Enhanced Superconductivity and Critical Current Density Due to the Interaction of InSe2 Bonded Layer in (InSe2)0.12NbSe2

Superconductivity was discovered in (InSe2)xNbSe2. The materials are crystallized in a unique layered structure where bonded InSe2 layers are intercalated into the van der Waals gaps of 2H-phase NbSe2. The (InSe2)0.12NbSe2 superconductor exhibits a superconducting transition at 11.6 K and critical current density of 8.2 × 105 A/cm2. Both values are the highest among all transition metal dichalcogenide superconductors at ambient pressure. The present finding provides an ideal material platform for further investigation of superconducting-related phenomena in transition metal dichalcogenides.


Growth of NbSe2 and (InSe2)xNbSe2 single crystals
The (InSe2)xNbSe2 single crystals were grown using a two-step self-flux method.Firstly, we employed the chemical vapor transportation method with iodine as the transport agent to grow the single crystal of NbSe2.Stoichiometric ratio of Nb powder, Se powder and 100 mg iodine were weight and sealed in an evacuated quartz tube.The quartz tube was placed in a two-zone furnace with the temperature setting at 800 ℃ and 725 ℃, respectively.The single crystal growth processes were maintained for two weeks.When the furnace is cooled down, shiny and black single crystals of NbSe2 were obtained from the cold side of the tube.The dimensions of the pristine NbSe2 single crystals could be as large as 0.40.40.05cm 3 .Subsequently, we placed the large pieces of NbSe2 single crystal and indium pellets into an alumina crucible, which was then sealed under vacuum in a quartz tube.The molar ratio of NbSe2:In was adjusted to range from 1:2 to 1:7.Here large amount of excess In was added because In plays dual roles of selfflux and insertions.The mixture of pellets was heated to 900 °C and maintained at that temperature for 3 days followed by slow cooling down to 600 °C.After that, the excess indium flux was removed through centrifuging, and the resultant samples were meticulously polished to eliminate any residual indium flux from the surfaces.

Characterization
For structural and compositional characterization, an atomic resolution microscope of JEOL ARM300F equipped with scanning transmission electron microscopy (STEM) and TEM ETA correctors was used.Single crystal and powder X-ray diffraction data were collected by a PANalytical X'Pert Pro MPD detector using monochromated Cu Kα1 radiation as the X-ray source.Magnetization measurements were performed using a vibrating sample magnetometer (Quantum Design MPMS-3).Electrical measurements were conducted on a home-built Multiple Measurement System on a Janis-9T magnet.A fourpoint probe method was adopted in the electrical measurements.DC current of 1 mA was applied via a Keithley 6221 current source meter and the voltages were measured using a Keithley 2182A nanovoltmeter.Delta Mode measurements were used to improve signal-to-noise ratio.

Single crystal and powder X-ray diffraction patterns of the pristine and intercalated NbSe2
samples.The c-axis lattice constant of the pristine NbSe2 determined from the single crystal X-ray diffraction (XRD) pattern is 12.569 Å.And the lattice constants of NbSe2 determined from the powder XRD pattern are a=3.472Å and c=12.567Å, respectively.These lattice parameters are consistent with those reported in literatures.
For the (InSe2)xNbSe2 samples, the a-axis lattice constant is slightly larger than that of NbSe2.Strikingly, the c-axis lattice constant is significantly enlarged with the intercalation of InSe2.The c-axis lattice constant of the (InSe2)0.12NbSe2sample is about 18.22 Å, which is approximately 50% larger than that of undoped NbSe2.
The lattice constants determined from XRD patterns are consistent with those calculated from the high-angle annular dark-field aberration-corrected scanning transmission electron microscopy (HAADF-STEM) images.Table S1.Crystallographic data of (InSe2)xNbSe2 based on the Rietveld refinements to the powder X-ray diffraction data.
The large Uiso values could be due to the randomness of the intercalated InSe2 bonds.For some specific diffraction peaks, the difference between theoretical calculation and the experimental data is still a little bit large in the Rietveld refinement profile of the (InSe2)0.12NbSe2sample.This relatively large difference could come from two facts.The first one is that we are performing the powder X-ray diffraction measurement by grinding the pieces of single crystal samples into fine powder.Though we are trying our best to grind the single crystal samples, there could be some small single crystal grains which exhibiting some preferred crystallographic orientation.For examples, the large difference on the diffraction intensity of the patterns of (006), ( 008), (0010), (0012), and (0016) diffraction peaks could be due to the preferred crystallographic orientation.The second fact is that the intercalated InSe2 could be randomly distributed in the van der Waals gaps.It is possible that there are some regions which have rich intercalated InSe2 content and some regions with poor intercalated InSe2 content, leading to more complicated crystallographic information.Further experimental measurements such as neutron diffraction and scanning tunnelling microscopy could contribute to a comprehensive understanding of the structural and physical properties of this and related materials.

Formula
For the pristine NbSe2, the difference between theoretical calculation and the experimental data is also large for the (00l) diffraction peaks, which is due to the preferred orientation of the small single crystal grains.
Comparing the crystallographic data of the (InSe2)0.12NbSe2sample with those of the pristine NbSe2 sample, it is found that the atomic positions of both Nb and Se1 exhibit some misfit.This misfit is reflected in the HAADF-STEM images and illustrated in Figure S4.It is noted that there is a substantial amount of Se site vacancy (~17%) in the (InSe2)xNbSe2 samples.In order to learn more about the Se site vacancy, we perform the energy dispersive X-ray spectroscopy (EDS) experiments on the pristine NbSe2 single crystal (Figure S6).The Se-site vacancy of the NbSe2 sample is determined to be about 5%.The presence of more Se-site vacancy in (InSe2)xNbSe2 could be explained according to the following two possibilities: The first one is that we are growing the (InSe2)xNbSe2 single crystals using the NbSe2 single crystal and In as the starting materials.Some Se atoms are probably escaped from the NbSe2 layers to form the InSe2 layers, leaving more Se site vacancy in the NbSe2 layers.The second one is that there might be some isolated In atoms which are inserted into the Van der Waals gaps of 2H-phase NbSe2.The presence of isolated In atoms could be further checked by a comprehensive scanning tunneling microscopy measurement.Figure S9.A comparison of the superconducting transition temperature between this work and previous reports.  Theuperconducting transition temperature of (InSe2)0.12NbSe2 is the highest among all TMD superconductors under ambient pressure.It is noted that the transition temperature of 2H-TaS2 under high pressure is higher than the present work. 21. Computational methods and calculation details.
The calculations of geometrical relaxations and electronic properties were based on density functional theory (DFT), performed by using the Vienna Ab-initio Simulation Package (VASP). 38We used the projector augmented wave (PAW) pseudopotentials with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional in the generalized gradient approximation. 39,40To correct the dispersive interactions in the van der Waals materials, the semi-empirical DFT-D3 method were employed under the whole process of calculations. 41The kinetic energy cutoff of the plane-wave basis was chosen to be 500 eV.The self-consistent energy was converged within 10 -6 eV, and optimized atomic structures were achieved when forces on all the atoms were smaller than 5×10 -3 eV/Å.A Γ-centered 18×18×18 Monkhorst-Pack (MP) k-mesh was used to sample the Brillouin zone for density of states (DOS) calculations of 2Ha-NbSe2 and 10×10×10 MP k-mesh for DOS calculations of supercell after In intercalation. 42The band unfolding program KPROJ was used to process the band structures of supercell.Figure S10 is obtained from the self-consistent calculations according to the experimentally determined lattice parameters.Note that some individual In atoms should exist to maintain the atom ratio of Se:Nb:In=68:32:4 and to have the c-axis lattice constant be close to the experimentally determined value (~1.826 nm).The theoretically calculated data support that there are some individual In atoms which are inserted in the NbSe2 compound, which are consistent with the energy dispersive X-ray spectroscopy results.
Other similar structures without individual In atoms could lead to either a c-axis of more than 2 nm (about 10% relative error) or deformed lattice structures after geometric relaxation.As shown in Figure S10, the c-axis lattice parameter could be 2.03 nm if we do not consider any individual In atoms, which is much larger than the experimental value.If a uniaxial pressure of 3 GPa is artificial applied along the c-axis, a metastable structure with smaller c-axis lattice constant of 1.81 nm could be obtained.
The electronic structure shown in Figure S11 is nearly unchanged in comparison with the case in Figure 4. Thus, we suggest that the metastable structure shown in Figure S10c is a likely structure.However, the structure shown in Figure 4 and Figure S10 is the most probable one, which naturally follows all the experimental requirements without any artificial modulations.

Figure S1 .
Figure S1.The single crystal and powder X-ray diffraction patterns of the pristine NbSe2 and a typical (InSe2)xNbSe2sample.The wavelength of the irradiated X-ray is 1.5405 Å.

Figure S2 .
Figure S2.The Rietveld refinement results of the powder X-ray diffraction data of the (InSe2)xNbSe2 sample.The black dots mark the positions of (00l) diffraction peaks, which reflect the preferred crystallographic orientation of the fine single crystal grains.

Figure S3 .
Figure S3.The Rietveld refinement results of the powder X-ray diffraction data of the pristine NbSe2 sample.The black dots represent the diffraction peaks which are involving in the preferred crystallographic orientation.

Figure S4 .
Figure S4.(a) A typical HAADF-STEM image of (InSe2)xNbSe2 showing the misfit positions of Nb and Se in 2H-phase NbSe2 due to the dragging of intercalated InSe2 bonds.(b) The crystal structure of pristine NbSe2.(c) The crystal structure of (InSe2)xNbSe2.

3 .
Determining the chemical compositions of the samples.

Figure S6 . 5 .
Figure S6.The Scanning electron microscope patterns of three pieces of NbSe2 single crystals.The quantitative analyses of the EDS data are shown in the images.The Se site vacancy rate is approximately 5% in pristine NbSe2 single crystals.

Figure S10 .
Figure S10.(a) Crystal structure of an ordered phase of (InSe2)xNbSe2 with Se:Nb:In=68:32:4.The c-axis lattice constant is determined to be 18.72 Å after geometric optimization, which is consistent with the experimental data.(b) The band structure and density of states for primitive cell of NbSe2 without intercalation.(c) The band structure and density of states for bulk 2Ha-NbSe2.(d) The band structure and density of states for monolayer 2Ha-NbSe2.(e) Comparison of density of states with/without InSe2 layers based on crystal structure (a).The density of states near Fermi level does not change significantly with (red line) of without (bule line) InSe2 layers.

Figure S11 .
Figure S11.(a) Unfolding effective band structure (EBS) and density of states (DOS) of an ordered stacking phase of (InSe2)xNbSe2 shown in (c).(b) Projected effective band structure.The bands coming from In atoms (cyan) have no contributions to the Fermi surface.(c) A structure of (InSe2)xNbSe2 without individual In atoms.

Table S2 .
Crystallographic data of NbSe2 based on the Rietveld refinements to the powder X-ray diffraction data.

Table S3 .
The quantitative EDS analyses of the chemical compositions of (InSe2)xNbSe2 samples grown with the NbSe2:In molar ratio between 1:2 and 1:7.