Nb2PdxSe5

Nb₂PᵪSe₅ is a high-field, anisotropic, 2-band superconductor with both electron-like and hole-like charge carriers at the Fermi level. The crystal structure is assembled such that 2D sheets of Nb₄Pd₁Se₁₀ are connected to each other by an inter-sheet non-stoichiometric palladium atom site, referred to as the Pd2 site. This work provides the first in-depth study of the crystal structure and physical properties of Nb₂PdᵪSe₅ as a function of Pd2 content. Employing a modified solid-state growth technique, single crystals were obtained over an extended range of stoichiometries with Pd2 occupancy from 0.36 to 0.90. The structure allows different Pd2 occupancy, up to a value of 1.0, however, unexpected Pd2 occ miscibility gaps are identified. The miscibility ranges are linked to the formation of different occupation density wave superstructures that are coherent over length scales of ~1000Å. For Pd2 occ near ½, the superstructure is well described with a 1-dimensional Pd2 occupation density wave along the monoclinic b-axis ([010], growth or needle axis) and approximate period of 68Å, about 19 times the b-axis length. The 1-dimensional Pd2 motif is retained for Pd2 occ up to 0.615~8/13 and modulation along b with periodicity about 12 times the b-axis length. In single crystals with Pd2 occ between 0.625=5/8 and 0.685~13/19, Pd2 order is 2-dimensional with longest range superstructure order for Pd2 occ=~2/3. In samples with Pd2 occ>0.70, Pd2 order is 3-dimensional. Sharp miscibility gap boundaries observed for stoichiometries with 1-dimensional Pd2 order likely result from discrete filling of Pd2 in a low dimensional motif that allows only a small number of microstates and therefore coarse Pd2 tunability. Conversely, blurred miscibility gaps observed for high Pd2 occ can be explained by increase in microstate number afforded by higher dimension Pd2 order modulation that allows finer Pd2 tunability in this range. We hypothesize that Pd2 occ changes within a superstructure motif allow tuning of the Fermi level, whereas dimension changes as noted above directly affect the Pd2-electronic bands and therefore modify the shape of the Fermi surface. Single crystal resistivity (ρ) vs temperature (T) measurements performed under zero magnetic field do not indicate superconductivity for single crystals with Pd2 occ below ½, above Pd2 occ=½, single crystals show a turning point in ρ vs T at temperatures ranging from 0.73K for Pd2 occ=0.501~½ to 1.14K for Pd2 occ=0.587~7/12, but do not reach ρ=0 at temperatures as low as 40mK, further increasing Pd2 to Pd2 occ>7/12 single crystal ρ vs T curves show complete superconducting transitions. Incomplete transitions observed for samples with ½2/3 respectively. High magnetic field orientation dependent resistivity experiments performed for single crystals spanning the range of superconducting Pd2 occ show highest critical field anisotropy and highest H[subscript c2]/T[subscript c] ratios present in samples having lowest Pd2 occ and 1-dimensional Pd2 order. These have anisotropy γ=H[subscript c2||010]/H[subscript c2||[201]~4 and ratio H[subscript c2||010]/T[subscript c]~8.5 exceeding the Pauli spin polarization limit (H[subscript c2]/T[subscript c])=1.84[T/K] by a factor of 4.5. For comparison, middle Pd2 occ single crystals with 2-dimensional Pd2 order have H[subscript c2] anisotropy γ~3.5, and H[subscript c2||010]/T[subscript c]~7, exceeding the Pauli limit by a factor 3.7 while highest Pd2 superconductors with 3-dimensional Pd2 order show the lowest superconducting anisotropy with γ~2.7, and H[subscript c2||010]/T[subscript c]~4.3 still exceeding the Pauli limit, but by a factor of only 2.4, indicating that the Pd2 superstructure modified d-bands directly affect the superconducting state properties of Nb₂PdᵪSe₅. Density functional theory (DFT) calculations indicate that d-electrons of Pd2 are added to an electron pocket at the Fermi level, while Nb1 and Pd1 contribute predominantly to the hole pockets. Additionally, DFT calculations performed for the fully occupied structure with Pd2 occ=1 and for the ideal superstructure with Pd2 occ=½ indicate that the electron-like Fermi surface sheet changes from 3-dimensional for the fully occupied structure to a more 1-dimensional surface for Pd2 occ=½. In calculations, both stoichiometries result in 2-band Fermi surfaces that demonstrate perfect compensation of electrons with holes. We hypothesize that balance of holes and electrons exists at precise Pd2 occ where superstructures are centered, i.e. at Pd2 occ=½,⅔, and perhaps ¾ and that increasing or decreasing Pd2 occ within a superstructure motif allows shifting from hole-dominant conduction for Pd2 poor to electron-dominant for Pd2 rich samples. We observe highest H[subscript c2]s, H[subscript c2] anisotropy and T[subcript c]s approaching the miscibility boundary between 1-dimensional and 2-dimensional Pd2 order.