Realization of continuous electron doping in bulk iron selenides and identification of a new superconducting zone

It is known that iron selenide superconductors exhibit unique characteristics distinct from iron pnictides, especially in the electron-doped region. However, a comprehensive study of continuous carrier doping and the corresponding crystal structures of FeSe is still lacking, mainly due to the difficulties in controlling the carrier density in bulk materials. Here we report the successful synthesis of a new family of bulk $\mathrm{L}{\mathrm{i}}_x{\left({\mathrm{C}}_3{\mathrm{N}}_2{\mathrm{H}}_{10}\right)}_{0.37}\mathrm{FeSe}$, which features a continuous superconducting dome harboring Lifshitz transition within the wide range of $0.06\le x\le 0.68$. We demonstrate that with electron doping, the anion height of FeSe layers deviates linearly away from the optimized values of pnictides and pressurized FeSe. This feature leads to a new superconducting zone with unique doping dependence of the electronic structures and strong orbital-selective electronic correlation. Optimal superconductivity is achieved when the $\mathrm{Fe}3d{t}_{2g}$ orbitals have almost the same intermediate electronic correlation strength, with moderate mass enhancement between $3\sim 4$ in the two separate superconducting zones. Our results shed new light on achieving unified mechanism of superconductivity in iron-based superconductors.

Figure 1

Crystal structure and Rietveld refinement against NPD data for $\mathrm{L}{\mathrm{i}}_{0.26}{\left({\mathrm{C}}_3{\mathrm{N}}_2{\mathrm{H}}_{10}\right)}_{0.37}\mathrm{FeSe}$. (a) A schematic view of the structure of $\mathrm{L}{\mathrm{i}}_{0.26}{\left({\mathrm{C}}_3{\mathrm{N}}_2{\mathrm{H}}_{10}\right)}_{0.37}\mathrm{FeSe}$. In the model the anti-PbO-type FeSe layers and the ${\mathrm{C}}_3{\mathrm{N}}_2{\mathrm{H}}_{10}$ layers stack alternately. Li atoms are found bonded to four adjacent Se atoms. (b) Charge density along the $c$ axis from a Fourier synthesis of the (00l) integrated intensities using the 298 K x-ray data. The peaks labeled Fe, Se, C, and N represent the iron, selenide, carbon, and nitrogen bounding layers, respectively. (c) Observed (crosses) and calculated (red solid line) NPD pattern for $\mathrm{L}{\mathrm{i}}_{0.26}{\left({\mathrm{C}}_3{\mathrm{N}}_2{\mathrm{H}}_{10}\right)}_{0.37}\mathrm{FeSe}$ ($\lambda =1.9395\AA$) at 295 K. Differences between the observed and calculated intensities are shown at the bottom of the figure. Bragg peak positions are indicated by short purple vertical bars below the NPD patterns.

Figure 2

Structural evolution of $\mathrm{L}{\mathrm{i}}_x{\left({\mathrm{C}}_3{\mathrm{N}}_2{\mathrm{H}}_{10}\right)}_{0.37}\mathrm{FeSe}$ as a function of Li doping level $\mathit{x}$. (a) The x-ray diffraction patterns obtained at different Li doping levels between 0.06 and 0.68. The inset displays the enlarged (002) and (200) peaks, where the shift of (002) peaks to higher angles corresponds to the lattice contraction along the $\mathit{c}$ axis. (b) The $\mathit{a}$- and $\mathit{c}$-lattice constants of the tetragonal cell as a function of Li doping. There is no obvious variation in $\mathit{a}$ while there is significant lattice contraction along the $\mathit{c}$ axis with increasing Li doping. (c), (d) The Se anion height, Fe–Se bond distance, and Se–Fe–Se bond angles versus Li doping. The error bars indicate one standard deviation and the inset of (c) presents the $\mathrm{Fe}E4$ tetrahedra model.

Figure 3

Superconducting properties of $\mathrm{L}{\mathrm{i}}_x{\left({\mathrm{C}}_3{\mathrm{N}}_2{\mathrm{H}}_{10}\right)}_{0.37}\mathrm{FeSe}$. (a) Zero-field-cooled magnetization ($H_{\mathrm{dc}}=10\mathrm{Oe}$) for underdoped and optimal-doped superconducting $\mathrm{L}{\mathrm{i}}_x{\left({\mathrm{C}}_3{\mathrm{N}}_2{\mathrm{H}}_{10}\right)}_{0.37}\mathrm{FeSe}$ samples with Li doping levels $x=0.06$ to 0.37. (b) Magnetization data for overdoped zone with Li doping levels $x=0.37$ to 0.68. Inset shows the doping dependence of the superconducting temperature. (c) Temperature dependence of the electric resistivity $\rho$ of ${\mathrm{Li}}_{0.37}{\left({\mathrm{C}}_3{\mathrm{N}}_2{\mathrm{H}}_{10}\right)}_{0.37}\mathrm{FeSe}$ under increasing magnetic fields. (d) The fluctuation contribution to the conductivity $\mathrm{\Delta }\sigma$ varies with temperature under external magnetic fields up to 9 T. The inset is $\mathrm{\Delta }\sigma$ vs temperature curve and the quasi-2D and 3D fitting.

Figure 4

(a) Momentum-resolved spectral function and (b) the unfolded orbital-resolved Fermi surfaces in the one-Fe Brillouin zone of $\mathrm{L}{\mathrm{i}}_x{\left({\mathrm{C}}_3{\mathrm{N}}_2{\mathrm{H}}_{10}\right)}_{0.37}\mathrm{FeSe}$ at different doping levels $x$ based on $\mathrm{DFT}+\mathrm{DMFT}$ calculations. The blue/green color in panel (b) denotes dominating $d_{xz}/d_{yz}$ orbital character and red color denotes dominating $d_{xy}$ orbital character. The hole pocket with dominating $d_{xy}$ orbital character persists in the whole doping range, while the other two-hole pockets with mostly $d_{xz/yz}$ orbital character gradually disappear with increasing doping level toward $x=0.2$, at which doping level a new electron pocket appears at Γ. Notably, a Lifshitz transition between $x=0.1$ and 0.2 occurs which is probably responsible for the experimental $T_{\mathrm{c}}$ jump around $x=0.15$. The expansion of electron pockets at the zone corner as Li doping increases is within expectation. The calculation model is based on the resolved experimental structures in Fig. 2.

Figure 5

Maximum $T\mathrm{c}$, mass enhancement, and fluctuating local spin. (a) Maximum experimental $T\mathrm{c}$ achieved by electron or hole doping near the parent compound in iron chalcogenides and iron pnictides. (b) The $\mathrm{DFT}+\mathrm{DMFT}$ calculated mass enhancement $m*/m_{\mathrm{band}}$ of the iron $3dxz,yz$, and $xy$ orbitals in the paramagnetic state [32]. Maximum $T\mathrm{c}$ is achieved in both iron chalcogenides and iron pnictides when the $d_{xz/yz}$ orbital and $d_{xy}$ orbital have almost the same, intermediate mass enhancement ($\sim 3$ and $\sim 4$, respectively). $T\mathrm{c}$ is smaller when there is larger orbital selectivity or differentiation among the $\mathrm{Fe}3d{t}_{2g}$ orbitals. (c) Mass enhancements of $\mathrm{Fe}3d$ orbitals as a function of doping in $\mathrm{L}{\mathrm{i}}_x{\left({\mathrm{C}}_3{\mathrm{N}}_2{\mathrm{H}}_{10}\right)}_{0.37}\mathrm{FeSe}$. The maximal $T\mathrm{c}$ occurs in the doping region where there is a crossover of the mass enhancement of the $d_{xz/yz}$ orbital and the $d_{xy}$ orbital, further confirming the observation in (a) and (b). Fluctuating local spin of $\mathrm{Fe}3d$ states versus doping in $\mathrm{L}{\mathrm{i}}_x{\left({\mathrm{C}}_3{\mathrm{N}}_2{\mathrm{H}}_{10}\right)}_{0.37}\mathrm{FeSe}$. The fluctuating local spin strongly correlates with the experimental superconducting transition temperature in the doping region $0.1<x<0.7$ where nematic phase and magnetic ordering are absent, suggesting spin fluctuations are the driving force for the observed superconductivity in this family of materials.

Figure 6

Two superconducting zones in iron-based superconductors. The superconducting temperature as a function of anion height in many iron-based superconductors is shown here. The $T\mathrm{c}$ values were obtained from resistivity or susceptibility measurements. The iron pnictides, stoichiometric FeSe under pressure, and electron-doped FeSe-based samples show two different superconducting zones (SC-I and SC-II) separated by a critical anion height of around 1.45 Å. The SC-I superconducting region features optimal superconductivity near-perfect Fe-anion tetrahedron with anion height $\sim 1.38\AA$, where the $d_{xz/yz}$ and $d_{xy}$ orbitals have almost the same intermediate mass enhancement around 3 as indicated in Figs. 5 and 5. The maximum $Tc\sim 55\mathrm{K}$ was found in $\mathrm{NdFeAs}{\mathrm{O}}_{0.83}$. The SC-II superconducting region has strongly distorted Fe-anion tetrahedron with large anion height. The maximum $T\mathrm{c}$ is found to be 46 K at anion height of $\sim 1.50\AA$, where the $d_{xz/yz}$ and $d_{xy}$ orbitals have almost the same intermediate mass enhancement around 4 as indicated in Figs. 5–5. Error bars are within the size of the symbols.