Two-dimensional superconducting MoSi2N4(MoN)4n homologous compounds

ABSTRACT The number and stacking order of layers are two important degrees of freedom that can modulate the properties of 2D van der Waals (vdW) materials. However, the layers’ structures are essentially limited to the known layered 3D vdW materials. Recently, a new 2D vdW material, MoSi2N4, without known 3D counterparts, was synthesized by passivating the surface dangling bonds of non-layered 2D molybdenum nitride with elemental silicon, whose monolayer can be viewed as a monolayer MoN (-N-Mo-N-) sandwiched between two Si-N layers. This unique sandwich structure endows the MoSi2N4 monolayer with many fascinating properties and intriguing applications, and the surface-passivating growth method creates the possibility of tuning the layer's structure of 2D vdW materials. Here we synthesized a series of MoSi2N4(MoN)4n structures confined in the matrix of multilayer MoSi2N4. These super-thick monolayers are the homologous compounds of MoSi2N4, which can be viewed as multilayer MoN (Mo4n+1N4n+2) sandwiched between two Si-N layers. First-principles calculations show that MoSi2N4(MoN)4 monolayers have much higher Young's modulus than MoN, which is attributed to the strong Si-N bonds on the surface. Importantly, different from the semiconducting nature of the MoSi2N4 monolayer, the MoSi2N4(MoN)4 monolayer is identified as a superconductor with a transition temperature of 9.02 K. The discovery of MoSi2N4(MoN)4n structures not only expands the family of 2D materials but also brings a new degree of freedom to tailor the structure of 2D vdW materials, which may lead to unexpected novel properties and applications.

The cutoff energy for plane-wave expansion was 500 eV and the k-point sampling grid in the relaxation and self-consistent step was 15  15  1 for monolayers, 15  15  5 and 15  15  3 for the stacking order calculations of bulk phase with two and three monolayers, respectively.And the optPBE-vdW was used to consider the vdW interactions between monolayers.The crystal structures were relaxed enough until the forces on each atom became less than 0.001 eV/Å and the energy difference on the primitive cell between the last two steps became less than 10 -6 eV.A vacuum of 20 Å between layers with periodic images was considered to minimize the interactions between them.The Young's modulus of 2D materials [2] was calculated by (C11  C22 -C12 2 )/C11  (d +3.1)/D,where d was the thickness of MoSi 2 N 4 (MoN) n and Mo n+1 N n+2 monolayer (listed in Table S3), 3.1 was the assumed distance of 3.1 Å between two monolayers obtained from two times the van der Waals radius of the N atom (1.55 Å), and the D was the length of unit-cell along z-direction.For the QE calculations, the exchange-correlation potential was treated by local density approximation (LDA) [3] with norm-conserving pseudopotentials.The kinetic energy cutoff and the charge density cutoff of plane-wave basis were chosen to be 80 and 800 Ry.All the structures were fully relaxed to their equilibrium state such that the forces acting on each atom became smaller than 10 -6 Ry/Bohr.Marzari-Vanderbilt cold smearing of 0.02 Ry was used to improve convergence.The self-consistent electron density was evaluated by employing a k-mesh of 24  24  1.The EPC and superconductivity for each MoSi 2 N 4 (MoN) n (n = 1 -4) and Mo 5 N 6 were calculated by using the density functional perturbation theory (DFPT) [4], in which the q-mesh of 4  4  1 was used.Finally, the superconducting transition temperature T c was derived by following Allen-Dynes-modified McMillan formula [5,6] , where λ is the electron-phonon coupling constant obtained by λ(ω max ), μ * is the effectively screened Coulomb interaction treated as a constant of 0.1, and ω log is the logarithmic average phonon frequencies.Both λ and ω log can be calculated from the , where ω is the frequencies of phonon, ω qv is the frequency of phonon of the mode v at the wave vector q, and γ qv is the phonon linewidth of the mode v at the wave vector q, obtained from electron-phonon matrix element calculations performed in QE, indicating the interaction strength between electron and phonon.N(E F ) is the density of states at Fermi level E F .

Figure S2 .
Figure S2.The multilayer MoSi 2 N 4 structure containing AA, AB and AC stacking

Figure S4 .
Figure S4.(a) EELS profiles of multilayer MoSi 2 N 4 from the red frame and MoN

Figure S9 .
Figure S9.The screening of energetically favorable structure of MoSi 2 N 4 (MoN) n with

Figure S14 .
Figure S14.The LDOS of N atoms of Mo 5 N 6 .The black solid line denotes the LDOS

Table S1 .
The formation energies of bulk MoSi 2 N 4 crystals with different stacking orders.

Table S2 .
Calculated crystallographic parameters of bulk MoSi 2 N 4 crystal with ABC-typed stacking order by the First-principles calculations.The experimentally obtained crystallographic parameters were also given for comparison.

Table S3 .
The Young's modulus Y 2D , Poisson ratio ν, thickness d and in-plane lattice constants a of MoSi 2 N 4 (MoN) n and Mo n+1 N n+2 (n = 0 -4).The Young's modulus and Poisson ratio of Mo 2 N 3 were not given because of its mechanical instability.