# Structure, Stability, and Superconductivity of Two-Dimensional Janus NbSH Monolayers: A First-Principle Investigation

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}/MoSe

_{2}with other chalcogen (Se/S) atoms [12,15]. The novel structural characteristics with the breaking out-plane symmetry make 2D Janus materials have great potential applications in many special fields.

_{2}. Furthermore, both the monolayer and multilayer of Janus MoSSe have been identified as efficient photocatalysts for water splitting [17]. These materials show excellent capability in harvesting solar energy and converting it into hydrogen fuel. In addition, the introduction of doping As and Si atoms in the S or Se sites of the 2D JTMDs VSSe monolayer greatly enhances HER performance [18]. This type of doping results in a significant reduction of the hydrogen adsorption free energy, which is even better than that of the traditional Pt catalyst. The Janus Pd-based TMD monolayers, including PdSSe, PdSTe, and PdSeTe, have also been found to have the ability to simultaneously facilitate the hydrogen and oxygen evolution reactions as efficient photocatalysts for water splitting [19].

_{2}XY (M = Ga, In, and X, Y = S, Se, Te) [23], and multilayer MoSTe [24]. For MoSSe, the out-of-plane piezoelectricity has been finally identified experimentally [12]. The 2D Janus MoSTe [25], ZnAXY [26] (A = Si, Ge, Sn, and X/Y = S, Se, Te, X < Y), and BMX

_{2}(M = Ga, In, and X = S, Se) [27] monolayers were also predicted to have excellent electronic, spintronic, and piezoelectric properties. In addition to piezoelectricity, 2D Janus monolayers possess other interesting properties such as magnetism [28], valley polarization [29,30], and Rashba spin splitting (RSS) [31,32]. The RSS effect refers to the momentum-dependent spin splitting in bands that occurs due to spin–orbit coupling (SOC) in asymmetric structures. Hence the Janus 2D materials, with their natural antisymmetric structure, exhibit RSS in the presence of SOC. This property allows the control of electron current by manipulating spin precession, which forms the basis of spin field-effect transistors (SFETs) [33] and spin injectors [34]. Recent studies have shown that the strong SOC and mirror asymmetry of 2D Janus materials give rise to the RSS phenomenon, making them promising candidates for next-generation spintronic devices. For example, the Janus Ge

_{2}XY (X ≠ Y = P, As, Sb, and Bi) monolayers exhibit the out-of-plane piezoelectricity and giant Rashba spin-band splitting [35]. The Janus 2D materials Bi

_{2}X

_{3}(X = S, Se) monolayers were reported to exhibit coexistence of anisotropic colossal out-of-plane piezoelectricity, giant RSS, and ultrahigh carrier mobilities [36]. The Janus Sn

_{2}XY (X/Y = S, Se, Te) monolayers were also found to have strong piezoelectricity with high electron mobility [37]. All the reported 2D Janus materials show great potential for nano-electronic applications.

_{2}stands out as a unique case. In contrast to other TMDCs such as 2H-NbSe

_{2}and 2H-MoS

_{2}, 2H-NbS

_{2}is the only known superconductor without any charge density wave (CDW) instabilities [41]. This observation is quite unusual and suggests a different behavior of 2H-NbS

_{2}compared to its isostructural and isoelectronic counterparts. Based on this understanding, we anticipate that Janus NbSH will exhibit significant differences in both structure and properties compared to Janus MoSH. Considering the contrasting behavior of 2H-NbS

_{2}and 2H-MoS

_{2}, it is expected that Janus NbSH may exhibit distinct properties not observed in Janus MoSH. These different features could manifest themselves in various aspects, including electronic, structure, and stability, making Janus NbSH an intriguing material for further exploration and potential applications.

## 2. Computational Methods

^{−1}/atom. The Brillouin zone was sampled using a k-point grid spacing of 2π × 0.03 Å

^{−1}[47]. The vacuum thickness was set to 20 Å for eliminating interlayer interaction. The vdW interactions were treated using the (Grimme) DFT-D2 approximation [48]. Ab initio molecular dynamics simulations (AIMD) with the Nosé–Hoover thermostat and NVT ensemble [49] were used to estimate the thermal stability by using the 4 × 4 supercell at 300 K with the time step of 2 fs.

_{C}) was calculated using the Allen–Dynes formula based on BCS theory [50]

_{ij}(i, j = 1, 2, 6) is the in-plane stiffness tensor. The corresponding strain tensor ${\epsilon}^{2\mathrm{D}}$ can be expressed as follows, when a small strain $\epsilon $ is applied in a 2D crystal.

_{11}, C

_{12}, C

_{16}, C

_{22}, C

_{26}, and C

_{66}.

_{11}and C

_{12}. The elastic constants C

_{11}and C

_{12}were calculated via two strain modes as listed in Table 1. Finally, to obtain accurate elastic constants, a total of nine strains were used to fit the strain-energy Equation (7).

_{ij}, we further evaluated angular-dependent Young’s modulus ${Y}_{2\mathrm{D}}$ and Poisson’s ratio $\nu $, to examine the mechanical characteristics of the three 2D structures. The angular-dependent ${Y}_{2\mathrm{D}}(\theta )$ and $\nu (\theta )$ were calculated with the following equations [57,58]

## 3. Results and Discussion

#### 3.1. Structure and Stability

_{2}(−4.97 eV/atom) [59], silicene (−3.98 eV/atom), germanene (−3.2 eV/atom) [60], and phosphorene (−3.61 eV/atom) [61,62], demonstrating good thermodynamic stability of the predicted phase.

_{11}and C

_{12}, while the non-independent elastic constant is determined as ${C}_{66}=({C}_{11}-{C}_{12})/2$. It is obvious that all the elastic constants satisfy the necessary mechanical equilibrium conditions ${C}_{11}{C}_{22}-{C}_{12}^{2}>0$ and ${C}_{11}$, ${C}_{22}$, ${C}_{66}>0$ [62], confirming the mechanical stability of all the 2D NbSH. Moreover, the Poisson’s ratio and Young’s modulus as a function of the angle for the three NbSH phases are shown in Figure 3a,b, respectively. It can be seen that all three phases display isotropic mechanical behavior. The in-plane Young’s modulus of NbSH are 122.8, 103.1, 118.8 N/m for 2H-NbSH, 1T-NbSH, and new NbSH phases, respectively. The in-plane Young’s moduli of all three structures are higher than those of silicene (61 N/m), germanene (42 N/m) [59], and black phosphorene (83 N/m) [63], and comparable to that of MoS

_{2}(129 N/m) [64]. The Poisson’s ratio characterizes the material’s resultant strain in the longitudinal direction for a material under lateral stress. All the Poisson’s ratios of the three phases also show isotropic behaviors, just like the Young’s moduli. The Poisson’s ratio values of the 2H-NbSH, 1T-NbSH, and new NbSH phases are 0.22, 0.17, and 0.32. The predicted NbSH has the largest Possion’s ratio, indicating a more sensitive structural response to external strain of the predicted structure.

#### 3.2. Electronic Properties

#### 3.3. Superconductivity

_{2}[65] and 2D Janus MoSH [39]. Our predicted 2D NbSH phase exhibits a similar ${T}_{\mathrm{C}}$ value when compared with other reported layered TMDS, such as TaS

_{2}with ${T}_{\mathrm{C}}$ below 2.0 K [66], NbS

_{2}with a ${T}_{\mathrm{C}}$ of approximately 3 K [67], and WS

_{2}with a ${T}_{\mathrm{C}}$ of 8.8 K [68]. However, the ${T}_{\mathrm{C}}$ of our predicted NbSH phase is lower than that of the Janus 1T/2H-MoSH, which has a ${T}_{\mathrm{C}}$ range of about 25–26 K [39]. In addition, from Figure 5a, we can see that there are no negative phonons in the whole BZ zone, indicating the predicted 2D NbSH is also dynamically stable.

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Sample Availability

## References

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**Figure 1.**Top view structural diagrams of 2H-NbSH (

**a**), 1T-NbSH (

**b**), and predicted NbSH (

**c**); Side view structural diagrams of 2H-NbSH (

**d**), 1T-NbSH (

**e**), and predicted NbSH (

**f**). Nb, S, and H atoms are represented by green, yellow, and grey spheres, respectively.

**Figure 2.**Vibration of total potential energy of 2H−NbSH (

**a**), 1T−NbSH (

**b**), and predicted NbSH (

**c**) during the AIMD at the temperature 300 K. The inset is the final snapshot of NbSH with its top view and side view at the end of 10 ps.

**Figure 3.**The orientation angle-dependent 2D Young’s modulus (

**a**) and Possion’s ratio (

**b**) of various NbSH monolayers.

**Figure 4.**Energy band structures of the NbSH derived from the calculation of DFT-PBE (black lines) and DFT-PBE-SOC (red lines) for (

**a**) 2H-NbSH, (

**b**) 1T-NbSH, and (

**c**) predicted NbSH; the Fermi level (dotted line) is set to zero. The projected density of states of NbSH for (

**d**) 2H-structure, (

**e**) 1T-structure, and (

**f**) predicted structure.

**Figure 5.**(

**a**) Calculated phonon dispersion, (

**b**) total and partial phonon density of states, and (

**c**) Eliashberg function with integrated EP coupling constant λ(ω) for predicted NbSH monolayer. Hollow red circles in (

**a**) indicate the phonon linewidth γ with a radius proportional to the strength.

**Table 1.**List of strain modes and the derived elastic constants for the 2D hexagonal system used, based on energy-strain approach.

Strain Index | Strain Vector $\mathit{\epsilon}$ | Elastic Energy $\frac{\mathit{\Delta}\mathit{E}}{\mathit{V}}$ |
---|---|---|

1 | (δ, 0, 0) | $\frac{1}{2}{\mathrm{C}}_{11}{\delta}^{2}$ |

2 | (δ, δ, 0) | ${(\mathrm{C}}_{11}+{\mathrm{C}}_{12}){\delta}^{2}$ |

Structure | C_{11} | C_{22} | C_{12} | C_{66} |
---|---|---|---|---|

2H-NbSH | 129.0 | 129 | 28.3 | 50.4 |

1T-NbSH | 106.3 | 106.3 | 18.5 | 43.9 |

Predicted NbSH | 132.3 | 122.5 | 42.2 | 45.0 |

**Table 3.**Dependence of the λ, ω

_{log}, and T

_{C}on the in-plane biaxial strain of the predicted NbSH.

Biaxial Strain | λ | ω_{log} (cm^{−1}) | T_{C} (K) |
---|---|---|---|

+0.01% | 0.70 | 163.6 | 5.40 |

0.00% | 0.71 | 171.1 | 6.10 |

−0.06% | 0.80 | 162.3 | 7.62 |

−1.08% | 0.81 | 194.7 | 9.38 |

−1.38% | 0.73 | 196.1 | 7.43 |

−0.02% | 0.64 | 221.8 | 6.03 |

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## Share and Cite

**MDPI and ACS Style**

Li, Y.; Pu, C.; Zhou, D.
Structure, Stability, and Superconductivity of Two-Dimensional Janus NbSH Monolayers: A First-Principle Investigation. *Molecules* **2023**, *28*, 5522.
https://doi.org/10.3390/molecules28145522

**AMA Style**

Li Y, Pu C, Zhou D.
Structure, Stability, and Superconductivity of Two-Dimensional Janus NbSH Monolayers: A First-Principle Investigation. *Molecules*. 2023; 28(14):5522.
https://doi.org/10.3390/molecules28145522

**Chicago/Turabian Style**

Li, Yan, Chunying Pu, and Dawei Zhou.
2023. "Structure, Stability, and Superconductivity of Two-Dimensional Janus NbSH Monolayers: A First-Principle Investigation" *Molecules* 28, no. 14: 5522.
https://doi.org/10.3390/molecules28145522