures, Electronic Structures, and Topological Signatures in Equiatomic TT′ X Compounds (T = Sc, Zr, Hf; T′ = Co, Pt, Pd, Ir, Rh; X = Al, Ga, Sn). J. Phys. Chem. C 2020, 124, 7378–7385. [Google Scholar] [CrossRef]
  18. Wang, X.T.; Ding, G.Q.; Cheng, Z.X.; Surucu, G.; Wang, X.L.; Yang, T. Novel topological nodal lines and exotic drum-head-like surface states in synthesized CsCl-type binary alloy TiOs. J. Adv. Res. 2020, 22, 137–144. [Google Scholar] [CrossRef]
  19. Wang, X.T.; Ding, G.Q.; Cheng, Z.X.; Surucu, G.; Wang, X.L.; Yang, T. Rich topological nodal line bulk states together with drum-head-like surface states in NaAlGe with anti-PbFCl type structure. J. Adv. Res. 2020, 23, 95–100. [Google Scholar] [CrossRef]
  20. Zhong, C.Y.; Chen, Y.P.; Xie, Y.; Yang, S.A.; Cohen, M.L.; Zhang, S.B. Towards three-dimensional Weyl-surface semimetals in graphene networks. Nanoscale 2016, 8, 7232–7239. [Google Scholar] [CrossRef]
  21. Liang, Q.F.; Zhou, J.; Yu, R.; Wang, Z.; Weng, H.M. Node-surface and node-line fermions from nonsymmorphic lattice symmetries. Phys. Rev. B 2016, 93, 085427. [Google Scholar] [CrossRef]
  22. Wu, W.K.; Liu, Y.; Li, S.; Zhong, C.Y.; Yu, Z.M.; Sheng, X.L.; Zhao, Y.X.; Yang, S.A. Nodal surface semimetals: Theory and material realization. Phys. Rev. B 2018, 97, 115125. [Google Scholar] [CrossRef]
  23. Zhang, X.M.; Yu, Z.M.; Zhu, Z.M.; Wu, W.K.; Wang, S.S.; Sheng, X.L.; Yang, S.A. Nodal loop and nodal surface states in the Ti3Al family of materials. Phys. Rev. B 2018, 97, 235150. [Google Scholar] [CrossRef]
  24. Li, S.; Yu, Z.M.; Liu, Y.; Guan, S.; Wang, S.S.; Zhang, X.M.; Yao, Y.; Yang, S.A. Type-II nodal loops: Theory and material realization. Phys. Rev. B 2017, 96, 081106. [Google Scholar] [CrossRef]
  25. Zhang, X.M.; Jin, L.; Dai, X.F.; Liu, G.D. Topological Type-II Nodal Line Semimetal and Dirac Semimetal State in Stable Kagome Compound Mg3Bi2. J. Phys. Chem. Lett. 2017, 8, 4814–4819. [Google Scholar] [CrossRef] [PubMed]
  26. Zhang, X.M.; Jin, L.; Dai, X.F.; Liu, G.D. Highly anisotropic type-II nodal line state in pure titanium metal. App. Phys. Lett. 2018, 112, 122403. [Google Scholar] [CrossRef]
  27. Zhang, X.M.; Yu, Z.M.; Lu, Y.H.; Sheng, X.L.; Yang, H.Y.; Yang, S.A. Hybrid nodal loop metal: Unconventional magnetoresponse and material realization. Phys. Rev. B 2018, 97, 125143. [Google Scholar] [CrossRef]
  28. Gao, Y.; Chen, Y.P.; Xie, Y.; Chang, P.Y.; Cohen, M.L.; Zhang, S.B. A class of topological nodal rings and its realization in carbon networks. Phys. Rev. B 2018, 97, 121108. [Google Scholar] [CrossRef]
  29. Chang, T.R.; Xu, S.Y.; Chang, G.Q.; Lee, C.C.; Huang, S.M.; Wang, B.K.; Bian, G.; Zheng, H.; Sanchez, D.S.; Belopolski, I.; et al. Prediction of an arc-tunable Weyl Fermion metallic state in MoxW1−xTe2. Nat. Commun. 2016, 7, 10639. [Google Scholar] [CrossRef]
  30. O’Brien, T.E.; Diez, M.; Beenakker, C.W.J. Magnetic Breakdown and Klein Tunneling in a Type-II Weyl Semimetal. Phys. Rev. Lett. 2016, 116, 236401. [Google Scholar] [CrossRef]
  31. Isobe, H.; Nagaosa, N. Coulomb Interaction Effect in Weyl Fermions with Tilted Energy Dispersion in Two Dimensions. Phys. Rev. Lett. 2016, 116, 116803. [Google Scholar] [CrossRef]
  32. Koshino, M. Cyclotron resonance of figure-of-eight orbits in a type-II Weyl semimetal. Phys. Rev. B 2016, 94, 035202. [Google Scholar] [CrossRef]
  33. Yu, Z.M.; Yao, Y.G.; Yang, S.A. Predicted Unusual Magnetoresponse in Type-II Weyl Semimetals. Phys. Rev. Lett. 2016, 117, 077202. [Google Scholar] [CrossRef] [PubMed]
  34. Meng, W.Z.; Zhang, X.M.; Liu, Y.; Dai, X.F.; Liu, G.D. Antiferromagnetism caused by excess electrons and multiple topological electronic states in the electride Ba4Al5⋅e−. Phys. Rev. B 2021, 104, 195145. [Google Scholar] [CrossRef]
  35. Singha, R.; Pariari, A.K.; Satpati, B.; Mandal, P. Large nonsaturating magnetoresistance and signature of nondegenerate Dirac nodes in ZrSiS. Proc. Natl. Acad. Sci. USA 2017, 114, 2468–2473. [Google Scholar] [CrossRef] [PubMed]
  36. Ali, M.N.; Schoop, L.M.; Garg, C.; Lippmann, J.M.; Lara, E.; Lotsch, B.; Parkin, S.P. Butterfly magnetoresistance, quasi-2D Dirac Fermi surface and topological phase transition in ZrSiS. Sci. Adv. 2016, 2, e1601742. [Google Scholar] [CrossRef]
  37. Wang, Z.J.; Weng, H.M.; Wu, Q.S.; Dai, X.; Fang, Z. Three-dimensional Dirac semimetal and quantum transport in Cd3As2. Phys. Rev. B 2013, 88, 125427. [Google Scholar] [CrossRef]
  38. Yang, B.J.; Nagaosa, N. Classification of stable three-dimensional Dirac semimetals with nontrivial topology. Nat. Commun. 2014, 5, 4898. [Google Scholar] [CrossRef]
  39. Soluyanov, A.A.; Gresch, D.; Wang, Z.J.; Wu, Q.S.; Troyer, M.; Dai, X.; Bernevig, B.A. Type II Weyl Semimetals. Nature 2015, 527, 495–498. [Google Scholar] [CrossRef]
  40. Zhu, Z.M.; Winkler, G.W.; Wu, Q.S.; Li, J.; Soluyanov, A.A. Triple Point Topological Metals. Phys. Rev. X 2016, 6, 031003. [Google Scholar] [CrossRef]
  41. Bradlyn, B.; Cano, J.; Wang, Z.J.; Vergniory, M.G.; Felser, C.; Cava, R.J.; Bernevig, B.A. Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals. Science 2016, 353, aaf5037. [Google Scholar] [CrossRef] [PubMed]
  42. Huang, H.Q.; Zhou, S.Y.; Duan, W.H. Type-II Dirac fermions in the PtSe2 class of transition metal dichalcogenides. Phys. Rev. B 2016, 94, 121117. [Google Scholar] [CrossRef]
  43. Le, C.C.; Qin, S.S.; Wu, X.X.; Dai, X.; Fu, P.Y.; Fang, C.; Hu, J.P. Three-dimensional topological critical Dirac semimetal in AMgBi(A = K, Rb, Cs). Phys. Rev. B 2017, 96, 115121. [Google Scholar] [CrossRef]
  44. Chang, T.R.; Xu, S.Y.; Sanchez, D.S.; Tsai, W.F.; Huang, S.M.; Chang, G.Q.; Hsu, C.H.; Bian, G.; Belopolski, I.; Yu, Z.M.; et al. Type-II Symmetry-Protected Topological Dirac Semimetals. Phys. Rev. Lett. 2017, 119, 026404. [Google Scholar] [CrossRef]
  45. Guo, P.J.; Yang, H.C.; Liu, K.; Lu, Z.Y. Type-II Dirac semimetals in the YPd2Sn class. Phys. Rev. B 2017, 95, 155112. [Google Scholar] [CrossRef]
  46. Pavlosiuk, O.; Kaczorowski, D. Galvanomagnetic properties of the putative type-II Dirac semimetal PtTe2. Sci. Rep. 2018, 8, 11297. [Google Scholar] [CrossRef] [PubMed]
  47. Dulal, R.P.; Dahal, B.R.; Forbes, A.; Bhattarai, N.; Pegg, I.L.; Philip, J. Nanostructures of type-II topological Dirac semimetal NiTe2. J. Vac. Sci. Technol. B 2019, 37, 042903. [Google Scholar] [CrossRef]
  48. Safeer, A.; Ahmad, N.; Khan, S.; Azam, L.A.; Bashir, D. Magnetization behavior of electrochemically synthesized Co2MnSn full Heusler alloy nanowire arrays. J. Appl. Phys. 2019, 125, 034302. [Google Scholar] [CrossRef]
Nanomaterials 13 01389 g001 550
Figure 1. (a) Crystal structure and (b) the bulk Brillouin zone of the Sn2CoS with L21 structure.
Figure 1. (a) Crystal structure and (b) the bulk Brillouin zone of the Sn2CoS with L21 structure.
Nanomaterials 13 01389 g001
Nanomaterials 13 01389 g002 550
Figure 2. (a) Electronic band structure and the projected density of states (PDOS) of Sn2CoS without SOC. Two crossing points near the Fermi level along the Γ−X−K path have been labeled as P1 and P2, respectively. (b) The nodal loop in Sn2CoS. (c) Illustration of the nodal loop. The points a, b, c, and d are equally spaced between K and Γ. (d) Band structures along the k-paths as indicated in (c). (e) The surface state band structure on the (1 1 0) of Sn2CoS without SOC.
Figure 2. (a) Electronic band structure and the projected density of states (PDOS) of Sn2CoS without SOC. Two crossing points near the Fermi level along the Γ−X−K path have been labeled as P1 and P2, respectively. (b) The nodal loop in Sn2CoS. (c) Illustration of the nodal loop. The points a, b, c, and d are equally spaced between K and Γ. (d) Band structures along the k-paths as indicated in (c). (e) The surface state band structure on the (1 1 0) of Sn2CoS without SOC.
Nanomaterials 13 01389 g002
Nanomaterials 13 01389 g003 550
Figure 3. (a) Electronic band structure of Sn2CoS with SOC. The nodal point and gapped nodal point are indicated by D1 and D2. (b) The 3D plot of band dispersions near the D1. (c) The surface state band structure of Sn2CoS with SOC. The Fermi arcs are pointed by the white arrows.
Figure 3. (a) Electronic band structure of Sn2CoS with SOC. The nodal point and gapped nodal point are indicated by D1 and D2. (b) The 3D plot of band dispersions near the D1. (c) The surface state band structure of Sn2CoS with SOC. The Fermi arcs are pointed by the white arrows.
Nanomaterials 13 01389 g003
Nanomaterials 13 01389 g004 550
Figure 4. (a,b) The orbital-projected band structure of Sn2CoS without SOC. (c,d) The orbital-projected band structure of Sn2CoS with SOC. (e) The density of states (DOS) of Sn atom, Co atom, and S atom. (f) The DOS of Co-d, Sn-s, Sn-p, and S-p.
Figure 4. (a,b) The orbital-projected band structure of Sn2CoS without SOC. (c,d) The orbital-projected band structure of Sn2CoS with SOC. (e) The density of states (DOS) of Sn atom, Co atom, and S atom. (f) The DOS of Co-d, Sn-s, Sn-p, and S-p.
Nanomaterials 13 01389 g004
Nanomaterials 13 01389 g005 550
Figure 5. (a) The band structure of Sn2CoS without SOC by the modified Becke−Johnson (MBJ) potential. (b) The band structure of Sn2CoS with SOC by the modified Becke−Johnson (MBJ) potential.
Figure 5. (a) The band structure of Sn2CoS without SOC by the modified Becke−Johnson (MBJ) potential. (b) The band structure of Sn2CoS with SOC by the modified Becke−Johnson (MBJ) potential.
Nanomaterials 13 01389 g005
Nanomaterials 13 01389 g006 550
Figure 6. (a) The X-ray diffraction patterns of Sn2CoS nanowires prepared at −1 V. (b) EDX spectroscopy of nanowires at −1 V. (c) The X−ray diffraction patterns of Sn2CoS nanowires prepared at −0.5 V. (d) shows EDX spectroscopy of nanowires at −0.5 V. (e) Typical image of nanowire array by SEM. (f) The image of single nanowire by SEM.
Figure 6. (a) The X-ray diffraction patterns of Sn2CoS nanowires prepared at −1 V. (b) EDX spectroscopy of nanowires at −1 V. (c) The X−ray diffraction patterns of Sn2CoS nanowires prepared at −0.5 V. (d) shows EDX spectroscopy of nanowires at −0.5 V. (e) Typical image of nanowire array by SEM. (f) The image of single nanowire by SEM.
Nanomaterials 13 01389 g006
Nanomaterials 13 01389 g007 550
Figure 7. (a,b) The results of Sn2CoS alloy nanowires without AAO template at 200 nm scale by TEM. (c) The image of the Sn2CoS by HRTEM. (d–f) The SAED pattern of the Sn2CoS single-crystal structure recorded along the [111] crystal orientation.
Figure 7. (a,b) The results of Sn2CoS alloy nanowires without AAO template at 200 nm scale by TEM. (c) The image of the Sn2CoS by HRTEM. (d–f) The SAED pattern of the Sn2CoS single-crystal structure recorded along the [111] crystal orientation.
Nanomaterials 13 01389 g007
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Share and Cite

MDPI and ACS Style

Chen, G.; Long, B.; Jin, L.; Zhang, H.; Cheng, Z.; Zhang, X.; Liu, G. Nontrivial Topological Properties and Synthesis of Sn2CoS with L21 Structure. Nanomaterials 2023, 13, 1389. https://0-doi-org.brum.beds.ac.uk/10.3390/nano13081389

AMA Style

Chen G, Long B, Jin L, Zhang H, Cheng Z, Zhang X, Liu G. Nontrivial Topological Properties and Synthesis of Sn2CoS with L21 Structure. Nanomaterials. 2023; 13(8):1389. https://0-doi-org.brum.beds.ac.uk/10.3390/nano13081389

Chicago/Turabian Style

Chen, Guifeng, Bolin Long, Lei Jin, Hui Zhang, Zishuang Cheng, Xiaoming Zhang, and Guodong Liu. 2023. "Nontrivial Topological Properties and Synthesis of Sn2CoS with L21 Structure" Nanomaterials 13, no. 8: 1389. https://0-doi-org.brum.beds.ac.uk/10.3390/nano13081389

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop